Approximate 1-sided tolerance limits for future observations for the Rayleigh distribution, using regression

Two types of tolerance limits are derived for future values of a response variable which has the Rayleigh distribution whose parameter depends on a set of fixed explanatory variables. The Fisher Scoring method is used to approximate maximum likelihood estimates of the regression parameters. Simulation results show the adequacy of the approximation. A real data-set illustrates the computations in finding the tolerance limits. The computations can be handled using software that allows matrix arithmetic and has a programming capability