Distribution properties and estimation of the ratio of independent Weibull random variables

The important problem of the ratio of Weibull random variables is considered. Two motivating examples from engineering are discussed. Exact expressions are derived for the probability density function, cumulative distribution function, hazard rate function, shape characteristics, moments, factorial moments, skewness, kurtosis and percentiles of the ratio. Estimation procedures by the methods of moments and maximum likelihood are provided. The performances of the estimates from these methods are compared by simulation. Finally, an application is discussed for aspect and performance ratios of systems.