# 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

 ```1 2 3 4``` ```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

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

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```## 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.