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 \alpha
) computed by parcau
. The cumulative distribution function is
F(x) = \frac{\arctan(Y)}{\pi}+0.5 \mbox{,}
where Y
is
Y = \frac{x - \xi}{\alpha}\mbox{, and}
where F(x)
is the nonexceedance probability for quantile x
, \xi
is a location parameter, and \alpha
is a scale parameter.
Usage
cdfcau(x, para)
Arguments
x |
A real value vector. |
para |
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
para <- c(12,12)
cdfcau(50,vec2par(para,type='cau'))
[Package lmomco version 2.5.1 Index]