Abstract
Recently, the use of mixed models for analyzing real data sets with infinite domains has gained favor. However, only a specific type of mixture model using mostly maximum likelihood estimation technique has been exercised in the literature, and fitting the mixture models for bounded data (between zero and one) has been neglected. In statistical mechanics, unit distributions are widely utilized to explain practical numeric values ranging between zero and one. We presented a classical examination for the trade share data set using a mixture of two log-Bilal distributions (MLBDs). We examine the features and statistical estimation of the MLBD in connection with three techniques. The sensitivity of the presented estimators with respect to model parameters, weighting proportions, sample size, and different evaluation methodologies has also been discussed. A simulation investigation is also used to endorse the estimation results. The findings on maximum likelihood estimation were more persuasive than those of existing mixture models. The flexibility and importance of the proposed distribution are illustrated by means of real datasets.