KAPPA: Four parameter kappa distribution and L-moments
In homtest: Homogeneity tests for Regional Frequency Analysis
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
KAPPA provides the link between L-moments of a sample and the four parameter
kappa distribution.
Usage
1
2
3
4
5
6
f.kappa (x, xi, alfa, k, h)
F.kappa (x, xi, alfa, k, h)
invF.kappa (F, xi, alfa, k, h)
Lmom.kappa (xi, alfa, k, h)
par.kappa (lambda1, lambda2, tau3, tau4)
rand.kappa (numerosita, xi, alfa, k, h)
Arguments
x
vector of quantiles
xi
vector of kappa location parameters
alfa
vector of kappa scale parameters
k
vector of kappa third parameters
h
vector of kappa fourth parameters
F
vector of probabilities
lambda1
vector of sample means
lambda2
vector of L-variances
tau3
vector of L-CA (or L-skewness)
tau4
vector of L-kurtosis
numerosita
numeric value indicating the length of the vector to be generated
Details
Definition
Parameters (4): ξ (location), α (scale), k, h.
Range of x: upper bound is ξ + α/k if k>0, inf if k ≤ 0;
lower bound is xi + α(1-h^(-k))/k if h>0, ξ + α/k if h ≤ 0 and k<0 and -inf if h ≤ 0 and k ≥ 0
Probability density function:
f(x) = α^(-1) [1 - k (x - ξ)/α]^(1/k-1) [F(x)]^(1-h)
Cumulative distribution function:
F(x) = {1 - h[1 - k(x - ξ)/α]^(1/k)}^(1/h)
Quantile function:
x(F) = ξ + α/k [1 - ((1-F^h)/h)^k]
h=-1 is the generalized logistic distribution;
h=0 is the generalized eztreme value distribution;
h=1 is the generalized Pareto distribution.
L-moments
L-moments are defined for h ≥ 0 and k>-1, or if h<0 and -1<k<-1/h.
λ1 = ξ + α(1 - g1)/k
λ2 = α(g1 - g2)/k
τ3 = (-g1 + 3g2 - 2g3)/(g1 - g2)
τ4 = (-g1 + 6g2 - 10g3 + 5g4)/(g1 - g2)
where
gr = (r Γ(1+k)Γ(r/h))/(h^(1+k) Γ(1+k+r/h)) if h>0;
gr = (rΓ(1+k)Γ(-k-r/h))/((-h)^(1+k)Γ(1-r/h)) if h<0;
Here Γ denote the gamma function
Γ(x) = integral[from 0 to inf] t^(x-1) e^(-t) dt
Parameters
There are no simple expressions for the parameters in terms of the L-moments.
However they can be obtained with a numerical algorithm considering the formulations of τ3 and τ4 in terms of k and h.
Here we use the function optim to minimize (t3-τ3)^2 + (t4-τ4)^2 where t3 and t4 are the sample L-moment ratios.
Value
f.kappa gives the density f, F.kappa gives the distribution function F, invFkappa gives
the quantile function x, Lmom.kappa gives the L-moments (λ1, λ2, τ3, τ4), par.kappa gives the parameters (xi, alfa, k, h), and rand.kappa generates random deviates.
Note
Lmom.kappa and par.kappa accept input as vectors of equal length. In f.kappa, F.kappa, invF.kappa and rand.kappa parameters (xi, alfa, k, h) must be atomic.
Author(s)
Alberto Viglione, e-mail: alviglio@tiscali.it.
References
Hosking, J.R.M. and Wallis, J.R. (1997) Regional Frequency Analysis: an approach based on L-moments, Cambridge University Press, Cambridge, UK.
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
data(annualflows)
annualflows
summary(annualflows)
x <- annualflows["dato"][,]
fac <- factor(annualflows["cod"][,])
split(x,fac)
camp <- split(x,fac)$"45"
ll <- Lmoments(camp)
parameters <- par.kappa(ll[1],ll[2],ll[4],ll[5])
f.kappa(1800,parameters$xi,parameters$alfa,parameters$k,parameters$h)
F.kappa(1800,parameters$xi,parameters$alfa,parameters$k,parameters$h)
invF.kappa(0.771088,parameters$xi,parameters$alfa,parameters$k,parameters$h)
Lmom.kappa(parameters$xi,parameters$alfa,parameters$k,parameters$h)
rand.kappa(100,parameters$xi,parameters$alfa,parameters$k,parameters$h)
Rll <- regionalLmoments(x,fac); Rll
parameters <- par.kappa(Rll[1],Rll[2],Rll[4],Rll[5])
Lmom.kappa(parameters$xi,parameters$alfa,parameters$k,parameters$h)
Example output
cod anno dato
1 1 1956 1494.00
2 1 1957 1309.00
3 1 1958 1699.00
4 1 1959 1467.00
5 1 1960 1918.00
6 1 1961 1469.00
7 1 1962 1267.00
8 1 1963 1523.00
9 1 1964 1338.00
10 1 1965 1438.00
11 1 1966 1788.00
12 1 1967 1591.00
13 1 1968 1697.00
14 1 1969 1780.00
15 1 1970 1769.00
16 2 1933 1144.00
17 2 1934 1652.00
18 2 1935 1807.00
19 2 1936 1881.00
20 2 1937 1741.00
21 2 1938 1124.00
22 2 1939 2064.00
23 2 1940 1434.00
24 2 1941 1678.00
25 2 1942 1239.00
26 2 1943 921.00
27 2 1944 983.00
28 2 1945 1093.00
29 2 1946 1744.00
30 2 1947 1213.00
31 2 1948 1590.00
32 2 1949 956.00
33 2 1950 1124.00
34 2 1951 2181.00
35 2 1952 1077.00
36 2 1953 1345.00
37 2 1954 1219.00
38 2 1955 988.00
39 2 1956 1325.00
40 2 1957 1277.00
41 2 1958 1479.00
42 2 1959 1307.00
43 2 1960 2053.00
44 2 1961 1232.00
45 2 1962 973.00
46 2 1963 1407.00
47 2 1964 912.00
48 3 1951 2596.00
49 3 1952 954.00
50 3 1953 1115.00
51 3 1954 1248.00
52 3 1955 867.00
53 3 1956 1280.00
54 3 1957 1588.00
55 3 1958 1055.00
56 3 1959 1764.00
57 3 1960 3045.00
58 4 1921 871.00
59 4 1922 1238.00
60 4 1923 1505.00
61 4 1924 1636.00
62 4 1925 1553.00
63 4 1926 1936.00
64 4 1927 1739.00
65 4 1928 1867.00
66 4 1929 1184.00
67 4 1930 1630.00
68 4 1931 1311.00
69 4 1932 1520.00
70 4 1933 1201.00
71 4 1934 1614.00
72 4 1935 1971.00
73 4 1936 1829.00
74 4 1937 1781.00
75 4 1938 1093.00
76 4 1939 1996.00
77 4 1940 1328.00
78 4 1941 1662.00
79 4 1942 1199.00
80 4 1943 860.00
81 4 1944 961.00
82 4 1945 949.00
83 4 1946 1536.00
84 4 1947 1016.00
85 4 1948 1386.00
86 4 1949 820.00
87 4 1950 1023.00
88 4 1951 2329.00
89 4 1952 1209.00
90 4 1953 1305.00
91 4 1954 1334.00
92 4 1955 1024.00
93 4 1956 1364.00
94 4 1957 1310.00
95 4 1958 1410.00
96 4 1959 1247.00
97 4 1960 2393.00
98 4 1961 1317.00
99 4 1962 909.00
100 4 1963 1808.00
101 4 1964 1020.00
102 4 1965 1181.00
103 4 1966 1365.00
104 4 1967 1218.00
105 4 1968 1644.00
106 4 1969 1160.00
107 4 1970 1002.00
108 4 1971 1243.00
109 4 1972 1332.00
110 4 1973 1033.00
111 4 1974 1170.00
112 4 1975 1685.00
113 4 1976 1478.00
114 4 1977 2434.00
115 4 1978 1600.00
116 4 1979 1369.00
117 4 1980 1215.00
118 4 1981 1614.00
119 4 1982 1449.00
120 4 1983 1518.00
121 4 1984 1490.00
122 4 1985 1191.00
123 7 1955 1481.00
124 7 1956 1758.00
125 7 1957 1774.00
126 7 1958 1625.00
127 7 1959 1607.00
128 7 1960 2826.00
129 7 1961 1488.00
130 7 1962 928.00
131 7 1963 2379.00
132 7 1964 1173.00
133 7 1965 1801.00
134 7 1966 1824.00
135 7 1967 1309.00
136 7 1968 2220.00
137 7 1969 1733.00
138 8 1933 1086.00
139 8 1934 1810.00
140 8 1935 2244.00
141 8 1936 2138.00
142 8 1937 2028.00
143 8 1938 1308.00
144 8 1939 1947.00
145 8 1940 1528.00
146 8 1941 2244.00
147 8 1942 1594.00
148 8 1943 861.00
149 8 1944 1378.00
150 8 1946 1795.00
151 8 1947 1344.00
152 8 1948 1558.00
153 8 1949 696.00
154 8 1950 724.00
155 8 1951 2497.00
156 8 1952 660.00
157 8 1953 1388.00
158 8 1954 1484.00
159 8 1955 952.00
160 8 1956 1987.00
161 8 1957 2646.00
162 8 1958 1689.00
163 8 1959 1443.00
164 8 1960 2688.00
165 8 1961 1249.00
166 8 1962 1145.00
167 8 1963 2392.00
168 8 1964 1001.00
169 8 1965 1380.00
170 9 1937 2075.00
171 9 1938 1607.00
172 9 1939 1717.00
173 9 1940 1261.00
174 9 1941 1824.00
175 9 1942 1330.00
176 9 1943 963.00
177 9 1944 1313.00
178 9 1951 2276.00
179 9 1952 682.00
180 9 1953 1440.00
181 9 1954 1304.00
182 9 1955 1193.00
183 10 1925 1096.00
184 10 1926 1387.00
185 10 1927 1289.00
186 10 1928 1461.00
187 10 1929 1054.00
188 10 1930 1474.00
189 10 1931 1137.00
190 10 1932 1256.00
191 10 1933 981.00
192 10 1934 1696.00
193 10 1935 1468.00
194 10 1936 1850.00
195 10 1937 1644.00
196 10 1938 1248.00
197 10 1939 1498.00
198 10 1940 1317.00
199 10 1941 1500.00
200 10 1942 1109.00
201 10 1943 859.00
202 10 1944 931.00
203 10 1945 1020.00
204 10 1946 1493.00
205 10 1947 954.00
206 10 1948 1133.00
207 10 1949 1144.00
208 10 1950 1056.00
209 11 1927 1320.00
210 11 1928 1706.00
211 11 1929 948.00
212 11 1930 1643.00
213 11 1931 944.00
214 11 1932 1402.00
215 11 1933 1202.00
216 11 1934 1788.00
217 11 1935 1665.00
218 11 1936 1833.00
219 11 1937 1679.00
220 11 1938 1166.00
221 11 1939 1833.00
222 11 1940 1661.00
223 11 1941 1938.00
224 11 1942 1457.00
225 11 1943 830.00
226 11 1944 1221.00
227 11 1945 1398.00
228 11 1946 1674.00
229 11 1947 1311.00
230 11 1948 1611.00
231 11 1949 1003.00
232 11 1950 1021.00
233 12 1925 890.00
234 12 1926 1247.00
235 12 1927 1040.00
236 12 1928 1047.00
237 12 1929 875.00
238 12 1930 1060.00
239 12 1931 913.00
240 12 1932 968.00
241 12 1933 749.00
242 12 1934 1218.00
243 12 1935 1104.00
244 12 1936 1489.00
245 12 1937 1300.00
246 12 1938 833.00
247 12 1939 994.00
248 12 1940 1002.00
249 12 1941 1134.00
250 12 1942 854.00
251 12 1943 826.00
252 12 1944 695.00
253 12 1945 939.00
254 12 1946 1230.00
255 12 1947 830.00
256 12 1948 1096.00
257 12 1949 876.00
258 12 1950 704.00
259 12 1951 1111.00
260 12 1952 780.00
261 12 1953 791.00
262 12 1954 709.00
263 12 1955 812.00
264 12 1956 686.00
265 12 1957 812.00
266 12 1958 755.00
267 12 1959 802.00
268 12 1960 1098.00
269 12 1961 868.00
270 12 1962 735.00
271 12 1963 829.00
272 12 1964 750.00
273 12 1965 635.00
274 12 1966 887.00
275 12 1967 711.00
276 12 1968 753.00
277 12 1969 935.00
278 12 1970 862.00
