Speaker
Description
Applications of modified Bessel functions frequently occur in statistics, for instance, it is a constituting term of the probability density function of the non-central $\chi^2$ distribution, having $n$ degrees of freedom and non-centrality parameter $\lambda>0$. The random variable with such distribution is usually denoted by $\chi_n'^{\;2}(\lambda)$.
Bearing in mind a great application of the non-central $\chi^2$ distribution, for example in finance, estimation and decision theory, in mathematical physics and, among others, in communication theory in which case the appropriate cumulative distribution function (CDF) is given in terms of the so-called generalized Marcum Q-function, the appropriate CDF has been widely considered in mathematical literature.
The aim of this talk is to present several new formulae for such CDF in the case of even number of the degrees of freedom. The main advantages of these expressions are that they are given in terms of some familiar special functions as the modified Bessel functions and generalized incomplete gamma function, which have computational advantages and a wide range of applications having numerous in build routines. Also, numerical simulations shows the quality of newly derived formulae in comparison with certain earlier results.
