# Chen: The Chen distribution In reliaR: Package for some probability distributions.

## Description

Density, distribution function, quantile function and random generation for the Chen distribution with shape parameter `beta` and scale parameter `lambda`.

## Usage

 ```1 2 3 4``` ```dchen(x, beta, lambda, log = FALSE) pchen(q, beta, lambda, lower.tail = TRUE, log.p = FALSE) qchen(p, beta, lambda, lower.tail = TRUE, log.p = FALSE) rchen(n, beta, 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. `beta` 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 Chen distribution has density

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

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

## Value

`dchen` gives the density, `pchen` gives the distribution function, `qchen` gives the quantile function, and `rchen` generates random deviates.

## References

Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, 49, 155-161.

Murthy, D.N.P., Xie, M. and Jiang, R. (2004). Weibull Models, Wiley, New York.

Pham, H. (2006). System Software Reliability, Springer-Verlag.

Pham, H. and Lai, C.D. (2007). On recent generalizations of the Weibull distribution, IEEE Trans. on Reliability, Vol. 56(3), 454-458.

`.Random.seed` about random number; `schen` for Chen survival / hazard etc. functions

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## Load data sets data(sys2) ## Maximum Likelihood(ML) Estimates of beta & lambda for the data(sys2) ## beta.est = 0.262282404, lambda.est = 0.007282371 dchen(sys2, 0.262282404, 0.007282371, log = FALSE) pchen(sys2, 0.262282404, 0.007282371, lower.tail = TRUE, log.p = FALSE) qchen(0.25, 0.262282404, 0.007282371, lower.tail = TRUE, log.p = FALSE) rchen(10, 0.262282404, 0.007282371) ```

### Example output

``` [1] 0.0026484612 0.0022857138 0.0020825882 0.0018664948 0.0016889696
[6] 0.0016641566 0.0016129490 0.0015826349 0.0015777295 0.0015710929
[11] 0.0015668347 0.0015325287 0.0015238245 0.0015075501 0.0015004687
[16] 0.0014863087 0.0014854925 0.0014838667 0.0014805495 0.0014765804
[21] 0.0014743615 0.0014630467 0.0014607256 0.0014588787 0.0014566259
[26] 0.0014535527 0.0014519145 0.0014497159 0.0014464464 0.0014424352
[31] 0.0014405593 0.0014312022 0.0014248049 0.0014230818 0.0014091054
[36] 0.0013937648 0.0013907415 0.0013815726 0.0013748194 0.0013435123
[41] 0.0013434493 0.0013415662 0.0013281682 0.0012943421 0.0012876379
[46] 0.0012792670 0.0012622573 0.0012554642 0.0012407855 0.0011655393
[51] 0.0011528775 0.0011496438 0.0011227702 0.0011088516 0.0010495194
[56] 0.0010087735 0.0009915753 0.0009516765 0.0009225129 0.0009114870
[61] 0.0009018183 0.0008901159 0.0008552353 0.0008535616 0.0007979592
[66] 0.0007938078 0.0007576403 0.0007482106 0.0007197955 0.0006392962
[71] 0.0006136891 0.0005954944 0.0005023030 0.0004779438 0.0004276679
[76] 0.0003885234 0.0003588366 0.0003141478 0.0003053910 0.0002825164
[81] 0.0002398526 0.0002290163 0.0002266302 0.0002152595 0.0002061168
[86] 0.0001729893
[1] 0.02529607 0.03180080 0.03782637 0.04869207 0.06693566 0.07110941
[7] 0.08245195 0.09198593 0.09383471 0.09651113 0.09834679 0.11806958
[13] 0.12523611 0.14302386 0.15344581 0.18193031 0.18393627 0.18804882
[19] 0.19688267 0.20807528 0.21452307 0.24727608 0.25366454 0.25862788
[25] 0.26453180 0.27231657 0.27634065 0.28160713 0.28916617 0.29802069
[31] 0.30201365 0.32068110 0.33240528 0.33543828 0.35838108 0.38082009
[37] 0.38496902 0.39708436 0.40560173 0.44149235 0.44155953 0.44355986
[43] 0.45736288 0.48937674 0.49531533 0.50256691 0.51678726 0.52228851
[49] 0.53385891 0.58757055 0.59584739 0.59793117 0.61480458 0.62325136
[55] 0.65729409 0.67906165 0.68790325 0.70769581 0.72157430 0.72670033
[61] 0.73114293 0.73645601 0.75189353 0.75261977 0.77603707 0.77773230
[67] 0.79220672 0.79589604 0.80681027 0.83616795 0.84505110 0.85123586
[73] 0.88133455 0.88878360 0.90363139 0.91471010 0.92283494 0.93461760
[79] 0.93686332 0.94263164 0.95300786 0.95556287 0.95612104 0.95875869
[85] 0.96085269 0.96823494
[1] 146.8924
[1] 20.397607 19.533130  3.732811 22.461291 19.544294 20.028798  5.987082
[8] 20.310589 16.694068 22.107104
```

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