lmomco (version 2.0.1)

pdfsla: Probability Density Function of the Slash Distribution

Description

This function computes the probability density of the Slash distribution given parameters ($\xi$ and $\alpha$) of the distribution provided by parsla or vec2par. The probability density function of the distribution is

$$f(x) = \frac{\phi(0) - \phi(y)}{y^2} \mbox{,}$$

where $f(x)$ is the probability density for quantile $x$, $y = (x - \xi)/\alpha$, $\xi$ is a location parameter, and $\alpha$ is a scale parameter. The function $\phi(y)$ is the probability density function of the standard normal distribution.

Usage

pdfsla(x, para)

Arguments

x

A real value.

para

The parameters from parsla or vec2par.

Value

• Probability density ($f$) for $x$.

References

Rogers, W.H., and Tukey, J.W., 1972, Understanding some long-tailed symmetrical distributions: Statistica Neerlandica, v. 26, no. 3, pp. 211-226.

See Also

cdfsla, quasla, parsla, vec2par

Examples

sla <- vec2par(c(12,1.2),type='sla')
  x <- quasla(0.5,sla)
  pdfsla(x,sla)