A Contour-Integral Derivation of the Non-Central Chi-Square Distribution
نویسندگان
چکیده
منابع مشابه
On Some Central and Non - Central Multivariate Chi - Square Distributions
Let R be a non-singular m-factorial correlation matrix, i.e. R = D + AA0 with a diagonal matrixD > 0 and a not necessarily de nite matrix AA0 of the minimal possible rank m. From an expression for the general non-central multivariate distribution function with the accompanying correlation matrix R some simpler cases are derived: The p-variate central -distribution with q degrees of freedom is g...
متن کاملA new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables
This note proposes a new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. The unknown parameters are determined by the first four cumulants of the quadratic forms. The proposed method is compared with Pearson’s three-moment central χ2 approximation approach, by means of numerical examples. Our method yields a better approxima...
متن کاملNon-Central Multivariate Chi-Square and Gamma Distributions
A 1 ( ) p -variate integral representation is given for the cumulative distribution function of the general p variate non-central gamma distribution with a non-centrality matrix of any admissible rank. The real part of products of well known analytical functions is integrated over arguments from ( , ). To facilitate the computation, these formulas are given more detailed for 3. p Furthe...
متن کاملThe bivariate noncentral chi-square distribution - A compound distribution approach
This paper proposes the bivariate noncentral chi-square (BNC) distribution by compounding the Poisson probabilities with the bivariate central chi-square distribution. The probability density and cumulative distribution functions of the joint distribution of the two noncentral chi-square variables are derived for arbitrary values of the correlation coefficient, degrees of freedom(s), and noncen...
متن کاملMISS DISTANCE – GENERALIZED VARIANCE NON - CENTRAL CHI DISTRIBUTION Ken
In many current practical applications, the probability of collision is often considered as the most meaningful criterion for determining the risk to a spacecraft. However, when the miss distance is very small (say 100 m or less), the collision probability may not comfortably serve well as the only metric for measuring the risk. In these cases, it is also important to know the statistics of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Mathematical Statistics
سال: 1962
ISSN: 0003-4851
DOI: 10.1214/aoms/1177704598