Chen: The Chen distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The Chen distribution

Description

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

Usage

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 \le x] otherwise, P[X > x].

Details

The Chen distribution has density

f(x; \lambda, \beta) = \lambda \beta x^{\beta -1} \exp \left(x^{\beta} \right) \exp \left[\lambda \left\{1-\exp \left(x^{\beta} \right)\right\}\right];\; (\lambda ,\; \beta )>0,\; x > 0,

where \beta and \lambda 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.

See Also

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

Examples

## 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)

reliaR documentation built on Nov. 5, 2025, 6:57 p.m.