Cumulative Distribution Function of the Cauchy Distribution

Description

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

F(x) = \frac{\arctan(Y)}{π}+0.5 \mbox{,}

where Y is

Y = \frac{x - ξ}{α}\mbox{, and}

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

Usage

 1 cdfcau(x, para) 

Arguments

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

Value

Nonexceedance probability (F) for x.

W.H. Asquith

References

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

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

See Also

pdfcau, quacau, lmomcau, parcau

Examples

 1 2  para <- c(12,12) cdfcau(50,vec2par(para,type='cau')) 

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