Gorgees Shaheed Mohammed

Statistical distributions are important to describe phenomena in the real world. A new two-parameter extension of the Lindley distribution, called new Lindley (NLi) is introduced and studied in detail. This model is right-skewed and left-skewed in PDF. It is a unimodal PDF. The hazard rate function of this model is very flexible. Statistically important properties, including the quantile function, a asymptotic for CDF, PDF, and HRF, extreme value, and moments of the new model, are obtained. Parameter estimates process are conducted by the well-known methods of maximum likelihood, weighted least squares method, Cram ́er–von Mises method, and Anderson-Darling method. The tables of simulation show that the Anderson-Darling method and Cram ́er–von Mises methods are better for estimating the parameters of the NLi model. We fit our new model to five real data sets and compare it with some Lindley extensions and some well-known two-parameter distributions like Gamma, Weibull, and Generalized Exponential distribution. The results of tables 12-16 verified that this model is more consistent than other competitive models for real data sets

In this study, we suggest the weighted Exp-G (WExp-G) continuous distributions as a novel class of continuous distributions with an additional shape parameter. Then we study the basic mathematical properties. We study Lindley and X-Gamma special cases. This model is flexible for modelling right skew data sets. The hazard rate of this model is decreasing, increasing and bathtub shape. By performing a simulation analysis, we compared different common methods of estimation. Finally we analyzed and used lifetime, failure time and stress real data sets to illustrate the purposes. This model is perfrom better than other two-parameter distribution.