A New Proof for Monotone Likelihood Ratio for the Sum of Independent Bernoulli Random Variables

Abstract

By use of an inequality of Marcus and Lopes for elementary symmetric functions, a new proof is presented for the following result by Ghurye and Wallace: Given that the independent random variables X j are Bernoulli with success probability p j ( θ ) strictly between 0 and 1 and nondecreasing in θ , the sum Σ X j has monotone likelihood ratio.