LogisRayleigh: The Logistic-Rayleigh(LR) distribution

In reliaR: Comprehensive Tools for some Probability Distributions

The Logistic-Rayleigh(LR) distribution

Description

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

Usage

dlogis.rayleigh(x, alpha, lambda, log = FALSE)
plogis.rayleigh(q, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
qlogis.rayleigh(p, alpha, lambda, lower.tail = TRUE, log.p = FALSE)
rlogis.rayleigh(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].

Details

The cummulative distribution function(cdf) of Logistic-Rayleigh(LR) is given by

F(x) = 1 - \frac{1}{1+\left(e^{(\lambda x^2 / 2)} - 1\right)^{\alpha}};\, x \ge 0, \alpha > 0, \lambda > 0.

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

Value

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

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.rayleigh for ExpExt survival / hazard etc. functions

Examples

## Load data sets
data(stress)
## Maximum Likelihood(ML) Estimates of alpha & lambda for the data(stress)
## Estimates of alpha & lambda using 'maxLik' package
## alpha.est = 1.4779388, lambda.est = 0.2141343
dlogis.rayleigh(stress, 1.4779388, 0.2141343, log = FALSE)
plogis.rayleigh(stress, 1.4779388, 0.2141343, lower.tail = TRUE, log.p = FALSE)
qlogis.rayleigh(0.25, 1.4779388, 0.2141343, lower.tail=TRUE, log.p = FALSE)
rlogis.rayleigh(30, 1.4779388, 0.2141343)

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