tprd {new.dist}

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)

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.

Value

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

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)