Difference of Chi-Square Random Variables

2007 ◽  
pp. 25-34
Keyword(s):  
Random Variables ◽  
Chi Square

Approximations to densities in geometric probability

1980 ◽  
Vol 17 (01) ◽  
pp. 145-153 ◽  
Author(s):  
H. Solomon ◽  
M. A. Stephens
Keyword(s):  
Monte Carlo ◽  
Random Variables ◽  
Monte Carlo Sampling ◽  
Geometric Probability ◽  
Simple Approximation ◽  
Chi Square ◽  
Percentage Points ◽  
Random Polygons

Many random variables arising in problems of geometric probability have intractable densities, and it is very difficult to find probabilities or percentage points based on these densities. A simple approximation, a generalization of the chi-square distribution, is suggested, to approximate such densities; the approximation uses the first three moments. These may be theoretically derived, or may be obtained from Monte Carlo sampling. The approximation is illustrated on random variables (the area, the perimeter, and the number of sides) associated with random polygons arising from two processes in the plane. Where it can be checked theoretically, the approximation gives good results. It is compared also with Pearson curve fits to the densities.

On the Distribution of a Difference of Two Scaled Chi-Square Random Variables

1970 ◽  
Vol 24 (5) ◽  
pp. 29-30
Author(s):  
Toke Jayachandran ◽  
D. R. Barr
Keyword(s):  
Random Variables ◽  
Chi Square

On the Distribution of a Difference of Two Scaled Chi-Square Random Variables

1970 ◽  
Vol 24 (5) ◽  
pp. 29 ◽  
Author(s):  
Toke Jayachandran ◽  
D. R. Barr
Keyword(s):  
Random Variables ◽  
Chi Square

scholarly journals On chi-square type distributions with geometric degrees of freedom in relation to geometric sums

2019 ◽  
Vol 22 (1) ◽  
pp. 180-184
Author(s):  
Tran Loc Hung
Keyword(s):  
Degrees Of Freedom ◽  
Limit Theorems ◽  
Random Variables ◽  
Weak Limit ◽  
Random Sums ◽  
Chi Square ◽  
Asymptotic Behaviors ◽  
Weak Limit Theorems ◽  
Geometric Sums ◽  
Applied Fields

The chi-square distribution with degrees of freedom has an important role in probability, statistics and various applied fields as a special probability distribution. This paper concerns the relations between geometric random sums and chi-square type distributions whose degrees of freedom are geometric random variables. Some characterizations of chi-square type random variables with geometric degrees of freedom are calculated. Moreover, several weak limit theorems for the sequences of chi-square type random variables with geometric random degrees of freedom are established via asymptotic behaviors of normalized geometric random sums.

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