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

Description Usage Arguments Details Value References See Also Examples

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

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)

`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].

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.

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

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

## 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)

 [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