New upper bounds for noncentral chi-square cdf

Valeriy A. Voloshko, Egor V. Vecherko
2020 Journal of the Belarusian State University. Mathematics and Informatics  
Some new upper bounds for noncentral chi-square cumulative density function are derived from the basic symmetries of the multidimensional standard Gaussian distribution: unitary invariance, components independence in both polar and Cartesian coordinate systems. The proposed new bounds have analytically simple form compared to analogues available in the literature: they are based on combination of exponents, direct and inverse trigonometric functions, including hyperbolic ones, and the cdf of
more » ... , and the cdf of the one dimensional standard Gaussian law. These new bounds may be useful both in theory and in applications: for proving inequalities related to noncentral chi-square cumulative density function, and for bounding powers of Pearson's chi-squared tests.
doi:10.33581/2520-6508-2020-1-70-74 fatcat:zemr4p5vwvh2jnuvsladiutyvi