A new generalization of logistic Weibull distribution with theory and practical illustration

Abstract

This study developed the exponentiated logistic Weibull distribution as a new generality of the logistic Weibull distribution to deal with real-life data sets. The newly developed model has numerous sub-models such as the logistic exponential, logistic Rayleigh, and the exponentiated logistic Rayleigh distribution revealed in the literature. We have derived and studied essential properties of the including moments, probability weighted moments, quantile function, entropies and stress-strength reliability. The maximum likelihood estimation method is being used to estimate the parameters efficiently. However, the Monte Carlos simulation study is used to observe the behavior of estimated parameters at different sample values based on bias and mean square error. Moreover, it is justified that the exponentiated logistic Weibull distribution can be used as a better alternative as compared to the other generalization of the Weibull distribution for lifetime data sets. It has observed from two-lifetime data sets that the newly developed model was a better fit as compared to other considered generalizations of the Weibull distribution.

Subject Classification:

• 97K80

Keywords:

• Exponentiated logistic Weibull distribution
• Maximum likelihood estimation
• Shannon entropy
• Probability weighted moments
• Order statistic