Mathematical tools for hazard function analysis. (Q1427259)

A hazard function is a characterization of the risk of an event occurring at a given point, conditioned by the fact that the event has not already occurred. Given the important role of the hazard functions in the mathematical psychology, the paper deals with mathematical techniques apt to prove several properties of hazard functions. This approach appears more significant than a computational one. Properties of hazard functions are investigated for both continuous and discrete probability distributions as well as methodologies to obtain the underlying probability distribution from a given hazard function. Finally the author studies the hazard for a mixture of stochastic processes, convolution of random variables, disjunctive and conjunctive systems.