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Two-parameter Rayleigh distribution with location \(\mu\) and scale \(\sigma\). The distribution is lower-bounded at the location parameter. Fitting uses closed-form L-moment expressions derived from gamma-function relationships; the location is obtained from the first two L-moments and the scale from the second L-moment ratio.

The probability density function is: $$f(x) = \frac{x - \mu}{\sigma^2} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right), \quad x \ge \mu$$ where:

  • \(\mu\) — location parameter (location)

  • \(\sigma\) — scale parameter (scale)

Usage

drayleigh(x, location, scale)

prayleigh(x, location, scale)

qrayleigh(p, location, scale)

rrayleigh(n, location, scale)

Arguments

x

vector of quantiles.

location

location parameter.

scale

scale parameter.

p

vector of probabilities.

n

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