  Continuing the work of [9] who defined the restrictiveness of stochastic
orders and calculated the restrictiveness of the usual stochastic order and the
likelihood ratio order, we calculate the restrictiveness of the hazard rate
order. Inspired by the works of [17] and [24], we propose a possible
application of the restrictiveness results in randomness testing. We then apply
a dimension reduction technique, that proved useful in obtaining the
restrictiveness results, and provide an alternative proof for Whitworth's
formula. By integrating the formula, we derive the moments of the maximal
coordinate of a random vector that is uniformly distributed on the probability
$n$-simplex.
