Abstract
The objective of this investigation is to provide framework to construct a threefold mixture model and its shifted version using Weibull, lognormal, and gamma distributions. The proposed models are examined by establishing the statistical and reliability indices. The parameter estimation using the maximum likelihood estimation method (MLE) and expectation-maximization has been proposed. The usefulness of the shifted mixture models by fitting them into the actual data set has revealed. The goodness-of-fit tests are used to compare the mixture models for the real-life data. Based on statistical testing, it is established that for small data set, shifted mixture model is the best fitted model in comparison with other single and mixed mixture distributions.