On New Formulas for the Cumulative Distribution Function of the Noncentral Chi-Square Distribution

2017 ◽  
Vol 14 (2) ◽  
Author(s):  
Dragana Jankov Maširević
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Chi Square

scholarly journals Approximation of CDF of Non-Central Chi-Square Distribution by Mean-Value Theorems for Integrals

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 129
Author(s):  
Árpád Baricz ◽  
Dragana Jankov Maširević ◽  
Tibor K. Pogány
Keyword(s):  
Distribution Function ◽  
Asymptotic Behavior ◽  
Degrees Of Freedom ◽  
Cumulative Distribution Function ◽  
Mean Value ◽  
Cumulative Distribution ◽  
Chi Square ◽  
Mean Value Theorems ◽  
Definite Integrals ◽  
Du Bois

The cumulative distribution function of the non-central chi-square distribution χn′2(λ) of n degrees of freedom possesses an integral representation. Here we rewrite this integral in terms of a lower incomplete gamma function applying two of the second mean-value theorems for definite integrals, which are of Bonnet type and Okamura’s variant of the du Bois–Reymond theorem. Related results are exposed concerning the small argument cases in cumulative distribution function (CDF) and their asymptotic behavior near the origin.

scholarly journals Hypergeometric Functions on Cumulative Distribution Function

2019 ◽  
pp. 1-11
Author(s):  
Pooja Singh
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Unified Approach ◽  
Exponential Functions ◽  
Chi Square

Exponential functions have been extended to Hypergeometric functions. There are many functions which can be expressed in hypergeometric function by using its analytic properties. In this paper, we will apply a unified approach to the probability density function and corresponding cumulative distribution function of the noncentral chi square variate to extract and derive hypergeometric functions.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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