# GenExp: The Generalized Exponential (GE) distribution In reliaR: Package for some probability distributions.

## Description

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

## Usage

 ```1 2 3 4``` ```dgen.exp(x, alpha, lambda, log = FALSE) pgen.exp(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE) qgen.exp(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE) rgen.exp(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 generalized exponential distribution has density

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

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

## Value

`dgen.exp` gives the density, `pgen.exp` gives the distribution function, `qgen.exp` gives the quantile function, and `rgen.exp` generates random deviates.

## References

Gupta, R. D. and Kundu, D. (2001). Exponentiated exponential family; an alternative to gamma and Weibull distributions. Biometrical Journal, 43(1), 117 - 130.

Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41(2), 173 - 188.

`.Random.seed` about random number; `sgen.exp` for GE survival / hazard etc. functions

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Load data set data(bearings) ## Estimates of alpha & lambda using 'maxLik' package ## alpha.est = 5.28321139, lambda.est = 0.03229609 dgen.exp(bearings, 5.28321139, 0.03229609, log = FALSE) pgen.exp(bearings, 5.28321139, 0.03229609, lower.tail = TRUE, log.p = FALSE) qgen.exp(0.25, 5.28321139, 0.03229609, lower.tail = TRUE, log.p = FALSE) rgen.exp(10, 5.28321139, 0.03229609) ```

### Example output

``` [1] 0.0028085519 0.0079037993 0.0096302793 0.0121772720 0.0122952977
[6] 0.0128219891 0.0130808408 0.0131462640 0.0131455392 0.0130930394
[11] 0.0130191482 0.0114874649 0.0113424824 0.0113424824 0.0113004906
[16] 0.0084137777 0.0067868385 0.0058880089 0.0049450364 0.0048479045
[21] 0.0025569374 0.0025477360 0.0006209358
[1] 0.01286358 0.07155254 0.10741060 0.20144342 0.20878560 0.25256674
[7] 0.29406620 0.33397324 0.33555075 0.36390160 0.38270591 0.53404257
[13] 0.54363137 0.54363137 0.54634853 0.69681369 0.76508716 0.80003070
[19] 0.83506297 0.83858833 0.91801056 0.91831684 0.98062023
[1] 45.39964
[1] 56.01547 63.18654 50.72547 53.41902 55.47022 63.29746 55.77808 57.20096
[9] 34.72875 59.88666
```

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