# KAPPA: Four parameter kappa distribution and L-moments In homtest: Homogeneity tests for Regional Frequency Analysis

## 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.

`HOMTESTS`, `rnorm`, `runif`.

## 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.