cdfcau {lmomco}R Documentation

Cumulative Distribution Function of the Cauchy Distribution

Description

This function computes the cumulative probability or nonexceedance probability of the Cauchy distribution given parameters (xi and α) of the distribution provided by parcau or vec2par. The cumulative distribution function of the distribution is

F(x) = frac{arctan(frac{x - xi}{α})}{π}+0.5 mbox{,}

where F(x) is the nonexceedance probability for quantile x, xi is a location parameter and α is a scale parameter.

Usage

cdfcau(x, para)

Arguments

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

Value

Nonexceedance probability (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.

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

See Also

quacau, parcau, vec2par

Examples

  para <- c(12,12)
  cdfcau(50,vec2par(para,type='cau'))

[Package lmomco version 0.96.3 Index]