1d:T7cc,# chiSqMatchFast.R Match the moments of a mixture of scaled chi-square random variables to a single non-central chi-square, assumes the quadratic form case where the mean of the multivariate normal V=RV is 0. ```r chiSqMatchFast(lambdaVec, alwaysCentral = FALSE) ``` ## Arguments - `lambdaVec`: Numeric vector holding the eigenvalues of the A term, where we are interested in x^TAX and x is multivariate normal. - `alwaysCentral`: Boolean determining whether to always set the noncentrality parameter to 0, as in SKAT package. ## Returns A list with the elements: - **sigmaQrho**: Standard deviation of the mixture distribution - **muQrho**: Mean of the mixture distribution - **delta**: Noncentrality parameter of the matched distribution - **l**: Degrees of freedom of the matched distribution ## Examples ```r set.seed(2) gMat <- matrix(data=rbinom(n=2000, size=2, prob=0.3), nrow=100) xMat <- matrix(data=rnorm(200), nrow=100) bhFunInv <- function(x) {x} obsTimes <- 1:5 etaVec <- rep(0, 100) outcomeDat <- gen_IC_data(bhFunInv = bhFunInv, obsTimes = obsTimes, windowHalf = 0.1, probMiss = 0.1, etaVec = etaVec) lt <- outcomeDat$leftTimes rt <- outcomeDat$rightTimes tpos_ind <- as.numeric(lt > 0) obs_ind <- as.numeric(rt != Inf) dmats <- make_IC_dmat(xMat, lt, rt, obs_ind, tpos_ind) nullFit <- ICSKAT_fit_null(init_beta = rep(0, 5), left_dmat = dmats$left_dmat, right_dmat=dmats$right_dmat, obs_ind = obs_ind, tpos_ind = tpos_ind, lt = lt, rt = rt) icskatOut <- ICskat(left_dmat = dmats$left_dmat, right_dmat=dmats$right_dmat, lt = lt, rt = rt, obs_ind = obs_ind, tpos_ind = tpos_ind, gMat = gMat, null_beta = nullFit$beta_fit, Itt = nullFit$Itt) Rrho <- matrix(data=0.5, nrow=20, ncol=20) diag(Rrho) <- 1 toDecomp <- Rrho %*% icskatOut$sig_mat tempEvals <- eigen(toDecomp, symmetric = TRUE, only.values = TRUE)$values idx1 <- which(tempEvals >= 0) idx2 <- which(tempEvals > mean(tempEvals[idx1])/100000) tempEvals <- tempEvals[idx2] chiSqMatchFast(lambdaVec = tempEvals) ```

chiSqMatchFast function