279 12 1971 830.00
280 12 1972 924.00
281 12 1973 735.00
282 12 1974 766.00
283 12 1975 930.00
284 12 1976 783.00
285 12 1977 1623.00
286 12 1978 1359.00
287 12 1979 1015.00
288 12 1980 922.00
289 12 1981 963.00
290 12 1982 848.00
291 12 1983 975.00
292 12 1984 760.00
293 12 1985 766.00
294 13 1928 1288.00
295 13 1929 854.00
296 13 1930 1324.00
297 13 1931 741.00
298 13 1932 1043.00
299 13 1933 756.00
300 13 1934 1477.00
301 13 1935 1160.00
302 13 1936 1426.00
303 13 1937 1360.00
304 13 1938 1109.00
305 13 1939 1211.00
306 13 1940 1094.00
307 13 1941 1666.00
308 13 1942 1002.00
309 13 1943 772.00
310 13 1948 1124.00
311 13 1949 997.00
312 13 1950 649.00
313 13 1951 1436.00
314 13 1952 762.00
315 13 1953 1293.00
316 13 1954 930.00
317 13 1955 721.00
318 13 1956 838.00
319 13 1957 1063.00
320 13 1958 710.00
321 13 1959 1002.00
322 13 1960 1625.00
323 13 1961 1002.00
324 13 1962 848.00
325 13 1963 1104.00
326 13 1964 869.00
327 13 1965 823.00
328 13 1966 992.00
329 13 1967 588.00
330 13 1968 894.00
331 13 1969 1073.00
332 13 1970 675.00
333 13 1971 1181.00
334 13 1972 1568.00
335 13 1973 817.00
336 13 1974 1068.00
337 13 1975 978.00
338 14 1930 1505.00
339 14 1931 928.00
340 14 1932 1223.00
341 14 1933 805.00
342 14 1934 1449.00
343 14 1935 1084.00
344 14 1936 1588.00
345 14 1937 1509.00
346 14 1938 1137.00
347 14 1939 1014.00
348 14 1940 1181.00
349 14 1941 1394.00
350 14 1942 922.00
351 14 1943 811.00
352 14 1946 1428.00
353 14 1947 1137.00
354 14 1948 1240.00
355 14 1949 1034.00
356 14 1950 581.00
357 14 1951 1501.00
358 14 1952 700.00
359 14 1953 1263.00
360 14 1954 962.00
361 14 1955 780.00
362 14 1956 919.00
363 14 1957 1068.00
364 14 1958 855.00
365 14 1959 1198.00
366 14 1960 1569.00
367 14 1961 1134.00
368 14 1962 1007.00
369 14 1963 1205.00
370 14 1964 973.00
371 14 1965 871.00
372 14 1966 1188.00
373 14 1967 581.00
374 14 1968 1027.00
375 14 1969 1192.00
376 14 1970 578.00
377 14 1971 875.00
378 14 1972 1553.00
379 14 1973 774.00
380 14 1975 958.00
381 14 1976 1187.00
382 14 1977 2152.00
383 14 1978 836.00
384 14 1979 834.00
385 14 1980 753.00
386 14 1981 1110.00
387 15 1961 969.00
388 15 1962 811.00
389 15 1963 1107.00
390 15 1964 769.00
391 15 1965 567.00
392 15 1966 925.00
393 15 1967 508.00
394 15 1968 598.00
395 15 1969 818.00
396 15 1970 495.00
397 16 1937 957.00
398 16 1938 625.00
399 16 1939 625.00
400 16 1940 658.00
401 16 1941 1022.00
402 16 1942 555.00
403 16 1943 496.00
404 16 1944 625.00
405 16 1945 593.00
406 16 1946 1115.00
407 16 1947 718.00
408 16 1948 957.00
409 16 1949 707.00
410 16 1950 332.00
411 16 1951 821.00
412 16 1952 469.00
413 16 1953 913.00
414 16 1954 663.00
415 16 1955 418.00
416 16 1956 523.00
417 16 1957 799.00
418 16 1958 469.00
419 16 1959 1000.00
420 16 1960 1104.00
421 16 1961 761.00
422 16 1962 598.00
423 16 1963 1033.00
424 16 1964 707.00
425 16 1965 469.00
426 16 1966 614.00
427 16 1967 270.00
428 16 1968 609.00
429 16 1969 1017.00
430 16 1970 367.00
431 17 1927 595.00
432 17 1928 718.00
433 17 1929 518.00
434 17 1930 548.00
435 17 1931 389.00
436 17 1932 567.00
437 17 1933 506.00
438 17 1934 985.00
439 17 1935 530.00
440 17 1936 1097.00
441 17 1937 934.00
442 17 1938 675.00
443 17 1939 614.00
444 17 1940 587.00
445 17 1941 722.00
446 17 1942 499.00
447 17 1943 459.00
448 17 1946 1087.00
449 17 1947 550.00
450 17 1948 860.00
451 17 1949 648.00
452 17 1950 296.00
453 17 1951 658.00
454 18 1927 686.00
455 18 1928 863.00
456 18 1929 488.00
457 18 1930 937.00
458 18 1931 453.00
459 18 1932 621.00
460 18 1933 484.00
461 18 1934 851.00
462 18 1935 599.00
463 18 1936 1161.00
464 18 1937 894.00
465 18 1938 598.00
466 18 1939 645.00
467 18 1940 606.00
468 18 1941 772.00
469 18 1942 449.00
470 18 1943 486.00
471 18 1944 510.00
472 18 1945 559.00
473 18 1946 829.00
474 18 1947 545.00
475 18 1948 898.00
476 18 1949 529.00
477 18 1950 392.00
478 18 1951 856.00
479 18 1952 625.00
480 18 1953 773.00
481 18 1954 651.00
482 18 1955 674.00
483 18 1956 432.00
484 19 1927 589.00
485 19 1928 715.00
486 19 1929 479.00
487 19 1930 696.00
488 19 1931 394.00
489 19 1932 533.00
490 19 1933 430.00
491 19 1934 845.00
492 19 1935 519.00
493 19 1936 1012.00
494 19 1937 805.00
495 19 1938 559.00
496 19 1939 569.00
497 19 1940 580.00
498 19 1941 725.00
499 19 1942 448.00
500 19 1943 412.00
501 19 1944 411.00
502 19 1945 407.00
503 19 1946 638.00
504 19 1947 506.00
505 19 1948 729.00
506 19 1949 538.00
507 19 1950 350.00
508 19 1951 736.00
509 19 1952 513.00
510 19 1953 787.00
511 20 1935 1237.00
512 20 1936 1908.00
513 20 1937 1263.00
514 20 1938 1066.00
515 20 1939 1401.00
516 20 1940 1263.00
517 20 1941 1134.00
518 20 1942 799.00
519 20 1943 919.00
520 20 1944 971.00
521 20 1945 1057.00
522 20 1946 1710.00
523 20 1947 1555.00
524 20 1948 1667.00
525 20 1949 1212.00
526 20 1950 799.00
527 20 1951 1366.00
528 20 1952 962.00
529 20 1953 1779.00
530 20 1954 1504.00
531 20 1955 808.00
532 20 1956 1031.00
533 20 1957 1186.00
534 20 1958 1031.00
535 20 1959 1796.00
536 20 1960 1882.00
537 20 1961 1487.00
538 20 1962 945.00
539 20 1963 1710.00
540 20 1964 1194.00
541 20 1965 919.00
542 20 1966 1418.00
543 20 1967 722.00
544 20 1968 1160.00
545 20 1969 1409.00
546 20 1970 894.00
547 20 1971 1279.00
548 20 1972 1884.00
549 20 1973 1307.00
550 21 1927 489.00
551 21 1928 704.00
552 21 1929 310.00
553 21 1930 665.00
554 21 1931 259.00
555 21 1932 501.00
556 21 1933 428.00
557 21 1934 820.00
558 21 1935 551.00
559 21 1936 994.00
560 21 1937 658.00
561 21 1938 425.00
562 21 1939 423.00
563 21 1940 409.00
564 21 1941 736.00
565 21 1942 440.00
566 21 1943 401.00
567 21 1944 398.00
568 21 1945 342.00
569 21 1946 658.00
570 21 1947 449.00
571 21 1948 665.00
572 21 1949 535.00
573 21 1950 247.00
574 21 1951 584.00
575 21 1952 338.00
576 21 1953 580.00
577 21 1954 569.00
578 21 1955 311.00
579 21 1956 412.00
580 21 1957 565.00
581 21 1958 403.00
582 21 1959 846.00
583 21 1960 917.00
584 21 1961 525.00
585 21 1962 411.00
586 21 1963 717.00
587 21 1964 526.00
588 21 1965 248.00
589 21 1966 451.00
590 21 1967 185.00
591 21 1968 356.00
592 21 1969 564.00
593 21 1970 256.00
594 22 1934 1197.00
595 22 1935 863.00
596 22 1936 1382.00
597 22 1937 1104.00
598 22 1938 649.00
599 22 1939 745.00
600 22 1940 615.00
601 22 1941 1116.00
602 22 1942 618.00
603 22 1943 739.00
604 22 1944 761.00
605 22 1945 720.00
606 22 1946 1147.00
607 22 1947 838.00
608 22 1948 1057.00
609 22 1949 739.00
610 22 1950 529.00
611 22 1951 962.00
612 22 1952 470.00
613 22 1953 881.00
614 22 1954 495.00
615 22 1955 417.00
616 22 1956 553.00
617 22 1957 819.00
618 22 1958 711.00
619 22 1959 1410.00
620 22 1960 1472.00
621 22 1961 727.00
622 22 1962 671.00
623 22 1963 1163.00
624 22 1964 751.00
625 22 1965 476.00
626 22 1966 819.00
627 22 1967 399.00
628 22 1968 612.00
629 22 1969 860.00
630 22 1970 507.00
631 22 1971 844.00
632 22 1972 1245.00
633 22 1973 953.00
634 22 1975 976.00
635 23 1933 835.00
636 23 1934 1345.00
637 23 1935 1085.00
638 23 1936 1655.00
639 23 1937 1291.00
640 23 1938 838.00
641 23 1939 974.00
642 23 1940 862.00
643 23 1941 1106.00
644 23 1942 699.00
645 23 1943 854.00
646 23 1944 721.00
647 23 1945 699.00
648 23 1946 1033.00
649 23 1947 892.00
650 23 1948 1213.00
651 23 1949 631.00
652 23 1950 554.00
653 23 1951 833.00
654 23 1952 911.00
655 23 1953 796.00
656 23 1954 721.00
657 23 1955 727.00
658 24 1934 1795.00
659 24 1935 1761.00
660 24 1936 1962.00
661 24 1937 1541.00
662 24 1938 1007.00
663 24 1939 1276.00
664 24 1940 1144.00
665 24 1941 1302.00
666 24 1942 947.00
667 24 1943 1210.00
668 24 1947 1113.00
669 24 1948 1532.00
670 24 1949 764.00
671 24 1950 849.00
672 24 1951 1412.00
673 24 1952 1105.00
674 24 1953 1048.00
675 24 1954 843.00
676 24 1955 1048.00
677 24 1956 1157.00
678 25 1941 1498.00
679 25 1942 880.00
680 25 1943 1028.00
681 25 1944 1046.00
682 25 1945 589.00
683 25 1946 1088.00
684 25 1947 1179.00
685 25 1948 1471.00
686 25 1949 761.00
687 25 1950 1106.00
688 25 1951 2017.00
689 25 1952 649.00
690 25 1953 1129.00
691 25 1954 1149.00
692 25 1955 1355.00
693 25 1956 1107.00
694 26 1934 1634.00
695 26 1935 1300.00
696 26 1936 1715.00
697 26 1937 1643.00
698 26 1938 1295.00
699 26 1939 1459.00
700 26 1940 1020.00
701 26 1941 1531.00
702 26 1942 919.00
703 26 1943 1095.00
704 26 1944 876.00
705 26 1945 857.00
706 26 1946 1534.00
707 26 1947 1183.00
708 26 1948 1405.00
709 26 1949 1051.00
710 26 1950 1159.00
711 26 1951 1478.00
712 26 1952 1472.00
713 26 1953 1364.00
714 26 1954 1140.00
715 26 1955 1126.00
716 26 1956 1007.00
717 27 1935 1157.00
718 27 1936 1759.00
719 27 1937 1245.00
720 27 1938 842.00
721 27 1939 1056.00
722 27 1940 800.00
723 27 1941 1244.00
724 27 1942 806.00
725 27 1943 925.00
726 27 1944 839.00
727 27 1958 782.00
728 27 1959 1236.00
729 27 1960 1601.00
730 27 1961 886.00
731 27 1962 768.00
732 27 1963 1109.00
733 27 1964 722.00
