Tests for the Validity of the Assumption that the Underlying Distribution of Life is Pareto

This article considers the problem of testing the validity of the assumption that the underlying distribution of life is Pareto. For complete and censored samples, the relationship between the Pareto and the exponential distributions could be of vital importance to test for the validity of this assumption. For grouped uncensored data the classical Pearson χ² test based on the multinomial model can be used. Attention is confined in this article to handle grouped data with withdrawals within intervals. Graphical as well as analytical procedures will be presented. Maximum likelihood estimators for the parameters of the Pareto distribution based on grouped data will be derived.