version 0.1.0

DESCRIPTION

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+Package: momentchi2
+Title: Moment-Matching Methods for Weighted Sums of Chi-Squared Random
+        Variables
+Version: 0.1.0
+Author: Dean Bodenham
+Maintainer: Dean Bodenham <dean.bodenham@bsse.ethz.ch>
+Description: A collection of moment-matching methods for computing the cumulative distribution function of a positively-weighted sum of chi-squared random variables. Methods include the Satterthwaite-Welch method, Hall-Buckley-Eagleson method, Wood's F method, and the Lindsay-Pilla-Basak method.
+Depends: R (>= 3.1.2)
+License: GPL-2 | GPL-3
+LazyData: true
+Packaged: 2015-02-25 10:34:38 UTC; dean
+NeedsCompilation: no
+Repository: CRAN
+Date/Publication: 2015-02-25 11:54:43

MD5

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+5ee40ec8495bffa3946acfdc6c39054f *DESCRIPTION
+0350d3b800d73c738d77906579aa2495 *NAMESPACE
+f3aafbc0da1b35c49183229768cd9f8a *R/hbe.R
+7d15925dcbc2d7ec07c809558e743c4d *R/lpb4.R
+7f4fd15940c235968698eb1f9f30164f *R/momentchi2.R
+e9cc77074cbb03e0ce1d7f063a6421c7 *R/sw.R
+03f2e03eb7f6dba4f7afeb34fdf567d0 *R/utils.R
+1082e3177e99757c5333d692355760eb *R/wf.R
+a87e85635b1d3db3872ab914b7a467fc *README
+5805ae87815034699b126bd958e5ff40 *man/hbe.Rd
+021af66111e31030b15b5c3bf33e1fc5 *man/lpb4.Rd
+fbc798aea43414d5c89e7e379f85eb93 *man/momentchi2.Rd
+6ef29cc9b124407db1e4e23b1a07a89f *man/sw.Rd
+bd1cd529a995c561698d9b31eb84d49c *man/wf.Rd

NAMESPACE

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+# Generated by roxygen2 (4.1.0): do not edit by hand
+
+export(hbe)
+export(lpb4)
+export(sw)
+export(wf)

R/hbe.R

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+#' Hall-Buckley-Eagleson method
+#'
+#' Computes the cdf of a positively-weighted sum of chi-squared random variables with the Hall-Buckley-Eagleson (HBE) method.
+#' @inheritParams sw
+#' @keywords distribution
+#' @references
+#' \itemize{
+#'   \item P. Hall. Chi squared approximations to the distribution of a sum of independent random variables. \emph{The Annals of Probability}, 11(4):1028-1036, 1983.
+#'   \item M. J. Buckley and G. K. Eagleson. An approximation to the distribution of quadratic forms in normal random variables. \emph{Australian Journal of Statistics}, 30(1):150-159, 1988.
+#' }
+#' @export
+#' @examples
+#' #Examples taken from Table 18.6 in N. L. Johnson, S. Kotz, N. Balakrishnan. 
+#' #Continuous Univariate Distributions, Volume 1, John Wiley & Sons, 1994.
+#'
+#' hbe(c(1.5, 1.5, 0.5, 0.5), 10.203)            # should give value close to 0.95
+#' hbe(coeff=c(1.5, 1.5, 0.5, 0.5), x=10.203)    # specifying parameters
+#' hbe(c(1.5, 1.5, 0.5, 0.5), c(0.627, 10.203))  # x is a vector, output approx. 0.05, 0.95
+
+hbe <- function(coeff, x){
+    if ( (missing(x)) || (missing(coeff)) )
+        stop("missing an argument - need to specify \"coeff\" and \"x\"")
+
+    if (checkCoeffsArePositiveError(coeff))
+        stop(getCoeffError(coeff))
+
+    if (checkXvaluesArePositiveError(x))
+        stop(getXvaluesError(x))
+    #end of error checking
+
+	#compute cumulants and nu
+	kappa <- c(sum(coeff), 2*sum(coeff^2), 8*sum(coeff^3) )
+    K_1 <- sum(coeff)
+    K_2 <- 2 * sum(coeff^2)
+    K_3 <- 8 * sum(coeff^3)
+	nu <- 8 * (K_2^3) / (K_3^2)
+
+	#gamma parameters for chi-square
+	gamma_k <- nu/2
+	gamma_theta <- 2
+
+	#need to transform the actual x value to x_chisqnu ~ chi^2(nu)
+	#This transformation is used to match the first three moments
+	#First x is normalised and then scaled to be x_chisqnu
+	x_chisqnu_vec <- sqrt(2 * nu / K_2) * (x - K_1) + nu
+
+	#now this is a chi_sq(nu) variable
+	p_chisqnu_vec <- pgamma(x_chisqnu_vec, shape=gamma_k, scale=gamma_theta)
+	return(p_chisqnu_vec)
+}
+