734 27 1965 440.00
735 28 1952 1121.00
736 28 1953 1488.00
737 28 1954 1158.00
738 28 1955 1287.00
739 28 1956 1210.00
740 28 1958 1468.00
741 28 1961 1445.00
742 28 1962 1304.00
743 28 1963 1967.00
744 28 1964 1408.00
745 29 1952 1121.00
746 29 1953 1482.00
747 29 1954 1163.00
748 29 1955 1378.00
749 29 1956 1201.00
750 29 1957 1677.00
751 29 1958 1360.00
752 29 1959 2230.00
753 29 1961 1117.00
754 29 1962 1093.00
755 29 1963 1647.00
756 29 1964 1358.00
757 30 1923 395.00
758 30 1924 342.00
759 30 1925 463.00
760 30 1926 649.00
761 30 1927 400.00
762 30 1928 703.00
763 30 1929 388.00
764 30 1930 570.00
765 30 1931 292.00
766 30 1932 490.00
767 30 1933 440.00
768 30 1934 885.00
769 30 1935 671.00
770 30 1936 1035.00
771 30 1937 729.00
772 30 1938 360.00
773 30 1939 467.00
774 30 1940 351.00
775 30 1941 765.00
776 30 1942 418.00
777 30 1943 455.00
778 30 1944 339.00
779 30 1945 311.00
780 30 1946 493.00
781 30 1947 432.00
782 30 1948 686.00
783 30 1949 353.00
784 30 1950 337.00
785 30 1953 449.00
786 30 1954 513.00
787 30 1955 374.00
788 30 1956 475.00
789 30 1957 628.00
790 30 1958 496.00
791 30 1959 844.00
792 30 1960 974.00
793 30 1961 375.00
794 30 1962 419.00
795 30 1963 651.00
796 30 1964 441.00
797 30 1965 226.00
798 30 1966 438.00
799 30 1967 218.00
800 30 1968 461.00
801 30 1969 504.00
802 30 1970 309.00
803 30 1971 543.00
804 30 1972 870.00
805 30 1973 433.00
806 30 1974 724.00
807 30 1975 604.00
808 30 1976 712.00
809 30 1977 865.00
810 30 1980 395.00
811 30 1981 324.00
812 30 1982 436.00
813 30 1984 607.00
814 30 1985 399.00
815 31 1931 754.00
816 31 1932 1025.00
817 31 1933 829.00
818 31 1934 1428.00
819 31 1936 1828.00
820 31 1937 1472.00
821 31 1938 771.00
822 31 1939 1144.00
823 31 1940 980.00
824 31 1941 1728.00
825 31 1942 720.00
826 31 1943 850.00
827 31 1946 995.00
828 31 1947 901.00
829 31 1948 1138.00
830 31 1949 678.00
831 31 1950 805.00
832 31 1951 1509.00
833 31 1952 616.00
834 31 1953 629.00
835 31 1954 716.00
836 31 1955 848.00
837 31 1956 767.00
838 31 1957 720.00
839 31 1958 1426.00
840 31 1959 1370.00
841 31 1960 1826.00
842 31 1962 1046.00
843 31 1963 1172.00
844 31 1964 869.00
845 31 1965 793.00
846 31 1966 1008.00
847 31 1967 571.00
848 31 1968 1161.00
849 32 1933 920.00
850 32 1934 1674.00
851 32 1935 1153.00
852 32 1936 1512.00
853 32 1937 1226.00
854 32 1938 647.00
855 32 1939 945.00
856 32 1940 822.00
857 32 1941 1665.00
858 32 1942 632.00
859 32 1943 746.00
860 32 1944 705.00
861 32 1947 759.00
862 32 1948 932.00
863 32 1949 617.00
864 32 1950 632.00
865 32 1951 1259.00
866 32 1952 506.00
867 32 1953 590.00
868 32 1954 743.00
869 32 1955 598.00
870 32 1956 747.00
871 32 1957 988.00
872 32 1958 855.00
873 32 1959 1229.00
874 32 1960 1461.00
875 32 1961 458.00
876 32 1962 804.00
877 32 1963 867.00
878 32 1964 652.00
879 32 1965 580.00
880 33 1942 684.00
881 33 1944 701.00
882 33 1945 486.00
883 33 1946 792.00
884 33 1947 727.00
885 33 1948 1086.00
886 33 1949 564.00
887 33 1950 624.00
888 33 1951 1205.00
889 33 1952 463.00
890 33 1953 846.00
891 33 1954 894.00
892 33 1955 707.00
893 33 1956 733.00
894 33 1957 892.00
895 33 1958 869.00
896 33 1959 1283.00
897 33 1960 1444.00
898 33 1961 474.00
899 33 1962 798.00
900 33 1963 935.00
901 33 1964 719.00
902 33 1965 445.00
903 33 1966 749.00
904 33 1967 428.00
905 33 1968 772.00
906 33 1969 854.00
907 33 1970 545.00
908 33 1976 1002.00
909 33 1977 939.00
910 33 1980 643.00
911 33 1981 603.00
912 33 1982 785.00
913 33 1983 775.00
914 33 1984 1025.00
915 33 1985 584.00
916 34 1931 636.00
917 34 1932 998.00
918 34 1933 1014.00
919 34 1934 1965.00
920 34 1935 1333.00
921 34 1936 1730.00
922 34 1937 1330.00
923 34 1938 825.00
924 34 1939 1112.00
925 34 1940 851.00
926 34 1941 1423.00
927 34 1942 960.00
928 34 1943 1031.00
929 34 1944 976.00
930 34 1945 561.00
931 34 1946 1055.00
932 34 1947 1076.00
933 34 1948 1224.00
934 34 1949 658.00
935 34 1950 707.00
936 34 1951 1453.00
937 34 1952 445.00
938 34 1953 966.00
939 34 1954 930.00
940 34 1955 939.00
941 34 1956 862.00
942 34 1957 1115.00
943 34 1958 1158.00
944 34 1959 1573.00
945 35 1931 845.00
946 35 1932 803.00
947 35 1933 746.00
948 35 1934 1036.00
949 35 1935 1160.00
950 35 1936 1038.00
951 35 1937 1285.00
952 35 1938 369.00
953 35 1939 1093.00
954 35 1940 732.00
955 35 1941 613.00
956 35 1942 620.00
957 35 1943 863.00
958 35 1952 579.00
959 35 1953 765.00
960 35 1954 819.00
961 35 1955 505.00
962 35 1956 594.00
963 35 1957 667.00
964 35 1958 651.00
965 35 1959 950.00
966 35 1960 1583.00
967 35 1961 688.00
968 35 1962 622.00
969 35 1963 1068.00
970 36 1935 924.00
971 36 1936 1676.00
972 36 1937 1765.00
973 36 1938 841.00
974 36 1939 796.00
975 36 1940 745.00
976 36 1941 1363.00
977 36 1942 663.00
978 36 1943 714.00
979 36 1944 382.00
980 36 1945 771.00
981 36 1946 796.00
982 36 1947 956.00
983 36 1948 1153.00
984 36 1949 669.00
985 36 1950 796.00
986 36 1951 1879.00
987 36 1952 643.00
988 36 1953 796.00
989 36 1954 994.00
990 36 1955 733.00
991 36 1956 1185.00
992 37 1945 597.00
993 37 1946 833.00
994 37 1947 902.00
995 37 1948 1207.00
996 37 1949 793.00
997 37 1950 598.00
998 37 1951 1328.00
999 37 1952 323.00
1000 37 1953 561.00
1001 37 1954 726.00
1002 37 1955 663.00
1003 37 1956 919.00
1004 37 1957 1139.00
1005 37 1958 1040.00
1006 37 1959 1264.00
1007 37 1960 1214.00
1008 38 1947 492.00
1009 38 1948 608.00
1010 38 1949 368.00
1011 38 1950 393.00
1012 38 1951 1123.00
1013 38 1952 172.00
1014 38 1953 281.00
1015 38 1954 539.00
1016 38 1955 424.00
1017 38 1956 585.00
1018 38 1957 632.00
1019 38 1958 528.00
1020 39 1938 339.00
1021 39 1939 929.00
1022 39 1940 560.00
1023 39 1941 727.00
1024 39 1942 490.00
1025 39 1943 684.00
1026 39 1950 979.00
1027 39 1951 1466.00
1028 39 1952 404.00
1029 39 1953 865.00
1030 39 1954 533.00
1031 39 1955 462.00
1032 39 1956 287.00
1033 39 1957 767.00
1034 39 1958 653.00
1035 39 1959 1176.00
1036 39 1960 1906.00
1037 39 1961 883.00
1038 40 1956 755.00
1039 40 1957 871.00
1040 40 1958 938.00
1041 40 1959 1175.00
1042 40 1960 1218.00
1043 40 1961 621.00
1044 40 1962 432.25
1045 40 1963 913.20
1046 40 1964 840.15
1047 40 1965 827.97
1048 40 1966 919.29
1049 40 1967 724.48
1050 40 1968 602.72
1051 41 1951 1449.00
1052 41 1952 1449.00
1053 41 1953 1546.00
1054 41 1954 1516.00
1055 41 1955 1254.00
1056 41 1956 1382.00
1057 42 1944 895.00
1058 42 1945 1006.00
1059 42 1946 1351.00
1060 42 1947 1215.00
1061 42 1950 1215.00
1062 42 1951 1279.00
1063 42 1952 1006.00
1064 42 1953 1156.00
1065 42 1954 821.00
1066 43 1935 948.00
1067 43 1936 1308.00
1068 43 1937 1185.00
1069 43 1938 801.00
1070 43 1939 848.00
1071 43 1940 926.00
1072 43 1941 932.00
1073 43 1942 755.00
1074 43 1943 764.00
1075 43 1948 891.00
1076 43 1949 677.00
1077 43 1950 835.00
1078 43 1951 1112.00
1079 43 1952 918.00
1080 43 1953 742.00
1081 43 1954 685.00
1082 43 1955 927.00
1083 44 1926 1607.00
1084 44 1927 1275.00
1085 44 1928 1613.00
1086 44 1929 1484.00
1087 44 1930 1487.00
1088 44 1931 1205.00
1089 44 1932 1367.00
1090 44 1933 1158.00
1091 44 1934 1583.00
1092 44 1935 1342.00
1093 44 1936 1848.00
1094 44 1937 1640.00
1095 44 1938 1225.00
1096 44 1939 1320.00
1097 44 1940 1202.00
1098 44 1941 1476.00
1099 44 1942 1190.00
1100 44 1948 1435.00
1101 44 1949 894.00
1102 44 1950 1326.00
1103 44 1951 1230.00
1104 44 1952 1042.00
1105 44 1953 1127.00
1106 45 1931 1953.00
1107 45 1932 1939.00
1108 45 1933 1677.00
1109 45 1934 1692.00
1110 45 1935 2051.00
1111 45 1936 2371.00
1112 45 1937 2022.00
1113 45 1938 1521.00
1114 45 1939 1448.00
1115 45 1940 1825.00
1116 45 1941 1363.00
1117 45 1942 1760.00
1118 45 1943 1672.00
1119 45 1949 1603.00
1120 45 1950 1244.00
1121 45 1951 1521.00
1122 45 1952 1783.00
1123 45 1953 1560.00
1124 45 1954 1357.00
1125 45 1955 1673.00
1126 45 1956 1625.00
1127 45 1957 1425.00
1128 45 1958 1688.00
1129 45 1959 1577.00
1130 45 1960 1736.00
1131 45 1961 1640.00
1132 45 1962 1584.00
1133 45 1964 1293.00
1134 45 1965 1277.00
1135 45 1966 1742.00
1136 45 1967 1491.00
1137 46 1952 1223.00
1138 46 1953 1077.00
1139 46 1954 671.00
1140 46 1955 1063.00
1141 46 1956 969.00
1142 46 1957 842.00
1143 46 1958 1037.00
1144 46 1959 903.00
1145 46 1960 1407.00
1146 46 1961 1153.00
1147 46 1962 1107.00
1148 46 1963 1293.00
1149 46 1964 813.00
1150 46 1965 834.00
1151 46 1966 1118.00
1152 46 1967 901.00
1153 46 1968 981.00
1154 47 1949 986.00
1155 47 1950 996.00
1156 47 1951 1335.00
1157 47 1952 964.00
1158 47 1953 1018.00
1159 47 1954 821.00
1160 47 1955 945.00
1161 47 1956 844.00
1162 47 1957 1133.00
1163 47 1958 975.00
1164 47 1959 1082.00
1165 47 1960 1252.00
1166 47 1961 1031.00
1167 47 1962 940.00
1168 47 1963 1078.00
1169 47 1964 933.00
1170 47 1965 709.00
1171 47 1966 923.00
1172 47 1967 899.00
1173 47 1968 747.00
1174 47 1969 1010.00
1175 47 1970 873.00
1176 47 1971 962.00
1177 47 1972 965.00
1178 47 1973 674.00
1179 47 1974 763.00
