momentchi2 (version 0.1.0)

lpb4: Lindsay-Pilla-Basak method

Description

Computes the cdf of a positively-weighted sum of chi-squared random variables with the Lindsay-Pilla-Basak (LPB4) method using four support points. Note that the coefficient vector must be of length at least four.

Usage

lpb4(coeff, x)

Arguments

coeff

The coefficient vector. All values must be greater than 0.

x

The vector of quantile values. All values must be greater than 0.

Details

Note that the coefficient vector must of length at least four. In some cases when the coefficient vector was of length two or three, the algorithm would be unable to find roots of a particular equation during an intermediate step, and so the algorithm would produce NaNs. If the coefficient vector is of length less than four, the Hall-Buckley-Eagleson method is used (and a warning is displayed).

References

• B. G. Lindsay, R. S. Pilla, and P. Basak. Moment-based approximations of distributions using mixtures: Theory and applications. Annals of the Institute of Statistical Mathematics, 52(2):215-230, 2000.

Examples

#Examples taken from Table 18.6 in N. L. Johnson, S. Kotz, N. Balakrishnan.
#Continuous Univariate Distributions, Volume 1, John Wiley & Sons, 1994.

lpb4(c(1.5, 1.5, 0.5, 0.5), 10.203)            # should give value close to 0.95
lpb4(coeff=c(1.5, 1.5, 0.5, 0.5), x=10.203)    # specifying parameters
lpb4(c(1.5, 1.5, 0.5, 0.5), c(0.627, 10.203))  # x is a vector, output approx 0.05, 0.95
lpb4(c(0.5, 0.3, 0.2), 2.708)                  # length(coeff) < 4, warning, uses hbe()