Compare Cramér–von Mises and Partial Estimation Methods for Weibull–Compertz Distribution

Abstract

This paper presents a new probabilistic model New Weibull Compertz Distribution (NWGD). It goes beyond the Compertz distribution in the New Weibull-X family and introduces an additional shape parameter, 6. The three-parameter form (α λ,b,) obtained is more flexible and more resilient to the data fitting in skewed, heavy tailed and lifetime data applications. Two estimation methods are obtained to the unknown parameters of NWGD. The first one is the partial fractional estimator (PM). The second one is the Cramer von Mises estimator (CVM). The analysis of the stability, accuracy and sensitivity of both procedures in small and moderate sample regimes at different parameter values and random seeds are analyzed. A Monte Carlo simulation experiment compares the two estimators at the sample sizes n = 10, 25, 50 and 100. The bias is used to measure performance and mean squared error (MSE). The outcomes suggest that PM and CVM are both consistent but CVM generally has lower bias and MSE; particularly with increased n. The most noticeable increase is at n = 100 as CVM has the lowest overall MSE of all settings to be tested. The paper recommends that PM and CVM should be benchmarked with maximum likelihood and method of moments to check their efficiency. Pareto and Campbell distributions are readily estimated using the same ideas as the estimation performed on distributions