1180 47 1975 915.00
1181 47 1976 1029.00
1182 47 1977 1452.00
1183 47 1978 1486.00
1184 48 1950 872.00
1185 48 1951 1528.00
1186 48 1952 1062.00
1187 48 1953 1345.00
1188 48 1954 1158.00
1189 48 1955 998.00
1190 48 1956 1197.00
1191 48 1957 1234.00
1192 48 1958 1469.00
1193 48 1959 1343.00
1194 48 1960 2103.00
1195 48 1961 1745.00
1196 48 1962 1084.00
1197 48 1963 1717.00
1198 48 1964 1131.00
1199 48 1965 990.00
1200 48 1966 1186.00
1201 48 1967 884.00
1202 48 1968 1118.00
1203 48 1969 1383.00
1204 48 1970 877.00
1205 48 1971 1072.00
1206 48 1972 1906.00
1207 48 1973 830.00
1208 49 1944 808.00
1209 49 1945 1088.00
1210 49 1946 1435.00
1211 49 1947 1265.00
1212 49 1948 1065.00
1213 49 1949 911.00
1214 49 1950 992.00
1215 49 1951 1273.00
1216 49 1952 1031.00
1217 49 1953 1100.00
1218 49 1954 769.00
1219 49 1955 865.00
1220 49 1956 781.00
1221 49 1959 1019.00
1222 49 1960 1761.00
cod anno dato
Min. : 1.0 Min. :1921 Min. : 172.0
1st Qu.:13.0 1st Qu.:1940 1st Qu.: 725.2
Median :22.0 Median :1951 Median : 981.0
Mean :23.7 Mean :1951 Mean :1041.4
3rd Qu.:34.0 3rd Qu.:1960 3rd Qu.:1308.8
Max. :49.0 Max. :1985 Max. :3045.0
$`1`
[1] 1494 1309 1699 1467 1918 1469 1267 1523 1338 1438 1788 1591 1697 1780 1769
$`2`
[1] 1144 1652 1807 1881 1741 1124 2064 1434 1678 1239 921 983 1093 1744 1213
[16] 1590 956 1124 2181 1077 1345 1219 988 1325 1277 1479 1307 2053 1232 973
[31] 1407 912
$`3`
[1] 2596 954 1115 1248 867 1280 1588 1055 1764 3045
$`4`
[1] 871 1238 1505 1636 1553 1936 1739 1867 1184 1630 1311 1520 1201 1614 1971
[16] 1829 1781 1093 1996 1328 1662 1199 860 961 949 1536 1016 1386 820 1023
[31] 2329 1209 1305 1334 1024 1364 1310 1410 1247 2393 1317 909 1808 1020 1181
[46] 1365 1218 1644 1160 1002 1243 1332 1033 1170 1685 1478 2434 1600 1369 1215
[61] 1614 1449 1518 1490 1191
$`7`
[1] 1481 1758 1774 1625 1607 2826 1488 928 2379 1173 1801 1824 1309 2220 1733
$`8`
[1] 1086 1810 2244 2138 2028 1308 1947 1528 2244 1594 861 1378 1795 1344 1558
[16] 696 724 2497 660 1388 1484 952 1987 2646 1689 1443 2688 1249 1145 2392
[31] 1001 1380
$`9`
[1] 2075 1607 1717 1261 1824 1330 963 1313 2276 682 1440 1304 1193
$`10`
[1] 1096 1387 1289 1461 1054 1474 1137 1256 981 1696 1468 1850 1644 1248 1498
[16] 1317 1500 1109 859 931 1020 1493 954 1133 1144 1056
$`11`
[1] 1320 1706 948 1643 944 1402 1202 1788 1665 1833 1679 1166 1833 1661 1938
[16] 1457 830 1221 1398 1674 1311 1611 1003 1021
$`12`
[1] 890 1247 1040 1047 875 1060 913 968 749 1218 1104 1489 1300 833 994
[16] 1002 1134 854 826 695 939 1230 830 1096 876 704 1111 780 791 709
[31] 812 686 812 755 802 1098 868 735 829 750 635 887 711 753 935
[46] 862 830 924 735 766 930 783 1623 1359 1015 922 963 848 975 760
[61] 766
$`13`
[1] 1288 854 1324 741 1043 756 1477 1160 1426 1360 1109 1211 1094 1666 1002
[16] 772 1124 997 649 1436 762 1293 930 721 838 1063 710 1002 1625 1002
[31] 848 1104 869 823 992 588 894 1073 675 1181 1568 817 1068 978
$`14`
[1] 1505 928 1223 805 1449 1084 1588 1509 1137 1014 1181 1394 922 811 1428
[16] 1137 1240 1034 581 1501 700 1263 962 780 919 1068 855 1198 1569 1134
[31] 1007 1205 973 871 1188 581 1027 1192 578 875 1553 774 958 1187 2152
[46] 836 834 753 1110
$`15`
[1] 969 811 1107 769 567 925 508 598 818 495
$`16`
[1] 957 625 625 658 1022 555 496 625 593 1115 718 957 707 332 821
[16] 469 913 663 418 523 799 469 1000 1104 761 598 1033 707 469 614
[31] 270 609 1017 367
$`17`
[1] 595 718 518 548 389 567 506 985 530 1097 934 675 614 587 722
[16] 499 459 1087 550 860 648 296 658
$`18`
[1] 686 863 488 937 453 621 484 851 599 1161 894 598 645 606 772
[16] 449 486 510 559 829 545 898 529 392 856 625 773 651 674 432
$`19`
[1] 589 715 479 696 394 533 430 845 519 1012 805 559 569 580 725
[16] 448 412 411 407 638 506 729 538 350 736 513 787
$`20`
[1] 1237 1908 1263 1066 1401 1263 1134 799 919 971 1057 1710 1555 1667 1212
[16] 799 1366 962 1779 1504 808 1031 1186 1031 1796 1882 1487 945 1710 1194
[31] 919 1418 722 1160 1409 894 1279 1884 1307
$`21`
[1] 489 704 310 665 259 501 428 820 551 994 658 425 423 409 736 440 401 398 342
[20] 658 449 665 535 247 584 338 580 569 311 412 565 403 846 917 525 411 717 526
[39] 248 451 185 356 564 256
$`22`
[1] 1197 863 1382 1104 649 745 615 1116 618 739 761 720 1147 838 1057
[16] 739 529 962 470 881 495 417 553 819 711 1410 1472 727 671 1163
[31] 751 476 819 399 612 860 507 844 1245 953 976
$`23`
[1] 835 1345 1085 1655 1291 838 974 862 1106 699 854 721 699 1033 892
[16] 1213 631 554 833 911 796 721 727
$`24`
[1] 1795 1761 1962 1541 1007 1276 1144 1302 947 1210 1113 1532 764 849 1412
[16] 1105 1048 843 1048 1157
$`25`
[1] 1498 880 1028 1046 589 1088 1179 1471 761 1106 2017 649 1129 1149 1355
[16] 1107
$`26`
[1] 1634 1300 1715 1643 1295 1459 1020 1531 919 1095 876 857 1534 1183 1405
[16] 1051 1159 1478 1472 1364 1140 1126 1007
$`27`
[1] 1157 1759 1245 842 1056 800 1244 806 925 839 782 1236 1601 886 768
[16] 1109 722 440
$`28`
[1] 1121 1488 1158 1287 1210 1468 1445 1304 1967 1408
$`29`
[1] 1121 1482 1163 1378 1201 1677 1360 2230 1117 1093 1647 1358
$`30`
[1] 395 342 463 649 400 703 388 570 292 490 440 885 671 1035 729
[16] 360 467 351 765 418 455 339 311 493 432 686 353 337 449 513
[31] 374 475 628 496 844 974 375 419 651 441 226 438 218 461 504
[46] 309 543 870 433 724 604 712 865 395 324 436 607 399
$`31`
[1] 754 1025 829 1428 1828 1472 771 1144 980 1728 720 850 995 901 1138
[16] 678 805 1509 616 629 716 848 767 720 1426 1370 1826 1046 1172 869
[31] 793 1008 571 1161
$`32`
[1] 920 1674 1153 1512 1226 647 945 822 1665 632 746 705 759 932 617
[16] 632 1259 506 590 743 598 747 988 855 1229 1461 458 804 867 652
[31] 580
$`33`
[1] 684 701 486 792 727 1086 564 624 1205 463 846 894 707 733 892
[16] 869 1283 1444 474 798 935 719 445 749 428 772 854 545 1002 939
[31] 643 603 785 775 1025 584
$`34`
[1] 636 998 1014 1965 1333 1730 1330 825 1112 851 1423 960 1031 976 561
[16] 1055 1076 1224 658 707 1453 445 966 930 939 862 1115 1158 1573
$`35`
[1] 845 803 746 1036 1160 1038 1285 369 1093 732 613 620 863 579 765
[16] 819 505 594 667 651 950 1583 688 622 1068
$`36`
[1] 924 1676 1765 841 796 745 1363 663 714 382 771 796 956 1153 669
[16] 796 1879 643 796 994 733 1185
$`37`
[1] 597 833 902 1207 793 598 1328 323 561 726 663 919 1139 1040 1264
[16] 1214
$`38`
[1] 492 608 368 393 1123 172 281 539 424 585 632 528
$`39`
[1] 339 929 560 727 490 684 979 1466 404 865 533 462 287 767 653
[16] 1176 1906 883
$`40`
[1] 755.00 871.00 938.00 1175.00 1218.00 621.00 432.25 913.20 840.15
[10] 827.97 919.29 724.48 602.72
$`41`
[1] 1449 1449 1546 1516 1254 1382
$`42`
[1] 895 1006 1351 1215 1215 1279 1006 1156 821
$`43`
[1] 948 1308 1185 801 848 926 932 755 764 891 677 835 1112 918 742
[16] 685 927
$`44`
[1] 1607 1275 1613 1484 1487 1205 1367 1158 1583 1342 1848 1640 1225 1320 1202
[16] 1476 1190 1435 894 1326 1230 1042 1127
$`45`
[1] 1953 1939 1677 1692 2051 2371 2022 1521 1448 1825 1363 1760 1672 1603 1244
[16] 1521 1783 1560 1357 1673 1625 1425 1688 1577 1736 1640 1584 1293 1277 1742
[31] 1491
$`46`
[1] 1223 1077 671 1063 969 842 1037 903 1407 1153 1107 1293 813 834 1118
[16] 901 981
$`47`
[1] 986 996 1335 964 1018 821 945 844 1133 975 1082 1252 1031 940 1078
[16] 933 709 923 899 747 1010 873 962 965 674 763 915 1029 1452 1486
$`48`
[1] 872 1528 1062 1345 1158 998 1197 1234 1469 1343 2103 1745 1084 1717 1131
[16] 990 1186 884 1118 1383 877 1072 1906 830
$`49`
[1] 808 1088 1435 1265 1065 911 992 1273 1031 1100 769 865 781 1019 1761
[1] 0.008464929
[1] 0.771088
[1] 1800
$lambda1
[1] 1648.806
$lambda2
[1] 138.2366
$tau3
[1] 0.1062002
$tau4
[1] 0.1771496
[1] 1782.410 1537.389 1715.139 1525.029 1807.044 1479.856 1461.058 1369.896
[9] 1525.347 2030.263 1798.348 1961.500 1853.753 1636.320 1623.466 1305.965
[17] 1971.441 1805.895 1600.679 1792.025 1240.418 1514.373 1887.707 1230.068
[25] 2186.379 1325.040 1298.012 1683.153 2033.411 1642.351 1729.944 1452.349
[33] 1410.345 1596.252 1668.297 1612.541 1573.790 1327.747 1662.734 1715.119
[41] 1592.847 1373.163 1814.630 1844.754 1547.727 1669.339 1409.356 1571.774
[49] 1934.689 1449.815 1821.313 1656.929 1514.189 1773.396 1673.634 1569.087
[57] 1328.189 1711.022 2023.489 1677.939 1820.261 1385.479 1607.867 1504.635
[65] 1664.142 1534.777 1459.840 1316.187 1625.160 1764.433 1373.577 1394.577
[73] 1692.781 1519.356 1790.479 1495.143 1473.605 1598.239 1707.849 2064.744
[81] 1619.661 1648.040 1504.173 1804.099 1653.993 2093.817 1309.224 1168.564
[89] 1300.777 1172.756 1718.477 1724.189 1828.236 1105.595 1315.432 1976.688
[97] 1290.695 1720.025 1351.754 1422.375
l1R l2R lcvR lcaR lkurR
1041.4321277 160.1783511 0.1597701 0.1489629 0.1356834
Warning messages:
1: In fn(par, ...) : value out of range in 'gammafn'
2: In fn(par, ...) : value out of range in 'gammafn'
$lambda1
[1] 1041.432
$lambda2
[1] 160.1784
$tau3
[1] 0.148968
$tau4
[1] 0.1356809
homtest documentation built on May 2, 2019, 1:45 p.m.
