reliaR (version 0.01)

LogisExp: The Logistic-Exponential(LE) distribution

Description

Density, distribution function, quantile function and random generation for the Logistic-Exponential(LE) distribution with shape parameter alpha and scale parameter lambda.

Usage

dlogis.exp(x, alpha, lambda, log = FALSE)
plogis.exp(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qlogis.exp(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rlogis.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 $P[X \le x]$ otherwise, $P[X > x]$.

Value

dlogis.exp gives the density, plogis.exp gives the distribution function, qlogis.exp gives the quantile function, and rlogis.exp generates random deviates.

Details

The Logistic-Exponential(LE) distribution has density $$f(x) = \frac{\lambda \; \alpha \; e^{\lambda x} \left(e^{\lambda x} -1\right)^{\alpha -1} }{\left\{1+\left(e^{\lambda x} -1\right)^{\alpha } \right\}^2 };\, x\ge 0,\; \alpha >0,\; \lambda >0.$$

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

References

Lan, Y. and Leemis, L. M. (2008). The Logistic-Exponential Survival Distribution, Naval Research Logistics, 55, 252-264.

See Also

.Random.seed about random number; slogis.exp for ExpExt survival / hazard etc. functions

Examples

## Load data sets
data(bearings)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(bearings)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 2.36754, lambda.est = 0.01059
dlogis.exp(bearings, 2.36754, 0.01059, log = FALSE)
plogis.exp(bearings, 2.36754, 0.01059, lower.tail = TRUE, log.p = FALSE)
qlogis.exp(0.25, 2.36754, 0.01059, lower.tail=TRUE, log.p = FALSE)
rlogis.exp(30, 2.36754, 0.01059)