The peak to average ratio is a measure used in engineering design. Peak refers TV the greatest observation of a population or sample and average refers to one of the familiar measures of central tendency. The density function of the peak to median ratio is derived in general for non-negative variates using applicable order statistics techniques. It is then derived specifically for a uniform distribution with lower limit a, and upper limit a + b. The effect of sample size on the density of the peak to median ratio is noted for observations drawn from a uniform distribution. Some remarks are made on the behavior of the peak to median ratio when the underlying distributions are exponential, Pareto, or triangular, and the sample size is large.
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Morrison et al. (1965) studied this question.