R Package Documentation
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Description Usage Arguments Details Value Note Author(s) References See Also Examples
Description
KAPPA provides the link between L-moments of a sample and the four parameter
kappa distribution.
Usage
1 2 3 4 5 6 | f.kappa (x, xi, alfa, k, h)
F.kappa (x, xi, alfa, k, h)
invF.kappa (F, xi, alfa, k, h)
Lmom.kappa (xi, alfa, k, h)
par.kappa (lambda1, lambda2, tau3, tau4)
rand.kappa (numerosita, xi, alfa, k, h)
|
Arguments
x |
vector of quantiles |
xi |
vector of kappa location parameters |
alfa |
vector of kappa scale parameters |
k |
vector of kappa third parameters |
h |
vector of kappa fourth parameters |
F |
vector of probabilities |
lambda1 |
vector of sample means |
lambda2 |
vector of L-variances |
tau3 |
vector of L-CA (or L-skewness) |
tau4 |
vector of L-kurtosis |
numerosita |
numeric value indicating the length of the vector to be generated |
Details
Definition
Parameters (4): ξ (location), α (scale), k, h.
Range of x: upper bound is ξ + α/k if k>0, inf if k ≤ 0; lower bound is xi + α(1-h^(-k))/k if h>0, ξ + α/k if h ≤ 0 and k<0 and -inf if h ≤ 0 and k ≥ 0
Probability density function:
f(x) = α^(-1) [1 - k (x - ξ)/α]^(1/k-1) [F(x)]^(1-h)
Cumulative distribution function:
F(x) = {1 - h[1 - k(x - ξ)/α]^(1/k)}^(1/h)
Quantile function:
x(F) = ξ + α/k [1 - ((1-F^h)/h)^k]
h=-1 is the generalized logistic distribution; h=0 is the generalized eztreme value distribution; h=1 is the generalized Pareto distribution.
L-moments
L-moments are defined for h ≥ 0 and k>-1, or if h<0 and -1<k<-1/h.
λ1 = ξ + α(1 - g1)/k
λ2 = α(g1 - g2)/k
τ3 = (-g1 + 3g2 - 2g3)/(g1 - g2)
τ4 = (-g1 + 6g2 - 10g3 + 5g4)/(g1 - g2)
where gr = (r Γ(1+k)Γ(r/h))/(h^(1+k) Γ(1+k+r/h)) if h>0; gr = (rΓ(1+k)Γ(-k-r/h))/((-h)^(1+k)Γ(1-r/h)) if h<0;
Here Γ denote the gamma function
Γ(x) = integral[from 0 to inf] t^(x-1) e^(-t) dt
Parameters
There are no simple expressions for the parameters in terms of the L-moments.
However they can be obtained with a numerical algorithm considering the formulations of τ3 and τ4 in terms of k and h.
Here we use the function optim to minimize (t3-τ3)^2 + (t4-τ4)^2 where t3 and t4 are the sample L-moment ratios.
Value
f.kappa gives the density f, F.kappa gives the distribution function F, invFkappa gives
the quantile function x, Lmom.kappa gives the L-moments (λ1, λ2, τ3, τ4), par.kappa gives the parameters (xi, alfa, k, h), and rand.kappa generates random deviates.
Note
Lmom.kappa and par.kappa accept input as vectors of equal length. In f.kappa, F.kappa, invF.kappa and rand.kappa parameters (xi, alfa, k, h) must be atomic.
Author(s)
Alberto Viglione, e-mail: alviglio@tiscali.it.
References
Hosking, J.R.M. and Wallis, J.R. (1997) Regional Frequency Analysis: an approach based on L-moments, Cambridge University Press, Cambridge, UK.
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | data(annualflows)
annualflows
summary(annualflows)
x <- annualflows["dato"][,]
fac <- factor(annualflows["cod"][,])
split(x,fac)
camp <- split(x,fac)$"45"
ll <- Lmoments(camp)
parameters <- par.kappa(ll[1],ll[2],ll[4],ll[5])
f.kappa(1800,parameters$xi,parameters$alfa,parameters$k,parameters$h)
F.kappa(1800,parameters$xi,parameters$alfa,parameters$k,parameters$h)
invF.kappa(0.771088,parameters$xi,parameters$alfa,parameters$k,parameters$h)
Lmom.kappa(parameters$xi,parameters$alfa,parameters$k,parameters$h)
rand.kappa(100,parameters$xi,parameters$alfa,parameters$k,parameters$h)
Rll <- regionalLmoments(x,fac); Rll
parameters <- par.kappa(Rll[1],Rll[2],Rll[4],Rll[5])
Lmom.kappa(parameters$xi,parameters$alfa,parameters$k,parameters$h)
|
Example output
cod anno dato
1 1 1956 1494.00
2 1 1957 1309.00
3 1 1958 1699.00
4 1 1959 1467.00
5 1 1960 1918.00
6 1 1961 1469.00
7 1 1962 1267.00
8 1 1963 1523.00
9 1 1964 1338.00
10 1 1965 1438.00
11 1 1966 1788.00
12 1 1967 1591.00
13 1 1968 1697.00
14 1 1969 1780.00
15 1 1970 1769.00
16 2 1933 1144.00
17 2 1934 1652.00
18 2 1935 1807.00
19 2 1936 1881.00
20 2 1937 1741.00
21 2 1938 1124.00
22 2 1939 2064.00
23 2 1940 1434.00
24 2 1941 1678.00
25 2 1942 1239.00
26 2 1943 921.00
27 2 1944 983.00
28 2 1945 1093.00
29 2 1946 1744.00
30 2 1947 1213.00
31 2 1948 1590.00
32 2 1949 956.00
33 2 1950 1124.00
34 2 1951 2181.00
35 2 1952 1077.00
36 2 1953 1345.00
37 2 1954 1219.00
38 2 1955 988.00
39 2 1956 1325.00
40 2 1957 1277.00
41 2 1958 1479.00
42 2 1959 1307.00
43 2 1960 2053.00
44 2 1961 1232.00
45 2 1962 973.00
46 2 1963 1407.00
47 2 1964 912.00
48 3 1951 2596.00
49 3 1952 954.00
50 3 1953 1115.00
51 3 1954 1248.00
52 3 1955 867.00
53 3 1956 1280.00
54 3 1957 1588.00
55 3 1958 1055.00
56 3 1959 1764.00
57 3 1960 3045.00
58 4 1921 871.00
59 4 1922 1238.00
60 4 1923 1505.00
61 4 1924 1636.00
62 4 1925 1553.00
63 4 1926 1936.00
64 4 1927 1739.00
65 4 1928 1867.00
66 4 1929 1184.00
67 4 1930 1630.00
68 4 1931 1311.00
69 4 1932 1520.00
70 4 1933 1201.00
71 4 1934 1614.00
72 4 1935 1971.00
73 4 1936 1829.00
74 4 1937 1781.00
75 4 1938 1093.00
76 4 1939 1996.00
77 4 1940 1328.00
78 4 1941 1662.00
79 4 1942 1199.00
80 4 1943 860.00
81 4 1944 961.00
82 4 1945 949.00
83 4 1946 1536.00
84 4 1947 1016.00
85 4 1948 1386.00
86 4 1949 820.00
87 4 1950 1023.00
88 4 1951 2329.00
89 4 1952 1209.00
90 4 1953 1305.00
91 4 1954 1334.00
92 4 1955 1024.00
93 4 1956 1364.00
94 4 1957 1310.00
95 4 1958 1410.00
96 4 1959 1247.00
97 4 1960 2393.00
98 4 1961 1317.00
99 4 1962 909.00
100 4 1963 1808.00
101 4 1964 1020.00
102 4 1965 1181.00
103 4 1966 1365.00
104 4 1967 1218.00
105 4 1968 1644.00
106 4 1969 1160.00
107 4 1970 1002.00
108 4 1971 1243.00
109 4 1972 1332.00
110 4 1973 1033.00
111 4 1974 1170.00
112 4 1975 1685.00
113 4 1976 1478.00
114 4 1977 2434.00
115 4 1978 1600.00
116 4 1979 1369.00
117 4 1980 1215.00
118 4 1981 1614.00
119 4 1982 1449.00
120 4 1983 1518.00
121 4 1984 1490.00
122 4 1985 1191.00
123 7 1955 1481.00
124 7 1956 1758.00
125 7 1957 1774.00
126 7 1958 1625.00
127 7 1959 1607.00
128 7 1960 2826.00
129 7 1961 1488.00
130 7 1962 928.00
131 7 1963 2379.00
132 7 1964 1173.00
133 7 1965 1801.00
134 7 1966 1824.00
135 7 1967 1309.00
136 7 1968 2220.00
137 7 1969 1733.00
138 8 1933 1086.00
139 8 1934 1810.00
140 8 1935 2244.00
141 8 1936 2138.00
142 8 1937 2028.00
143 8 1938 1308.00
144 8 1939 1947.00
145 8 1940 1528.00
146 8 1941 2244.00
147 8 1942 1594.00
148 8 1943 861.00
149 8 1944 1378.00
150 8 1946 1795.00
151 8 1947 1344.00
152 8 1948 1558.00
153 8 1949 696.00
154 8 1950 724.00
155 8 1951 2497.00
156 8 1952 660.00
157 8 1953 1388.00
158 8 1954 1484.00
159 8 1955 952.00
160 8 1956 1987.00
161 8 1957 2646.00
162 8 1958 1689.00
163 8 1959 1443.00
164 8 1960 2688.00
165 8 1961 1249.00
166 8 1962 1145.00
167 8 1963 2392.00
168 8 1964 1001.00
169 8 1965 1380.00
170 9 1937 2075.00
171 9 1938 1607.00
172 9 1939 1717.00
173 9 1940 1261.00
174 9 1941 1824.00
175 9 1942 1330.00
176 9 1943 963.00
177 9 1944 1313.00
178 9 1951 2276.00
179 9 1952 682.00
180 9 1953 1440.00
181 9 1954 1304.00
182 9 1955 1193.00
183 10 1925 1096.00
184 10 1926 1387.00
185 10 1927 1289.00
186 10 1928 1461.00
187 10 1929 1054.00
188 10 1930 1474.00
189 10 1931 1137.00
190 10 1932 1256.00
191 10 1933 981.00
192 10 1934 1696.00
193 10 1935 1468.00
194 10 1936 1850.00
195 10 1937 1644.00
196 10 1938 1248.00
197 10 1939 1498.00
198 10 1940 1317.00
199 10 1941 1500.00
200 10 1942 1109.00
201 10 1943 859.00
202 10 1944 931.00
203 10 1945 1020.00
204 10 1946 1493.00
205 10 1947 954.00
206 10 1948 1133.00
207 10 1949 1144.00
208 10 1950 1056.00
209 11 1927 1320.00
210 11 1928 1706.00
211 11 1929 948.00
212 11 1930 1643.00
213 11 1931 944.00
214 11 1932 1402.00
215 11 1933 1202.00
216 11 1934 1788.00
217 11 1935 1665.00
218 11 1936 1833.00
219 11 1937 1679.00
220 11 1938 1166.00
221 11 1939 1833.00
222 11 1940 1661.00
223 11 1941 1938.00
224 11 1942 1457.00
225 11 1943 830.00
226 11 1944 1221.00
227 11 1945 1398.00
228 11 1946 1674.00
229 11 1947 1311.00
230 11 1948 1611.00
231 11 1949 1003.00
232 11 1950 1021.00
233 12 1925 890.00
234 12 1926 1247.00
235 12 1927 1040.00
236 12 1928 1047.00
237 12 1929 875.00
238 12 1930 1060.00
239 12 1931 913.00
240 12 1932 968.00
241 12 1933 749.00
242 12 1934 1218.00
243 12 1935 1104.00
244 12 1936 1489.00
245 12 1937 1300.00
246 12 1938 833.00
247 12 1939 994.00
248 12 1940 1002.00
249 12 1941 1134.00
250 12 1942 854.00
251 12 1943 826.00
252 12 1944 695.00
253 12 1945 939.00
254 12 1946 1230.00
255 12 1947 830.00
256 12 1948 1096.00
257 12 1949 876.00
258 12 1950 704.00
259 12 1951 1111.00
260 12 1952 780.00
261 12 1953 791.00
262 12 1954 709.00
263 12 1955 812.00
264 12 1956 686.00
265 12 1957 812.00
266 12 1958 755.00
267 12 1959 802.00
268 12 1960 1098.00
269 12 1961 868.00
270 12 1962 735.00
271 12 1963 829.00
272 12 1964 750.00
273 12 1965 635.00
274 12 1966 887.00
275 12 1967 711.00
276 12 1968 753.00
