Cumulative Distribution Function of the Cauchy Distribution

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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.

Author(s)

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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