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Continuing the work of [9] who defined the restrictiveness of stochasticorders and calculated the restrictiveness of the usual stochastic order and thelikelihood ratio order, we calculate the restrictiveness of the hazard rateorder. Inspired by the works of [17] and [24], we propose a possibleapplication of the restrictiveness results in randomness testing. We then applya dimension reduction technique, that proved useful in obtaining therestrictiveness results, and provide an alternative proof for Whitworth'sformula. By integrating the formula, we derive the moments of the maximalcoordinate of a random vector that is uniformly distributed on the probability$n$-simplex.

The restrictiveness of the hazard rate order and the moments of the  maximal coordinate of a random vector uniformly distributed on the  probability n-simplex