277 12 1969 935.00
278 12 1970 862.00
279 12 1971 830.00
280 12 1972 924.00
281 12 1973 735.00
282 12 1974 766.00
283 12 1975 930.00
284 12 1976 783.00
285 12 1977 1623.00
286 12 1978 1359.00
287 12 1979 1015.00
288 12 1980 922.00
289 12 1981 963.00
290 12 1982 848.00
291 12 1983 975.00
292 12 1984 760.00
293 12 1985 766.00
294 13 1928 1288.00
295 13 1929 854.00
296 13 1930 1324.00
297 13 1931 741.00
298 13 1932 1043.00
299 13 1933 756.00
300 13 1934 1477.00
301 13 1935 1160.00
302 13 1936 1426.00
303 13 1937 1360.00
304 13 1938 1109.00
305 13 1939 1211.00
306 13 1940 1094.00
307 13 1941 1666.00
308 13 1942 1002.00
309 13 1943 772.00
310 13 1948 1124.00
311 13 1949 997.00
312 13 1950 649.00
313 13 1951 1436.00
314 13 1952 762.00
315 13 1953 1293.00
316 13 1954 930.00
317 13 1955 721.00
318 13 1956 838.00
319 13 1957 1063.00
320 13 1958 710.00
321 13 1959 1002.00
322 13 1960 1625.00
323 13 1961 1002.00
324 13 1962 848.00
325 13 1963 1104.00
326 13 1964 869.00
327 13 1965 823.00
328 13 1966 992.00
329 13 1967 588.00
330 13 1968 894.00
331 13 1969 1073.00
332 13 1970 675.00
333 13 1971 1181.00
334 13 1972 1568.00
335 13 1973 817.00
336 13 1974 1068.00
337 13 1975 978.00
338 14 1930 1505.00
339 14 1931 928.00
340 14 1932 1223.00
341 14 1933 805.00
342 14 1934 1449.00
343 14 1935 1084.00
344 14 1936 1588.00
345 14 1937 1509.00
346 14 1938 1137.00
347 14 1939 1014.00
348 14 1940 1181.00
349 14 1941 1394.00
350 14 1942 922.00
351 14 1943 811.00
352 14 1946 1428.00
353 14 1947 1137.00
354 14 1948 1240.00
355 14 1949 1034.00
356 14 1950 581.00
357 14 1951 1501.00
358 14 1952 700.00
359 14 1953 1263.00
360 14 1954 962.00
361 14 1955 780.00
362 14 1956 919.00
363 14 1957 1068.00
364 14 1958 855.00
365 14 1959 1198.00
366 14 1960 1569.00
367 14 1961 1134.00
368 14 1962 1007.00
369 14 1963 1205.00
370 14 1964 973.00
371 14 1965 871.00
372 14 1966 1188.00
373 14 1967 581.00
374 14 1968 1027.00
375 14 1969 1192.00
376 14 1970 578.00
377 14 1971 875.00
378 14 1972 1553.00
379 14 1973 774.00
380 14 1975 958.00
381 14 1976 1187.00
382 14 1977 2152.00
383 14 1978 836.00
384 14 1979 834.00
385 14 1980 753.00
386 14 1981 1110.00
387 15 1961 969.00
388 15 1962 811.00
389 15 1963 1107.00
390 15 1964 769.00
391 15 1965 567.00
392 15 1966 925.00
393 15 1967 508.00
394 15 1968 598.00
395 15 1969 818.00
396 15 1970 495.00
397 16 1937 957.00
398 16 1938 625.00
399 16 1939 625.00
400 16 1940 658.00
401 16 1941 1022.00
402 16 1942 555.00
403 16 1943 496.00
404 16 1944 625.00
405 16 1945 593.00
406 16 1946 1115.00
407 16 1947 718.00
408 16 1948 957.00
409 16 1949 707.00
410 16 1950 332.00
411 16 1951 821.00
412 16 1952 469.00
413 16 1953 913.00
414 16 1954 663.00
415 16 1955 418.00
416 16 1956 523.00
417 16 1957 799.00
418 16 1958 469.00
419 16 1959 1000.00
420 16 1960 1104.00
421 16 1961 761.00
422 16 1962 598.00
423 16 1963 1033.00
424 16 1964 707.00
425 16 1965 469.00
426 16 1966 614.00
427 16 1967 270.00
428 16 1968 609.00
429 16 1969 1017.00
430 16 1970 367.00
431 17 1927 595.00
432 17 1928 718.00
433 17 1929 518.00
434 17 1930 548.00
435 17 1931 389.00
436 17 1932 567.00
437 17 1933 506.00
438 17 1934 985.00
439 17 1935 530.00
440 17 1936 1097.00
441 17 1937 934.00
442 17 1938 675.00
443 17 1939 614.00
444 17 1940 587.00
445 17 1941 722.00
446 17 1942 499.00
447 17 1943 459.00
448 17 1946 1087.00
449 17 1947 550.00
450 17 1948 860.00
451 17 1949 648.00
452 17 1950 296.00
453 17 1951 658.00
454 18 1927 686.00
455 18 1928 863.00
456 18 1929 488.00
457 18 1930 937.00
458 18 1931 453.00
459 18 1932 621.00
460 18 1933 484.00
461 18 1934 851.00
462 18 1935 599.00
463 18 1936 1161.00
464 18 1937 894.00
465 18 1938 598.00
466 18 1939 645.00
467 18 1940 606.00
468 18 1941 772.00
469 18 1942 449.00
470 18 1943 486.00
471 18 1944 510.00
472 18 1945 559.00
473 18 1946 829.00
474 18 1947 545.00
475 18 1948 898.00
476 18 1949 529.00
477 18 1950 392.00
478 18 1951 856.00
479 18 1952 625.00
480 18 1953 773.00
481 18 1954 651.00
482 18 1955 674.00
483 18 1956 432.00
484 19 1927 589.00
485 19 1928 715.00
486 19 1929 479.00
487 19 1930 696.00
488 19 1931 394.00
489 19 1932 533.00
490 19 1933 430.00
491 19 1934 845.00
492 19 1935 519.00
493 19 1936 1012.00
494 19 1937 805.00
495 19 1938 559.00
496 19 1939 569.00
497 19 1940 580.00
498 19 1941 725.00
499 19 1942 448.00
500 19 1943 412.00
501 19 1944 411.00
502 19 1945 407.00
503 19 1946 638.00
504 19 1947 506.00
505 19 1948 729.00
506 19 1949 538.00
507 19 1950 350.00
508 19 1951 736.00
509 19 1952 513.00
510 19 1953 787.00
511 20 1935 1237.00
512 20 1936 1908.00
513 20 1937 1263.00
514 20 1938 1066.00
515 20 1939 1401.00
516 20 1940 1263.00
517 20 1941 1134.00
518 20 1942 799.00
519 20 1943 919.00
520 20 1944 971.00
521 20 1945 1057.00
522 20 1946 1710.00
523 20 1947 1555.00
524 20 1948 1667.00
525 20 1949 1212.00
526 20 1950 799.00
527 20 1951 1366.00
528 20 1952 962.00
529 20 1953 1779.00
530 20 1954 1504.00
531 20 1955 808.00
532 20 1956 1031.00
533 20 1957 1186.00
534 20 1958 1031.00
535 20 1959 1796.00
536 20 1960 1882.00
537 20 1961 1487.00
538 20 1962 945.00
539 20 1963 1710.00
540 20 1964 1194.00
541 20 1965 919.00
542 20 1966 1418.00
543 20 1967 722.00
544 20 1968 1160.00
545 20 1969 1409.00
546 20 1970 894.00
547 20 1971 1279.00
548 20 1972 1884.00
549 20 1973 1307.00
550 21 1927 489.00
551 21 1928 704.00
552 21 1929 310.00
553 21 1930 665.00
554 21 1931 259.00
555 21 1932 501.00
556 21 1933 428.00
557 21 1934 820.00
558 21 1935 551.00
559 21 1936 994.00
560 21 1937 658.00
561 21 1938 425.00
562 21 1939 423.00
563 21 1940 409.00
564 21 1941 736.00
565 21 1942 440.00
566 21 1943 401.00
567 21 1944 398.00
568 21 1945 342.00
569 21 1946 658.00
570 21 1947 449.00
571 21 1948 665.00
572 21 1949 535.00
573 21 1950 247.00
574 21 1951 584.00
575 21 1952 338.00
576 21 1953 580.00
577 21 1954 569.00
578 21 1955 311.00
579 21 1956 412.00
580 21 1957 565.00
581 21 1958 403.00
582 21 1959 846.00
583 21 1960 917.00
584 21 1961 525.00
585 21 1962 411.00
586 21 1963 717.00
587 21 1964 526.00
588 21 1965 248.00
589 21 1966 451.00
590 21 1967 185.00
591 21 1968 356.00
592 21 1969 564.00
593 21 1970 256.00
594 22 1934 1197.00
595 22 1935 863.00
596 22 1936 1382.00
597 22 1937 1104.00
598 22 1938 649.00
599 22 1939 745.00
600 22 1940 615.00
601 22 1941 1116.00
602 22 1942 618.00
603 22 1943 739.00
604 22 1944 761.00
605 22 1945 720.00
606 22 1946 1147.00
607 22 1947 838.00
608 22 1948 1057.00
609 22 1949 739.00
610 22 1950 529.00
611 22 1951 962.00
612 22 1952 470.00
613 22 1953 881.00
614 22 1954 495.00
615 22 1955 417.00
616 22 1956 553.00
617 22 1957 819.00
618 22 1958 711.00
619 22 1959 1410.00
620 22 1960 1472.00
621 22 1961 727.00
622 22 1962 671.00
623 22 1963 1163.00
624 22 1964 751.00
625 22 1965 476.00
626 22 1966 819.00
627 22 1967 399.00
628 22 1968 612.00
629 22 1969 860.00
630 22 1970 507.00
631 22 1971 844.00
632 22 1972 1245.00
633 22 1973 953.00
634 22 1975 976.00
635 23 1933 835.00
636 23 1934 1345.00
637 23 1935 1085.00
638 23 1936 1655.00
639 23 1937 1291.00
640 23 1938 838.00
641 23 1939 974.00
642 23 1940 862.00
643 23 1941 1106.00
644 23 1942 699.00
645 23 1943 854.00
646 23 1944 721.00
647 23 1945 699.00
648 23 1946 1033.00
649 23 1947 892.00
650 23 1948 1213.00
651 23 1949 631.00
652 23 1950 554.00
653 23 1951 833.00
654 23 1952 911.00
655 23 1953 796.00
656 23 1954 721.00
657 23 1955 727.00
658 24 1934 1795.00
659 24 1935 1761.00
660 24 1936 1962.00
661 24 1937 1541.00
662 24 1938 1007.00
663 24 1939 1276.00
664 24 1940 1144.00
665 24 1941 1302.00
666 24 1942 947.00
667 24 1943 1210.00
668 24 1947 1113.00
669 24 1948 1532.00
670 24 1949 764.00
671 24 1950 849.00
672 24 1951 1412.00
673 24 1952 1105.00
674 24 1953 1048.00
675 24 1954 843.00
676 24 1955 1048.00
677 24 1956 1157.00
678 25 1941 1498.00
679 25 1942 880.00
680 25 1943 1028.00
681 25 1944 1046.00
682 25 1945 589.00
683 25 1946 1088.00
684 25 1947 1179.00
685 25 1948 1471.00
686 25 1949 761.00
687 25 1950 1106.00
688 25 1951 2017.00
689 25 1952 649.00
690 25 1953 1129.00
691 25 1954 1149.00
692 25 1955 1355.00
693 25 1956 1107.00
694 26 1934 1634.00
695 26 1935 1300.00
696 26 1936 1715.00
697 26 1937 1643.00
698 26 1938 1295.00
699 26 1939 1459.00
700 26 1940 1020.00
701 26 1941 1531.00
702 26 1942 919.00
703 26 1943 1095.00
704 26 1944 876.00
705 26 1945 857.00
706 26 1946 1534.00
707 26 1947 1183.00
708 26 1948 1405.00
709 26 1949 1051.00
710 26 1950 1159.00
711 26 1951 1478.00
712 26 1952 1472.00
713 26 1953 1364.00
714 26 1954 1140.00
715 26 1955 1126.00
716 26 1956 1007.00
717 27 1935 1157.00
718 27 1936 1759.00
719 27 1937 1245.00
720 27 1938 842.00
721 27 1939 1056.00
722 27 1940 800.00
723 27 1941 1244.00
724 27 1942 806.00
725 27 1943 925.00
726 27 1944 839.00
727 27 1958 782.00
728 27 1959 1236.00
729 27 1960 1601.00
730 27 1961 886.00
731 27 1962 768.00
732 27 1963 1109.00
