LOG-CONCAVITY AND INEQUALITIES FOR CHI-SQUARE, F AND BETA DISTRIBUTIONS WITH APPLICATIONS IN MULTIPLE COMPARISONS

摘要: In several recent papers log-concavity results and related inequalities for a variety of distributions were obtained. This work is supposed to derive nearly complete list corresponding properties concerning the cdf's some functions Beta as well central non-central Chi-square F distributions, where hitherto only partial available. To this end we introduce generalized reproductive property, thereby extending relationships between total positivity order 2, reproductivity developed in Das Gupta Sarkar (1984). The key our are distribution with zero degrees freedom introduced by Siegel (1979). Finally one used solve monotonicity problem stepwise multiple F-test procedure all pairwise comparisons k means.