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lmomco (version 2.0.1)

cdfsla: Cumulative Distribution Function of the Slash Distribution

Description

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

$$F(x) = \Phi(y) - [\phi(0) - \phi(y)]/y \mbox{,}$$

for $y \ne 0$ and

$$F(x) = 1/2 \mbox{,}$$

for $y = 0$ and 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 cumulative distribution function of the standard normal distribution function, and $\phi(y)$ is the probability density function of the standard normal distribution.

Usage

cdfsla(x, para)

Arguments

x
A real value.
para
The parameters from parsla or vec2par.

Value

  • Nonexceedance probability ($F$) 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

quasla, parsla, vec2par

Examples

Run this code
para <- c(12,1.2)
  cdfsla(50,vec2par(para,type='sla'))

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