# chibarsq: Chi-bar-square distribution with nonnegativity cone... In varComp: Variance Component Models

## Description

`pchibarsq` is the distribution function of chi-bar-square distribution with nonnegativity cone constraint.

`wchibarsq` computes the mixing proportions for the chi-bar-square distribution.

`mchibarsq` computes the moments of the chi-bar-square distribution.

## Usage

 ```1 2 3``` ```pchibarsq(q, V, lower.tail = TRUE, log.p = FALSE) mchibarsq(V, order = 1:2) wchibarsq(V) ```

## Arguments

 `q` A vector of quantiles, as in `stats::pchisq`. `V` A positive-definite matrix, defining the distance measure used when projecting onto the cone. `lower.tail` logical, the same as in `stats::pchisq`. `log.p` logical, the same as in `stats::pchisq`. `order` A positive integer vector of the order of moments to be computed.

## Value

`pchibarsq` gives the distribution function, `wchibarsq` gives the mixing proportion, and `mchibarsq` gives the moments,

Long Qu

## References

A. Shapiro (1988) Towards a Unified Theory of Inequality Constrained Testing in Multivariate Analysis. Int. Stat. Rev. 56, 49–62.

Akio Kudo (1963) A multivariate analogue of the one-sided test. Biometrika 50, 403–418.

`stats::pchisq`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```set.seed(203490L) V=crossprod(matrix(rnorm(25),5)) VI=solve(V) L=t(chol(V)) chibarsq=replicate(1e3L, -2*quadprog::solve.QP(VI, VI%*%(L%*%rnorm(5)), diag(1,5), rep(0,5))[['value']] ) chibarsq=sort(chibarsq) p=pchibarsq(chibarsq, V) ## Not run: plot(ecdf(chibarsq)) lines(chibarsq, p, col=4, lwd=3, lty=3) ## End(Not run) mean(chibarsq); mean(chibarsq^2) mchibarsq(V) ```