Unimodality of probability distributions for sample maxima of independent Erlang random variables

Author(s):  Yu.P. Virchenko, Dr., Prof., Belgorod National Research University, Belgorod, Russia, virch@bsu.edu.ru

A.D. Novoseltsev, Belgorod National Research University, Belgorod, Russia

Issue:  Volume 51, № 3

Rubric:  Mathematics

Annotation:  Finite samples of independent identically distributed nonnegative random variables r̃ 1,…, r̃ N are under consideration. It is set the problem about sufficient conditions for their common probability distribution Q(x) = Pr{ r̃ j < x}, j = 1÷N which guarantee the unimodality of the probability distribution FN(x) = Pr{ r̃ < x} } of random value r̃ = max{ r̃j; j = 1 ÷ N}. It is proven that in the case when Q has the continuously differentiable density q that is the Erlang density with an arbitrary order nℕ, the distribution FN is unimodal.

Keywords:  equivalent independent random values, sample maxima, probability distribution, unimodality, probability density, Erlang distribution

Full text (PDF):  Download

Downloads count:  265