A goodness of fit test for two component two parameter Weibull mixtures

TL;DR

This paper introduces a goodness of fit test for two-component Weibull mixture models, useful for assessing how well such models fit data from inhomogeneous populations, with demonstrated empirical validation.

Contribution

It proposes a new goodness of fit test based on the empirical distribution function specifically for two-component Weibull mixtures, adaptable to other distributions.

Findings

Test procedure validated via Monte Carlo simulations

Applicable to mixtures with different component distributions

Provides a practical tool for mixture model assessment

Abstract

Fitting mixture distributions is needed in applications where data belongs to inhomogeneous populations comprising homogeneous sub-populations. The mixing proportions of the sub populations are in general unknown and need to be estimated as well. A goodness of fit test based on the empirical distribution function is proposed for assessing the goodness of fit in model fits comprising two components, each distributed as two parameter Weibull. The applicability of the proposed test procedure was empirically established using a Monte Carlo simulation study. The proposed test procedure can be easily altered to handle two component mixtures with different component distributions.