LogisRayleigh: The Logistic-Rayleigh(LR) 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 Logistic-Rayleigh(LR) distribution with shape parameter alpha and scale parameter lambda.

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)

`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 ≤ x] otherwise, P[X > x].

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

F(x) = 1 - 1 / {1 + (exp{(λ x^2 / 2)} - 1)^α}; x ≥ 0, α > 0, λ > 0.

where α and λ are the shape and scale parameters, respectively.

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

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

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

## 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)