ExpPower: The Exponential Power distribution

In reliaR: Package for some probability distributions.

Description

Density, distribution function, quantile function and random generation for the Exponential Power distribution with shape parameter alpha and scale parameter lambda.

Usage

dexp.power(x, alpha, lambda, log = FALSE)
pexp.power(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qexp.power(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rexp.power(n, alpha, lambda)

Arguments

x,q	vector of quantiles.
p	vector of probabilities.
n	number of observations. If length(n) > 1, the length is taken to be the number required.
alpha	shape parameter.
lambda	scale parameter.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X ≤ x] otherwise, P[X > x].

Details

The probability density function of exponential power distribution is

f(x; α, λ) = α λ^α x^{α - 1} exp{(λ x)^α} exp{1 - exp{(λ x)^α}}; (α, λ) > 0, x > 0.

where α and λ are the shape and scale parameters, respectively.

Value

dexp.power gives the density, pexp.power gives the distribution function, qexp.power gives the quantile function, and rexp.power generates random deviates.

References

Chen, Z.(1999). Statistical inference about the shape parameter of the exponential power distribution, Journal :Statistical Papers, Vol. 40(4), 459-468.

Pham, H. and Lai, C.D.(2007). On Recent Generalizations of theWeibull Distribution, IEEE Trans. on Reliability, Vol. 56(3), 454-458.

Smith, R.M. and Bain, L.J.(1975). An exponential power life-test distribution, Communications in Statistics - Simulation and Computation, Vol.4(5), 469 - 481

See Also

.Random.seed about random number; sexp.power for Exponential Power distribution survival / hazard etc. functions;

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## alpha.est = 0.905868898, lambda.est =  0.001531423

dexp.power(sys2, 0.905868898, 0.001531423, log = FALSE)
pexp.power(sys2, 0.905868898, 0.001531423, lower.tail = TRUE, log.p = FALSE)
qexp.power(0.25, 0.905868898, 0.001531423, lower.tail=TRUE, log.p = FALSE)
rexp.power(30, 0.905868898, 0.001531423)

Example output

 [1] 0.0022032323 0.0021133313 0.0020511274 0.0019685452 0.0018755689
 [6] 0.0018590474 0.0018198866 0.0017919159 0.0017869047 0.0017798576
[11] 0.0017751581 0.0017302839 0.0017160013 0.0016838819 0.0016667954
[16] 0.0016246642 0.0016218932 0.0016162776 0.0016044872 0.0015900130
[21] 0.0015818768 0.0015422551 0.0015347780 0.0015290106 0.0015221922
[26] 0.0015132620 0.0015086690 0.0015026786 0.0014941150 0.0014841242
[31] 0.0014796297 0.0014586664 0.0014455083 0.0014421015 0.0014162442
[36] 0.0013907057 0.0013859465 0.0013719699 0.0013620662 0.0013194909
[41] 0.0013194098 0.0013169916 0.0013001588 0.0012600416 0.0012524187
[46] 0.0012430278 0.0012243369 0.0012170044 0.0012013885 0.0011250947
[51] 0.0011127240 0.0011095815 0.0010837037 0.0010704505 0.0010148484
[56] 0.0009772899 0.0009615462 0.0009252041 0.0008987564 0.0008887747
[61] 0.0008800273 0.0008694456 0.0008379243 0.0008364119 0.0007861314
[66] 0.0007823720 0.0007495672 0.0007409960 0.0007151118 0.0006411965
[71] 0.0006174592 0.0006005157 0.0005125703 0.0004892190 0.0004404781
[76] 0.0004019763 0.0003724276 0.0003273379 0.0003184127 0.0002949544
[81] 0.0002506284 0.0002392483 0.0002367358 0.0002247294 0.0002150359
[86] 0.0001796214
 [1] 0.01165065 0.01738211 0.02314496 0.03426166 0.05409299 0.05874226
 [7] 0.07148475 0.08226382 0.08435742 0.08738913 0.08946880 0.11178753
[13] 0.11986869 0.13982153 0.15143095 0.18282174 0.18501316 0.18949801
[19] 0.19909570 0.21118656 0.21811708 0.25294598 0.25966927 0.26487770
[25] 0.27105637 0.27917617 0.28336154 0.28882713 0.29664874 0.30577701
[31] 0.30988180 0.32898052 0.34090212 0.34397743 0.36712994 0.38959961
[37] 0.39373683 0.40578894 0.41423712 0.44963474 0.44970071 0.45166483
[43] 0.46519558 0.49644394 0.50222261 0.50927226 0.52307728 0.52841162
[49] 0.53962093 0.59153152 0.59952056 0.60153175 0.61781710 0.62597060
[55] 0.65885726 0.67992443 0.68849410 0.70771077 0.72121720 0.72621335
[61] 0.73054691 0.73573410 0.75083566 0.75154726 0.77455402 0.77622448
[67] 0.79051709 0.79416896 0.80499487 0.83429691 0.84322044 0.84945025
[73] 0.87998010 0.88759310 0.90283837 0.91427497 0.92269449 0.93494858
[79] 0.93728934 0.94330784 0.95414778 0.95681731 0.95740038 0.96015494
[85] 0.96234034 0.97002649
[1] 143.1219
 [1] 1049.05531  107.02105  626.53563  206.66119  569.59479  634.69305
 [7]  753.90071  277.83209 1194.67752  398.25164 1549.97686 2502.07580
[13] 1626.11069  167.34917  380.71420  304.56536  233.11288  601.89964
[19]  519.28688  333.23740 1443.37391  212.94887  560.78149 1656.07049
[25]   15.83523 1373.98056   23.15305 1047.77517 1789.15752 1850.92156

reliaR documentation built on May 1, 2019, 9:51 p.m.