Restricted tests for and against the increasing failure rate ordering on multinomial parameters

We consider the likelihood ratio tests for (i) testing a constant failure rate (truncated geometric) against the alternative of increasing (nondecreasing) failure rate ordering of a collection of multinomial parameters, and for (ii) testing the null hypothesis that this parameter vector satisfies increasing failure rate ordering against all alternatives (unrestricted). For both tests the asymptotic distribution of the test statistic under the null hypothesis is shown to be of the chi-bar square type. A numerical example is presented to illustrate the procedure.