new.dist (version 0.1.1)

tprd: Two-Parameter Rayleigh Distribution

Description

Density, distribution function, quantile function and random generation for the Two-Parameter Rayleigh distribution with parameters location and scale.

Usage

dtprd(x, lambda = 1, mu, log = FALSE)
ptprd(q, lambda = 1, mu, lower.tail = TRUE, log.p = FALSE)
qtprd(p, lambda = 1, mu, lower.tail = TRUE)
rtprd(n, lambda = 1, mu)

Value

dtprd gives the density, ptprd gives the distribution function, qtprd gives the quantile function and rtprd generates random deviates.

Arguments

x, q

vector of quantiles.

lambda

a scale parameter.

mu

a location parameter.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are \(P\left[ X\leq x\right]\), otherwise, \(P\left[ X>x\right] \).

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

The Two-Parameter Rayleigh distribution with scale parameter \(\lambda\) and location parameter \(\mu\), has density $$f\left( x\right) =2\lambda \left( x-\mu \right) e^{-\lambda \left( x-\mu\right) ^{2}},$$ where $$x>\mu ,~\lambda >0.$$

References

Dey, S., Dey, T. ve Kundu, D., 2014, Two-parameter Rayleigh distribution: different methods of estimation, American Journal of Mathematical and Management Sciences, 33 (1), 55-74.

Examples

library(new.dist)
dtprd(5, lambda=4, mu=4)
ptprd(2,lambda=2,mu=1)
qtprd(.5,lambda=2,mu=1)
rtprd(10,lambda=2,mu=1)