Mavis Pararai

Exponentiated power Lindley–Poisson distribution: Properties and applications

ABSTRACT A new four-parameter distribution called the exponentiated power Lindley–Poisson distribution which is an extension of the power Lindley and Lindley–Poisson distributions is introduced. Statistical properties of the distribution including the shapes of the density and hazard functions, moments, entropy measures, and distribution of order statistics are given. Maximum likelihood estimation technique is used to estimate the parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators, and width of the confidence interval for each parameter. Finally, applications to real data sets are presented to illustrate the usefulness of the proposed distribution.

A new compound class of log-logistic Weibull–Poisson distribution: model, properties and applications

A new class of distributions called the log-logistic Weibull–Poisson distribution is introduced and its properties are explored. This new distribution represents a more flexible model for lifetime data. Some statistical properties of the proposed distribution including the expansion of the density function, quantile function, hazard and reverse hazard functions, moments, conditional moments, moment generating function, skewness and kurtosis are presented. Mean deviations, Bonferroni and Lorenz curves, Rényi entropy and distribution of the order statistics are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study is conducted to examine the bias, mean square error of the maximum likelihood estimators and width of the confidence interval for each parameter and finally applications of the model to real data sets are presented to illustrate the usefulness of the proposed distribution.