Performance of various sub-models of a new Lindley family of distributions: A comparative study based on the simulated data sets

In recent years, several efforts have been made to modify the well-known lifetime distributions to provide more flexibility for different types of lifetime data sets. The Lindley distribution is one of the finite mixture distributions. It has been highlighted by many researchers to handle the complexity of heterogeneity in lifetime data. This paper compares the performance of sub-models of a new Lindley family of distributions for different types of data sets. The different types of data sets are simulated from the new distribution. The maximum likelihood estimation method is used to estimate the unknown parameters, and the Akaike information criterion (AIC) value is used to evaluate the performance of the sub-models. The comparison study results suggest that two selected sub-models are effective for two different cases of data sets.