Reciprocal Moments of Linear Combinations of Exponential Variates
Abstract The reciprocal moments of a linear combination of exponential variates are derived. The resultant formula is used to obtain the moments of quantile and other similar estimators for the shape parameter of a Pareto distribution. The calculations show that such estimators are more biased and less “precise” than indicated by Monte Carlo estimates of the moments previously published. The general formula for the reciprocal moments is shown to be potentially useful in linear models and in studying models of the variation in the rate of births in a pure birth process.