Main Article Content

Abstract

This article introduces a new three-parameter lifetime model with an increasing and bathtub failure rate functions as an extension of the Mustapha type II distribution (MuII). The model can be very useful in statistical studies, reliability, computer sciences and engineering. Various mathematical and statistical properties of the distribution are discussed, such as moments, mean deviations, Bonferroni and Lorenz curves, entropy, order statistic, and extreme value distributions. Moreover, we consider the bivariate extension of the new model. Statistical inferences by the maximum likelihood method are discussed and assess by simulation studies. Applications of the proposed model to two right-skewed data are presented for illustration. The new model provides a better fit than some other existing distribution as measured by some model selection criteria and goodness of fits statistics.

Keywords

Mustapha type II distribution Moments Entropy Maximum Likelihood Estimation

Article Details

Author Biographies

Isyaku Muhammad, School of Technology, Kano State Polytechnic

Lecturer.

Department of Mechanical Engineering, 

Mouna Bouchane, College of Mathematics and Information Science, Hebei Normal University

PhD. Student 

Key Laboratory of Augmented Reality

Muhammad Aslam, Hebei Normal University

PhD Student

College of Physics and Information Engineering, Hebei Advanced Thin Films Laboratory

Sani Musa, Sule Lamido University, Kafin-Hausa

Assistant Lecturer

Department of Mathematics and Computer Science

Sadiya Ali Rano, Bayero University Kano

Lecturer

Department of Mathematical Sciences

How to Cite
Muhammad, M., Muhammad, I., Bouchane, M., Aslam, M., Musa, S., & Ali Rano, S. (2024). A new bathtub and increasing failure rate model: An extension of the Mustapha type II distribution. Pakistan Journal of Statistics and Operation Research, 20(1), 49-67. https://doi.org/10.18187/pjsor.v20i1.3614

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