733 27 1964 722.00
734 27 1965 440.00
735 28 1952 1121.00
736 28 1953 1488.00
737 28 1954 1158.00
738 28 1955 1287.00
739 28 1956 1210.00
740 28 1958 1468.00
741 28 1961 1445.00
742 28 1962 1304.00
743 28 1963 1967.00
744 28 1964 1408.00
745 29 1952 1121.00
746 29 1953 1482.00
747 29 1954 1163.00
748 29 1955 1378.00
749 29 1956 1201.00
750 29 1957 1677.00
751 29 1958 1360.00
752 29 1959 2230.00
753 29 1961 1117.00
754 29 1962 1093.00
755 29 1963 1647.00
756 29 1964 1358.00
757 30 1923 395.00
758 30 1924 342.00
759 30 1925 463.00
760 30 1926 649.00
761 30 1927 400.00
762 30 1928 703.00
763 30 1929 388.00
764 30 1930 570.00
765 30 1931 292.00
766 30 1932 490.00
767 30 1933 440.00
768 30 1934 885.00
769 30 1935 671.00
770 30 1936 1035.00
771 30 1937 729.00
772 30 1938 360.00
773 30 1939 467.00
774 30 1940 351.00
775 30 1941 765.00
776 30 1942 418.00
777 30 1943 455.00
778 30 1944 339.00
779 30 1945 311.00
780 30 1946 493.00
781 30 1947 432.00
782 30 1948 686.00
783 30 1949 353.00
784 30 1950 337.00
785 30 1953 449.00
786 30 1954 513.00
787 30 1955 374.00
788 30 1956 475.00
789 30 1957 628.00
790 30 1958 496.00
791 30 1959 844.00
792 30 1960 974.00
793 30 1961 375.00
794 30 1962 419.00
795 30 1963 651.00
796 30 1964 441.00
797 30 1965 226.00
798 30 1966 438.00
799 30 1967 218.00
800 30 1968 461.00
801 30 1969 504.00
802 30 1970 309.00
803 30 1971 543.00
804 30 1972 870.00
805 30 1973 433.00
806 30 1974 724.00
807 30 1975 604.00
808 30 1976 712.00
809 30 1977 865.00
810 30 1980 395.00
811 30 1981 324.00
812 30 1982 436.00
813 30 1984 607.00
814 30 1985 399.00
815 31 1931 754.00
816 31 1932 1025.00
817 31 1933 829.00
818 31 1934 1428.00
819 31 1936 1828.00
820 31 1937 1472.00
821 31 1938 771.00
822 31 1939 1144.00
823 31 1940 980.00
824 31 1941 1728.00
825 31 1942 720.00
826 31 1943 850.00
827 31 1946 995.00
828 31 1947 901.00
829 31 1948 1138.00
830 31 1949 678.00
831 31 1950 805.00
832 31 1951 1509.00
833 31 1952 616.00
834 31 1953 629.00
835 31 1954 716.00
836 31 1955 848.00
837 31 1956 767.00
838 31 1957 720.00
839 31 1958 1426.00
840 31 1959 1370.00
841 31 1960 1826.00
842 31 1962 1046.00
843 31 1963 1172.00
844 31 1964 869.00
845 31 1965 793.00
846 31 1966 1008.00
847 31 1967 571.00
848 31 1968 1161.00
849 32 1933 920.00
850 32 1934 1674.00
851 32 1935 1153.00
852 32 1936 1512.00
853 32 1937 1226.00
854 32 1938 647.00
855 32 1939 945.00
856 32 1940 822.00
857 32 1941 1665.00
858 32 1942 632.00
859 32 1943 746.00
860 32 1944 705.00
861 32 1947 759.00
862 32 1948 932.00
863 32 1949 617.00
864 32 1950 632.00
865 32 1951 1259.00
866 32 1952 506.00
867 32 1953 590.00
868 32 1954 743.00
869 32 1955 598.00
870 32 1956 747.00
871 32 1957 988.00
872 32 1958 855.00
873 32 1959 1229.00
874 32 1960 1461.00
875 32 1961 458.00
876 32 1962 804.00
877 32 1963 867.00
878 32 1964 652.00
879 32 1965 580.00
880 33 1942 684.00
881 33 1944 701.00
882 33 1945 486.00
883 33 1946 792.00
884 33 1947 727.00
885 33 1948 1086.00
886 33 1949 564.00
887 33 1950 624.00
888 33 1951 1205.00
889 33 1952 463.00
890 33 1953 846.00
891 33 1954 894.00
892 33 1955 707.00
893 33 1956 733.00
894 33 1957 892.00
895 33 1958 869.00
896 33 1959 1283.00
897 33 1960 1444.00
898 33 1961 474.00
899 33 1962 798.00
900 33 1963 935.00
901 33 1964 719.00
902 33 1965 445.00
903 33 1966 749.00
904 33 1967 428.00
905 33 1968 772.00
906 33 1969 854.00
907 33 1970 545.00
908 33 1976 1002.00
909 33 1977 939.00
910 33 1980 643.00
911 33 1981 603.00
912 33 1982 785.00
913 33 1983 775.00
914 33 1984 1025.00
915 33 1985 584.00
916 34 1931 636.00
917 34 1932 998.00
918 34 1933 1014.00
919 34 1934 1965.00
920 34 1935 1333.00
921 34 1936 1730.00
922 34 1937 1330.00
923 34 1938 825.00
924 34 1939 1112.00
925 34 1940 851.00
926 34 1941 1423.00
927 34 1942 960.00
928 34 1943 1031.00
929 34 1944 976.00
930 34 1945 561.00
931 34 1946 1055.00
932 34 1947 1076.00
933 34 1948 1224.00
934 34 1949 658.00
935 34 1950 707.00
936 34 1951 1453.00
937 34 1952 445.00
938 34 1953 966.00
939 34 1954 930.00
940 34 1955 939.00
941 34 1956 862.00
942 34 1957 1115.00
943 34 1958 1158.00
944 34 1959 1573.00
945 35 1931 845.00
946 35 1932 803.00
947 35 1933 746.00
948 35 1934 1036.00
949 35 1935 1160.00
950 35 1936 1038.00
951 35 1937 1285.00
952 35 1938 369.00
953 35 1939 1093.00
954 35 1940 732.00
955 35 1941 613.00
956 35 1942 620.00
957 35 1943 863.00
958 35 1952 579.00
959 35 1953 765.00
960 35 1954 819.00
961 35 1955 505.00
962 35 1956 594.00
963 35 1957 667.00
964 35 1958 651.00
965 35 1959 950.00
966 35 1960 1583.00
967 35 1961 688.00
968 35 1962 622.00
969 35 1963 1068.00
970 36 1935 924.00
971 36 1936 1676.00
972 36 1937 1765.00
973 36 1938 841.00
974 36 1939 796.00
975 36 1940 745.00
976 36 1941 1363.00
977 36 1942 663.00
978 36 1943 714.00
979 36 1944 382.00
980 36 1945 771.00
981 36 1946 796.00
982 36 1947 956.00
983 36 1948 1153.00
984 36 1949 669.00
985 36 1950 796.00
986 36 1951 1879.00
987 36 1952 643.00
988 36 1953 796.00
989 36 1954 994.00
990 36 1955 733.00
991 36 1956 1185.00
992 37 1945 597.00
993 37 1946 833.00
994 37 1947 902.00
995 37 1948 1207.00
996 37 1949 793.00
997 37 1950 598.00
998 37 1951 1328.00
999 37 1952 323.00
1000 37 1953 561.00
1001 37 1954 726.00
1002 37 1955 663.00
1003 37 1956 919.00
1004 37 1957 1139.00
1005 37 1958 1040.00
1006 37 1959 1264.00
1007 37 1960 1214.00
1008 38 1947 492.00
1009 38 1948 608.00
1010 38 1949 368.00
1011 38 1950 393.00
1012 38 1951 1123.00
1013 38 1952 172.00
1014 38 1953 281.00
1015 38 1954 539.00
1016 38 1955 424.00
1017 38 1956 585.00
1018 38 1957 632.00
1019 38 1958 528.00
1020 39 1938 339.00
1021 39 1939 929.00
1022 39 1940 560.00
1023 39 1941 727.00
1024 39 1942 490.00
1025 39 1943 684.00
1026 39 1950 979.00
1027 39 1951 1466.00
1028 39 1952 404.00
1029 39 1953 865.00
1030 39 1954 533.00
1031 39 1955 462.00
1032 39 1956 287.00
1033 39 1957 767.00
1034 39 1958 653.00
1035 39 1959 1176.00
1036 39 1960 1906.00
1037 39 1961 883.00
1038 40 1956 755.00
1039 40 1957 871.00
1040 40 1958 938.00
1041 40 1959 1175.00
1042 40 1960 1218.00
1043 40 1961 621.00
1044 40 1962 432.25
1045 40 1963 913.20
1046 40 1964 840.15
1047 40 1965 827.97
1048 40 1966 919.29
1049 40 1967 724.48
1050 40 1968 602.72
1051 41 1951 1449.00
1052 41 1952 1449.00
1053 41 1953 1546.00
1054 41 1954 1516.00
1055 41 1955 1254.00
1056 41 1956 1382.00
1057 42 1944 895.00
1058 42 1945 1006.00
1059 42 1946 1351.00
1060 42 1947 1215.00
1061 42 1950 1215.00
1062 42 1951 1279.00
1063 42 1952 1006.00
1064 42 1953 1156.00
1065 42 1954 821.00
1066 43 1935 948.00
1067 43 1936 1308.00
1068 43 1937 1185.00
1069 43 1938 801.00
1070 43 1939 848.00
1071 43 1940 926.00
1072 43 1941 932.00
1073 43 1942 755.00
1074 43 1943 764.00
1075 43 1948 891.00
1076 43 1949 677.00
1077 43 1950 835.00
1078 43 1951 1112.00
1079 43 1952 918.00
1080 43 1953 742.00
1081 43 1954 685.00
1082 43 1955 927.00
1083 44 1926 1607.00
1084 44 1927 1275.00
1085 44 1928 1613.00
1086 44 1929 1484.00
1087 44 1930 1487.00
1088 44 1931 1205.00
1089 44 1932 1367.00
1090 44 1933 1158.00
1091 44 1934 1583.00
1092 44 1935 1342.00
1093 44 1936 1848.00
1094 44 1937 1640.00
1095 44 1938 1225.00
1096 44 1939 1320.00
1097 44 1940 1202.00
1098 44 1941 1476.00
1099 44 1942 1190.00
1100 44 1948 1435.00
1101 44 1949 894.00
1102 44 1950 1326.00
1103 44 1951 1230.00
1104 44 1952 1042.00
1105 44 1953 1127.00
1106 45 1931 1953.00
1107 45 1932 1939.00
1108 45 1933 1677.00
1109 45 1934 1692.00
1110 45 1935 2051.00
1111 45 1936 2371.00
1112 45 1937 2022.00
1113 45 1938 1521.00
1114 45 1939 1448.00
1115 45 1940 1825.00
1116 45 1941 1363.00
1117 45 1942 1760.00
1118 45 1943 1672.00
1119 45 1949 1603.00
1120 45 1950 1244.00
1121 45 1951 1521.00
1122 45 1952 1783.00
1123 45 1953 1560.00
1124 45 1954 1357.00
1125 45 1955 1673.00
1126 45 1956 1625.00
1127 45 1957 1425.00
1128 45 1958 1688.00
1129 45 1959 1577.00
1130 45 1960 1736.00
1131 45 1961 1640.00
1132 45 1962 1584.00
1133 45 1964 1293.00
1134 45 1965 1277.00
1135 45 1966 1742.00
1136 45 1967 1491.00
1137 46 1952 1223.00
1138 46 1953 1077.00
1139 46 1954 671.00
1140 46 1955 1063.00
1141 46 1956 969.00
1142 46 1957 842.00
1143 46 1958 1037.00
1144 46 1959 903.00
1145 46 1960 1407.00
1146 46 1961 1153.00
1147 46 1962 1107.00
1148 46 1963 1293.00
1149 46 1964 813.00
1150 46 1965 834.00
1151 46 1966 1118.00
1152 46 1967 901.00
1153 46 1968 981.00
1154 47 1949 986.00
1155 47 1950 996.00
1156 47 1951 1335.00
1157 47 1952 964.00
1158 47 1953 1018.00
1159 47 1954 821.00
1160 47 1955 945.00
1161 47 1956 844.00
1162 47 1957 1133.00
1163 47 1958 975.00
1164 47 1959 1082.00
1165 47 1960 1252.00
1166 47 1961 1031.00
1167 47 1962 940.00
1168 47 1963 1078.00
1169 47 1964 933.00
1170 47 1965 709.00
1171 47 1966 923.00
1172 47 1967 899.00
1173 47 1968 747.00
1174 47 1969 1010.00
1175 47 1970 873.00
1176 47 1971 962.00
1177 47 1972 965.00
1178 47 1973 674.00
