cdfsla: Cumulative Distribution Function of the Slash Distribution

In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

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 is

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

for Y \ne 0 and

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

for Y = 0, where F(x) is the nonexceedance probability 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, and \phi(Y) is the probability density function of the Standard Normal distribution.

Usage

cdfsla(x, para)

Arguments

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

Value

Nonexceedance probability (F) for x.

Author(s)

W.H. Asquith

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

pdfsla, quasla, lmomsla, parsla

Examples

  para <- c(12, 1.2)
  cdfsla(50, vec2par(para, type="sla"))

lmomco documentation built on Nov. 7, 2025, 5:11 p.m.