SOME USEFUL FORMULAS FOR MONTE-CARLO SIMULATIONS RELATING TO THE WEIBULL AND TO THE EXPONENTIAL PROBABILITY-DISTRIBUTION FUNCTIONS

This paper develops some useful formulae relating the estimated and th e actual values of the parameters of the Weibull and of the Exponentia l Probability Distribution functions. These formulae simplify the calc ulations for Monte Carlo simulations executed for the estimation of so me reference statistics, for instance, the reliability function. The r eduction of the calculation is possible because of the reduction of th e possible values that the parameters of the random numbers generating function should assume. In some cases of the reliability function, on ly one Monte Carlo simulation is necessary for a given data sample amp litude. An explanation is made of the use of these formulae when estim ating the reliability function.