# ExpExt: The Exponential Extension(EE) distribution In reliaR: Package for some probability distributions.

## Description

Density, distribution function, quantile function and random generation for the Exponential Extension(EE) distribution with shape parameter `alpha` and scale parameter `lambda`.

## Usage

 ```1 2 3 4``` ```dexp.ext(x, alpha, lambda, log = FALSE) pexp.ext(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE) qexp.ext(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE) rexp.ext(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 Exponential Extension(EE) distribution has density

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

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

## Value

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

## References

Nikulin, M. and Haghighi, F. (2006). A Chi-squared test for the generalized power Weibull family for the head-and-neck cancer censored data, Journal of Mathematical Sciences, Vol. 133(3), 1333-1341.

`.Random.seed` about random number; `sexp.ext` for ExpExt 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) ## Estimates of alpha & lambda using 'maxLik' package ## alpha.est = 1.0126e+01, lambda.est = 1.5848e-04 dexp.ext(sys2, 1.012556e+01, 1.5848e-04, log = FALSE) pexp.ext(sys2, 1.012556e+01, 1.5848e-04, lower.tail = TRUE, log.p = FALSE) qexp.ext(0.25, 1.012556e+01, 1.5848e-04, lower.tail=TRUE, log.p = FALSE) rexp.ext(30, 1.012556e+01, 1.5848e-04) ```

### Example output

``` [1] 0.0016034341 0.0016026915 0.0016018876 0.0016001859 0.0015966736
[6] 0.0015957622 0.0015930911 0.0015906310 0.0015901316 0.0015893959
[11] 0.0015888826 0.0015829253 0.0015805623 0.0015742454 0.0015702469
[16] 0.0015582024 0.0015572926 0.0015554022 0.0015512263 0.0015457092
[21] 0.0015424159 0.0015243792 0.0015206044 0.0015176134 0.0015139889
[26] 0.0015090983 0.0015065204 0.0015030951 0.0014980759 0.0014920416
[31] 0.0014892654 0.0014758276 0.0014669969 0.0014646626 0.0014463334
[36] 0.0014272340 0.0014235726 0.0014126447 0.0014047486 0.0013694814
[41] 0.0013694123 0.0013673491 0.0013528232 0.0013171336 0.0013101955
[46] 0.0013015846 0.0012842465 0.0012773754 0.0012626189 0.0011883935
[51] 0.0011760662 0.0011729231 0.0011468722 0.0011334196 0.0010762535
[56] 0.0010370553 0.0010205022 0.0009820466 0.0009538664 0.0009431923
[61] 0.0009338219 0.0009224668 0.0008885237 0.0008868910 0.0008324184
[66] 0.0008283320 0.0007926056 0.0007832525 0.0007549669 0.0006739418
[71] 0.0006478698 0.0006292521 0.0005326264 0.0005070053 0.0004536306
[76] 0.0004116084 0.0003794694 0.0003306636 0.0003210427 0.0002958279
[81] 0.0002485122 0.0002364447 0.0002337852 0.0002211026 0.0002108954
[86] 0.0001738793
[1] 0.007683515 0.011947669 0.016386018 0.025255819 0.041783961 0.045758549
[7] 0.056808040 0.066311524 0.068172271 0.070874871 0.072734165 0.092939296
[13] 0.100357710 0.118876994 0.129772775 0.159620597 0.161723557 0.166034646
[19] 0.175292473 0.187014524 0.193762106 0.227960689 0.234614006 0.239778990
[25] 0.245918007 0.254004818 0.258181457 0.263643925 0.271477029 0.280641817
[31] 0.284770934 0.304044766 0.316125241 0.319247462 0.342827899 0.365832098
[37] 0.370079808 0.382474283 0.391180099 0.427805344 0.427873817 0.429912705
[43] 0.443976307 0.476567048 0.482609930 0.489988254 0.504456327 0.510053491
[49] 0.521826553 0.576527479 0.584968668 0.587094504 0.604319557 0.612950533
[55] 0.647801553 0.670150870 0.679245341 0.699641979 0.713977609 0.719279897
[61] 0.723878586 0.729382490 0.745400821 0.746155372 0.770535043 0.772303742
[67] 0.787426858 0.791287705 0.802724168 0.833595451 0.842966747 0.849499082
[73] 0.881365390 0.889265909 0.905017662 0.916762986 0.925363452 0.937797547
[79] 0.940159883 0.946212464 0.957025157 0.959667822 0.960243850 0.962959071
[85] 0.965105838 0.972597073
[1] 159.5484
[1]  76.18151 533.79438 550.34297 308.21254 317.17397 417.21090 671.92179
[8] 973.64593 685.79557 443.02469 111.63522  59.56529 325.51133 456.37737
[15] 350.42036 153.00333 557.08346 216.91177 558.21764 993.05607 416.99768
[22] 326.19418 598.37114 183.01135 237.91066 891.16401 201.37094 100.89105
[29]  56.91061 152.94923
```

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