1179 47 1974 763.00
1180 47 1975 915.00
1181 47 1976 1029.00
1182 47 1977 1452.00
1183 47 1978 1486.00
1184 48 1950 872.00
1185 48 1951 1528.00
1186 48 1952 1062.00
1187 48 1953 1345.00
1188 48 1954 1158.00
1189 48 1955 998.00
1190 48 1956 1197.00
1191 48 1957 1234.00
1192 48 1958 1469.00
1193 48 1959 1343.00
1194 48 1960 2103.00
1195 48 1961 1745.00
1196 48 1962 1084.00
1197 48 1963 1717.00
1198 48 1964 1131.00
1199 48 1965 990.00
1200 48 1966 1186.00
1201 48 1967 884.00
1202 48 1968 1118.00
1203 48 1969 1383.00
1204 48 1970 877.00
1205 48 1971 1072.00
1206 48 1972 1906.00
1207 48 1973 830.00
1208 49 1944 808.00
1209 49 1945 1088.00
1210 49 1946 1435.00
1211 49 1947 1265.00
1212 49 1948 1065.00
1213 49 1949 911.00
1214 49 1950 992.00
1215 49 1951 1273.00
1216 49 1952 1031.00
1217 49 1953 1100.00
1218 49 1954 769.00
1219 49 1955 865.00
1220 49 1956 781.00
1221 49 1959 1019.00
1222 49 1960 1761.00
cod anno dato
Min. : 1.0 Min. :1921 Min. : 172.0
1st Qu.:13.0 1st Qu.:1940 1st Qu.: 725.2
Median :22.0 Median :1951 Median : 981.0
Mean :23.7 Mean :1951 Mean :1041.4
3rd Qu.:34.0 3rd Qu.:1960 3rd Qu.:1308.8
Max. :49.0 Max. :1985 Max. :3045.0
$`1`
[1] 1494 1309 1699 1467 1918 1469 1267 1523 1338 1438 1788 1591 1697 1780 1769
$`2`
[1] 1144 1652 1807 1881 1741 1124 2064 1434 1678 1239 921 983 1093 1744 1213
[16] 1590 956 1124 2181 1077 1345 1219 988 1325 1277 1479 1307 2053 1232 973
[31] 1407 912
$`3`
[1] 2596 954 1115 1248 867 1280 1588 1055 1764 3045
$`4`
[1] 871 1238 1505 1636 1553 1936 1739 1867 1184 1630 1311 1520 1201 1614 1971
[16] 1829 1781 1093 1996 1328 1662 1199 860 961 949 1536 1016 1386 820 1023
[31] 2329 1209 1305 1334 1024 1364 1310 1410 1247 2393 1317 909 1808 1020 1181
[46] 1365 1218 1644 1160 1002 1243 1332 1033 1170 1685 1478 2434 1600 1369 1215
[61] 1614 1449 1518 1490 1191
$`7`
[1] 1481 1758 1774 1625 1607 2826 1488 928 2379 1173 1801 1824 1309 2220 1733
$`8`
[1] 1086 1810 2244 2138 2028 1308 1947 1528 2244 1594 861 1378 1795 1344 1558
[16] 696 724 2497 660 1388 1484 952 1987 2646 1689 1443 2688 1249 1145 2392
[31] 1001 1380
$`9`
[1] 2075 1607 1717 1261 1824 1330 963 1313 2276 682 1440 1304 1193
$`10`
[1] 1096 1387 1289 1461 1054 1474 1137 1256 981 1696 1468 1850 1644 1248 1498
[16] 1317 1500 1109 859 931 1020 1493 954 1133 1144 1056
$`11`
[1] 1320 1706 948 1643 944 1402 1202 1788 1665 1833 1679 1166 1833 1661 1938
[16] 1457 830 1221 1398 1674 1311 1611 1003 1021
$`12`
[1] 890 1247 1040 1047 875 1060 913 968 749 1218 1104 1489 1300 833 994
[16] 1002 1134 854 826 695 939 1230 830 1096 876 704 1111 780 791 709
[31] 812 686 812 755 802 1098 868 735 829 750 635 887 711 753 935
[46] 862 830 924 735 766 930 783 1623 1359 1015 922 963 848 975 760
[61] 766
$`13`
[1] 1288 854 1324 741 1043 756 1477 1160 1426 1360 1109 1211 1094 1666 1002
[16] 772 1124 997 649 1436 762 1293 930 721 838 1063 710 1002 1625 1002
[31] 848 1104 869 823 992 588 894 1073 675 1181 1568 817 1068 978
$`14`
[1] 1505 928 1223 805 1449 1084 1588 1509 1137 1014 1181 1394 922 811 1428
[16] 1137 1240 1034 581 1501 700 1263 962 780 919 1068 855 1198 1569 1134
[31] 1007 1205 973 871 1188 581 1027 1192 578 875 1553 774 958 1187 2152
[46] 836 834 753 1110
$`15`
[1] 969 811 1107 769 567 925 508 598 818 495
$`16`
[1] 957 625 625 658 1022 555 496 625 593 1115 718 957 707 332 821
[16] 469 913 663 418 523 799 469 1000 1104 761 598 1033 707 469 614
[31] 270 609 1017 367
$`17`
[1] 595 718 518 548 389 567 506 985 530 1097 934 675 614 587 722
[16] 499 459 1087 550 860 648 296 658
$`18`
[1] 686 863 488 937 453 621 484 851 599 1161 894 598 645 606 772
[16] 449 486 510 559 829 545 898 529 392 856 625 773 651 674 432
$`19`
[1] 589 715 479 696 394 533 430 845 519 1012 805 559 569 580 725
[16] 448 412 411 407 638 506 729 538 350 736 513 787
$`20`
[1] 1237 1908 1263 1066 1401 1263 1134 799 919 971 1057 1710 1555 1667 1212
[16] 799 1366 962 1779 1504 808 1031 1186 1031 1796 1882 1487 945 1710 1194
[31] 919 1418 722 1160 1409 894 1279 1884 1307
$`21`
[1] 489 704 310 665 259 501 428 820 551 994 658 425 423 409 736 440 401 398 342
[20] 658 449 665 535 247 584 338 580 569 311 412 565 403 846 917 525 411 717 526
[39] 248 451 185 356 564 256
$`22`
[1] 1197 863 1382 1104 649 745 615 1116 618 739 761 720 1147 838 1057
[16] 739 529 962 470 881 495 417 553 819 711 1410 1472 727 671 1163
[31] 751 476 819 399 612 860 507 844 1245 953 976
$`23`
[1] 835 1345 1085 1655 1291 838 974 862 1106 699 854 721 699 1033 892
[16] 1213 631 554 833 911 796 721 727
$`24`
[1] 1795 1761 1962 1541 1007 1276 1144 1302 947 1210 1113 1532 764 849 1412
[16] 1105 1048 843 1048 1157
$`25`
[1] 1498 880 1028 1046 589 1088 1179 1471 761 1106 2017 649 1129 1149 1355
[16] 1107
$`26`
[1] 1634 1300 1715 1643 1295 1459 1020 1531 919 1095 876 857 1534 1183 1405
[16] 1051 1159 1478 1472 1364 1140 1126 1007
$`27`
[1] 1157 1759 1245 842 1056 800 1244 806 925 839 782 1236 1601 886 768
[16] 1109 722 440
$`28`
[1] 1121 1488 1158 1287 1210 1468 1445 1304 1967 1408
$`29`
[1] 1121 1482 1163 1378 1201 1677 1360 2230 1117 1093 1647 1358
$`30`
[1] 395 342 463 649 400 703 388 570 292 490 440 885 671 1035 729
[16] 360 467 351 765 418 455 339 311 493 432 686 353 337 449 513
[31] 374 475 628 496 844 974 375 419 651 441 226 438 218 461 504
[46] 309 543 870 433 724 604 712 865 395 324 436 607 399
$`31`
[1] 754 1025 829 1428 1828 1472 771 1144 980 1728 720 850 995 901 1138
[16] 678 805 1509 616 629 716 848 767 720 1426 1370 1826 1046 1172 869
[31] 793 1008 571 1161
$`32`
[1] 920 1674 1153 1512 1226 647 945 822 1665 632 746 705 759 932 617
[16] 632 1259 506 590 743 598 747 988 855 1229 1461 458 804 867 652
[31] 580
$`33`
[1] 684 701 486 792 727 1086 564 624 1205 463 846 894 707 733 892
[16] 869 1283 1444 474 798 935 719 445 749 428 772 854 545 1002 939
[31] 643 603 785 775 1025 584
$`34`
[1] 636 998 1014 1965 1333 1730 1330 825 1112 851 1423 960 1031 976 561
[16] 1055 1076 1224 658 707 1453 445 966 930 939 862 1115 1158 1573
$`35`
[1] 845 803 746 1036 1160 1038 1285 369 1093 732 613 620 863 579 765
[16] 819 505 594 667 651 950 1583 688 622 1068
$`36`
[1] 924 1676 1765 841 796 745 1363 663 714 382 771 796 956 1153 669
[16] 796 1879 643 796 994 733 1185
$`37`
[1] 597 833 902 1207 793 598 1328 323 561 726 663 919 1139 1040 1264
[16] 1214
$`38`
[1] 492 608 368 393 1123 172 281 539 424 585 632 528
$`39`
[1] 339 929 560 727 490 684 979 1466 404 865 533 462 287 767 653
[16] 1176 1906 883
$`40`
[1] 755.00 871.00 938.00 1175.00 1218.00 621.00 432.25 913.20 840.15
[10] 827.97 919.29 724.48 602.72
$`41`
[1] 1449 1449 1546 1516 1254 1382
$`42`
[1] 895 1006 1351 1215 1215 1279 1006 1156 821
$`43`
[1] 948 1308 1185 801 848 926 932 755 764 891 677 835 1112 918 742
[16] 685 927
$`44`
[1] 1607 1275 1613 1484 1487 1205 1367 1158 1583 1342 1848 1640 1225 1320 1202
[16] 1476 1190 1435 894 1326 1230 1042 1127
$`45`
[1] 1953 1939 1677 1692 2051 2371 2022 1521 1448 1825 1363 1760 1672 1603 1244
[16] 1521 1783 1560 1357 1673 1625 1425 1688 1577 1736 1640 1584 1293 1277 1742
[31] 1491
$`46`
[1] 1223 1077 671 1063 969 842 1037 903 1407 1153 1107 1293 813 834 1118
[16] 901 981
$`47`
[1] 986 996 1335 964 1018 821 945 844 1133 975 1082 1252 1031 940 1078
[16] 933 709 923 899 747 1010 873 962 965 674 763 915 1029 1452 1486
$`48`
[1] 872 1528 1062 1345 1158 998 1197 1234 1469 1343 2103 1745 1084 1717 1131
[16] 990 1186 884 1118 1383 877 1072 1906 830
$`49`
[1] 808 1088 1435 1265 1065 911 992 1273 1031 1100 769 865 781 1019 1761
[1] 0.008464929
[1] 0.771088
[1] 1800
$lambda1
[1] 1648.806
$lambda2
[1] 138.2366
$tau3
[1] 0.1062002
$tau4
[1] 0.1771496
[1] 1782.410 1537.389 1715.139 1525.029 1807.044 1479.856 1461.058 1369.896
[9] 1525.347 2030.263 1798.348 1961.500 1853.753 1636.320 1623.466 1305.965
[17] 1971.441 1805.895 1600.679 1792.025 1240.418 1514.373 1887.707 1230.068
[25] 2186.379 1325.040 1298.012 1683.153 2033.411 1642.351 1729.944 1452.349
[33] 1410.345 1596.252 1668.297 1612.541 1573.790 1327.747 1662.734 1715.119
[41] 1592.847 1373.163 1814.630 1844.754 1547.727 1669.339 1409.356 1571.774
[49] 1934.689 1449.815 1821.313 1656.929 1514.189 1773.396 1673.634 1569.087
[57] 1328.189 1711.022 2023.489 1677.939 1820.261 1385.479 1607.867 1504.635
[65] 1664.142 1534.777 1459.840 1316.187 1625.160 1764.433 1373.577 1394.577
[73] 1692.781 1519.356 1790.479 1495.143 1473.605 1598.239 1707.849 2064.744
[81] 1619.661 1648.040 1504.173 1804.099 1653.993 2093.817 1309.224 1168.564
[89] 1300.777 1172.756 1718.477 1724.189 1828.236 1105.595 1315.432 1976.688
[97] 1290.695 1720.025 1351.754 1422.375
l1R l2R lcvR lcaR lkurR
1041.4321277 160.1783511 0.1597701 0.1489629 0.1356834
Warning messages:
1: In fn(par, ...) : value out of range in 'gammafn'
2: In fn(par, ...) : value out of range in 'gammafn'
$lambda1
[1] 1041.432
$lambda2
[1] 160.1784
$tau3
[1] 0.148968
$tau4
[1] 0.1356809
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