The cumulants of an analogue of pearson's chi-squared

Abstract

Pearson's chi-squared for a multinomial sample is defined as where An analogous or supplementary statistic Y_t: is defined as.The statistic Y_t, should be powerful when the alternative hypotheses:are obtained from the null hypothesis by adding to it bumps or dips wider than the bin width. Algorithms are supplied for calculating the cumulants of Y₁especially when the null hypothesis is Most of the formulae depend on an unproved but certainly true conjecture concerning the characteristic polynomial of the matrix product Formulae for the bivariate cumulants of X²,Y₁ are also provided.