reliaR (version 0.2)

ExpPower: The Exponential Power distribution

Description

Density, distribution function, quantile function and random generation for the Exponential Power distribution with shape parameter alpha and scale parameter lambda.

Usage

dexp.power(x, alpha, lambda, log = FALSE)
pexp.power(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qexp.power(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rexp.power(n, alpha, lambda)

Value

dexp.power gives the density,

pexp.power gives the distribution function,

qexp.power gives the quantile function, and

rexp.power generates random deviates.

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

Details

The probability density function of exponential power distribution is $$f(x; \alpha, \lambda) = \alpha \lambda^\alpha x^{\alpha - 1} e^{\left({\lambda x}\right)^\alpha} \exp\left\{{1 - e^{\left({\lambda x}\right)^\alpha}}\right\};\;(\alpha, \lambda) > 0, x > 0.$$

where \(\alpha\) and \(\lambda\) are the shape and scale parameters, respectively.

References

Chen, Z.(1999). Statistical inference about the shape parameter of the exponential power distribution, Journal :Statistical Papers, Vol. 40(4), 459-468.

Pham, H. and Lai, C.D.(2007). On Recent Generalizations of theWeibull Distribution, IEEE Trans. on Reliability, Vol. 56(3), 454-458.

Smith, R.M. and Bain, L.J.(1975). An exponential power life-test distribution, Communications in Statistics - Simulation and Computation, Vol.4(5), 469 - 481

See Also

.Random.seed about random number; sexp.power for Exponential Power distribution survival / hazard etc. functions;

Examples

## Load data sets
data(sys2)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(sys2)
## alpha.est = 0.905868898, lambda.est =  0.001531423

dexp.power(sys2, 0.905868898, 0.001531423, log = FALSE)
pexp.power(sys2, 0.905868898, 0.001531423, lower.tail = TRUE, log.p = FALSE)
qexp.power(0.25, 0.905868898, 0.001531423, lower.tail=TRUE, log.p = FALSE)
rexp.power(30, 0.905868898, 0.001531423)