lmomco (version 2.0.1)

pdfgov: Probability Density Function of the Govindarajulu Distribution

Description

This function computes the probability density of the Govindarajulu distribution given parameters ($\xi$, $\alpha$, and $\beta$) of the distribution computed by pargov. The probability density function of the distribution is

$$f(x) = [\alpha\beta(\beta+1)]^{-1} [F(x)]^{1-\beta} [1 - F(x)]^{-1} \mbox{,}$$

where $f(x)$ is the probability density for quantile $x$, $F(x)$ the cumulative distribution function of the distribution, $\xi$ is a location parameter, $\alpha$ is a scale parameter, and $\beta$ is a shape parameter.

Usage

pdfgov(x, para)

Arguments

x

A real value.

para

The parameters from pargov or similar.

Value

• Probability density ($f$) for $x$.

References

Gilchrist, W.G., 2000, Statistical modelling with quantile functions: Chapman and Hall/CRC, Boca Raton.

Nair, N.U., Sankaran, P.G., Balakrishnan, N., 2013, Quantile-based reliability analysis: Springer, New York.

See Also

cdfgov, quagov, pargov

Examples

lmr <- lmom.ub(c(123,34,4,654,37,78))
  gov <- pargov(lmr)
  x <- quagov(0.5,gov)
  pdfgov(x,gov)