Peer reviewed paper published: A New Generalisation of Sam-Solai’s Multivariate Additive Chi-Square Distribution

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MATHEMATICAL SCIENCES RESEARCH JOURNAL ISSN 1537-5978

This paper proposed a new generalization of Sam-Solai's Multivariate additive chi-square distribution from the univariate case. Further, we find its Marginal, Multivariate Conditional distributions, Multivariate Generating functions, Multivariate survival, hazard functions and also discussed its special cases. The special cases includes the transformation of Sam-Solai's Multivariate additive chi-square distribution into Multivariate additive Chi-square distribution with n d.f,Multivariate Inverse chi-square distribution, Multivariate log chi-square distribution. Multivariate chi-distribution and Multivariate Extreme value chi-square distribution. Moreover, it is found that the bivariate correlation between two chi-square variables purely depends on the d.f and we simulated and established selected standard bivariate chi-square correlation bounds from 2500 different combination of d.f. The simulation results shows, the correlation between any two chi-square variables bounded from -1 to +1 for certain combination of fractional d.f.