pdfcau: Probability Density Function of the Cauchy Distribution

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

Probability Density Function of the Cauchy Distribution

Description

This function computes the probability density of the Cauchy distribution given parameters (\xi and \alpha) provided by parcau. The probability density function is

f(x) = \left(\pi \alpha \left[1 + \left({\frac{x-\xi}{\alpha}}\right)^2\right] \right)^{-1}\mbox{,}

where f(x) is the probability density for quantile x, \xi is a location parameter, and \alpha is a scale parameter.

Usage

pdfcau(x, para)

Arguments

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

Value

Probability density (f) for x.

Author(s)

W.H. Asquith

References

Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, vol. 43, pp. 299–314.

Evans, Merran, Hastings, Nicholas, Peacock, J.B., 2000, Statistical distributions: 3rd ed., Wiley, New York.

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

See Also

cdfcau, quacau, lmomcau, parcau, vec2par

Examples

  cau <- vec2par(c(12,12),type='cau')
  x <- quacau(0.5,cau)
  pdfcau(x,cau)

lmomco documentation built on May 29, 2024, 10:06 a.m.