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A sequential sampling approach for discriminating log-normal, Weibull, and log-logistic distributions

Log-normal, Weibull, and log-logistic distributions are widely used in modeling nonnegative skewed data. We develop sequential methodologies to discriminate between any two of these three distributions as well as to discriminate among these three distributions. These methods are extended to discriminate M(≥ 2) distributions from location-scale, log-location-scale and regular families of distributions. Discriminating three or more distributions having similar shapes often requires large sample size (Marshall et al. (2001)). Sequential procedures allow early stopping which in turn reduce the sample size needed for discrimination. Proposed methods yield high probabilities of correct selection that are shown to converge to 1 asymptotically. Asymptotic behavior of expected sample size and error probabilities are studied as stopping boundaries tend to infinity. Extensive simulation study validates finite sample performances of the proposed procedures requiring significantly fewer samples on average. These methods are applied to three benchmark datasets on cancer trials and are shown to select the correct model with high probability.