Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimension

This paper focuses mainly on the problem of computing γth, γ>0, moment a random variable Yn:=∑i=1nαiXi in which αi’s are positive real numbers and Xi’s independent distributed according to noncentral chi-square distributions. Finding an analytical approach for solving such has remained challenge due lack understanding probability distribution Yn, especially when not all equal. We analytically solve this by showing that γth Yn can be expressed terms generalized hypergeometric functions. Additionally, we extend our result Xi is combination statistically Zi2 Gi Zi’s normal or Maxwell–Boltzmann distributions Gi’s gamma, Erlang, exponential Our immediate application interest rate modeling, where explicitly provide exact transition density function extended Cox–Ingersoll–Ross (ECIR) process with time-varying dimension as well corresponding conditional moment. Finally, conduct Monte Carlo simulations demonstrate accuracy efficiency explicit formulas through several numerical tests.