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Functions for calculating hazard functions and their relationship to Mills ratios. The hazard function h(x) = f(x)/(1-F(x)) is the reciprocal of the Mills ratio m(x).

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The hazard function (also called failure rate or force of mortality) represents the instantaneous rate of occurrence of an event at time x, given survival to time x.

Mathematical relationship: h(x) = 1/m(x)