Inequalities for noncentral chi-square distributions

An upper and lower bound are presented for the difference between the distribution functions of noncentral chi-square variables with the same degrees of freedom and different noncentralities. The inequalities are applied in a comparison of two approximations to the power of Pearson's chi-square test

Distribution of quadratic forms under skew normal settings

AbstractFor a class of multivariate skew normal distributions, the noncentral skew chi-square distribution is studied. The necessary and sufficient conditions under which a sequence of quadratic forms is generalized noncentral skew chi-square distributed random variables are obtained. Several examples are given to illustrate the results

Ranking Problems in Multivariate Normal (Statistical) Populations Semiannual Progress Report No. 1, 1 Jul. - 31 Dec. 1966

Differential difference equations involving noncentral chi-square density and distribution functions for solving minimization problem in selection from multivariate normal population

A Tractable Term Structure Model with Endogenous Interpolation and Positive Interest Rates

This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. The model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near-closed form solutions for a large class of fixed income contingent claims are derived in terms of a noncentral chi-square distribution whose noncentrality parameter is in turn noncentral chi-square distributed. Implementation details on this distribution are given in the appendix.term structure of interest rates, fixed income derivatives, square root process, chi-square distribution

The limiting distribution of the likelihood ratio statistic minus 21 n lambda sub n under a class of local alternatives, part 1. Minimum average risk decision procedures for the noncentral chi-square distribution, part 2

Limiting distribution of likelihood ratio statistic under class of local alternatives and minimum average risk decision procedures for noncentral chi-square distributio

Normal versus Noncentral Chi-square Asymptotics of Misspecified Models

The noncentral chi-square approximation of the distribution of the likelihood ratio (LR) test statistic is a critical part of the methodology in structural equations modeling (SEM). Recently, it was argued by some authors that in certain situations normal distributions may give a better approximation of the distribution of the LR test statistic. The main goal of this paper is to evaluate the validity of employing these distributions in practice. Monte Carlo simulation results indicate that the noncentral chi-square distribution describes behavior of the LR test statistic well under small, moderate and even severe misspecifications regardless of the sample size (as long as it is sufficiently large), while the normal distribution, with a bias correction, gives a slightly better approximation for extremely severe misspecifications. However, neither the noncentral chi-square distribution nor the theoretical normal distributions give a reasonable approximation of the LR test statistics under extremely severe misspecifications. Of course, extremely misspecified models are not of much practical interest