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.
Value
dtprd gives the density, ptprd gives the distribution
function, qtprd gives the quantile function and rtprd generates
random deviates.
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
$$x>\mu ,~\lambda >0.$$