LaguerreHalf: Laguerre Polynomial (Half)

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

Laguerre Polynomial (Half)

Description

This function computes the Laguerre polynomial, which is useful in applications involving the variance of the Rice distribution (see parrice). The Laguerre polynomial is

L_{1/2}(x) = \exp^{x/2}\times[(1-x)I_0(-x/2) - xI_1(-x/2)]\mbox{,}

where the modified Bessel function of the first kind is I_k(x), which has an R implementation in besselI, and for strictly integer k is defined as

I_k(x) = \frac{1}{\pi} \int_0^\pi \exp(x\cos(\theta)) \cos(k \theta)\; \mathrm{d}\theta\mbox{.}

Usage

LaguerreHalf(x)

Arguments

x

A value.

Value

The value for the Laguerre polynomial is returned.

Author(s)

W.H. Asquith

See Also

pdfrice

Examples

LaguerreHalf(-100^2/(2*10^2))

wasquith/lmomco documentation built on Nov. 13, 2024, 4:53 p.m.