The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation

Authors

  • Sajid Ali Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
  • Sanku Dey Department of Statistics, St. Anthony’s College, Shillong 793001, India
  • M. H. Tahir Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
  • Muhammad Mansoor Department of Statistics, Government Sadiq Egerton College, Bahawalpur, Pakistan

DOI:

https://doi.org/10.13052/jrss0974-8024.1423

Keywords:

Exponential distribution, hazard rate, lifetime data, maximum likelihood method, Bayesian estimation, Nadarajah-Haghighi distribution, Poisson distribution

Abstract

Estimation of parameters of Poisson Nadarajah-Haghighi (PNH) distribution from the frequentist and Bayesian point of view is discussed in this article. To this end, we briefly described ten different frequentist approaches, namely, the maximum likelihood estimators, percentile based estimators, least squares estimators, weighted least squares estimators, maximum product of spacings estimators, minimum spacing absolute distance estimators, minimum spacing absolute-log distance estimators, Cramér-von Mises estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. To assess the performance of different estimators, Monte Carlo simulations are done for small and large samples. The performance of the estimators is compared in terms of their bias, root mean squares error, average absolute difference between the true and estimated distribution functions, and the maximum absolute difference between the true and estimated distribution functions of the estimates using simulated data. For the Bayesian inference of the unknown parameters, we use Metropolis–Hastings (MH) algorithm to calculate the Bayes estimates and the corresponding credible intervals. Results from the simulation study suggests that among the considered classical methods of estimation, weighted least squares and the maximum product spacing estimators uniformly produces the least biases of the estimates with least root mean square errors. However, Bayes estimates perform better than all other estimates. Finally, we discuss a practical data set to show the application of the distribution.

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Author Biographies

Sajid Ali, Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan

Sajid Ali is currently Assistant Professor at the Department of Statistics, Quaid-i-Azam University (QAU), Islamabad, Pakistan. He graduated (PhD Statistics) from Bocconi University, Milan, Italy. His research interest is focused on Bayesian inference, construction of new flexible probability distributions, time series analysis, and process monitoring.

Sanku Dey, Department of Statistics, St. Anthony’s College, Shillong 793001, India

Sanku Dey, M.Sc., Ph.D.: An Associate Professor in the Department of Statistics, St. Anthony’s College, Shillong, Meghalaya, India. He has to his credit more than 220 research papers in journals of repute. He is a reviewer and associate editors of reputed international journals. He has a good number of contributions in almost all fields of Statistics viz., distribution theory, discretization of continuous distribution, reliability theory, multi-component stress-strength reliability, survival analysis, Bayesian inference, record statistics, statistical quality control, order statistics, lifetime performance index based on classical and Bayesian approach as well as different types of censoring schemes etc.

M. H. Tahir, Department of Statistics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

M. H. Tahir is currently Professor of Statistics, and Chair Department of Statistics at The University of Bahawalpur (IUB), Bahawalpur, Pakistan. He received BSc, MSc and PhD degree from IUB in 1988, 1990 and 2010, respectively. Dr Tahir has over 27 years of teaching experience to post-graduate classes, and has supervised 65 MPhil and 8 PhD students successfully. He has published more than 90 research papers in national and international journals, including Journal of Statistical Planning and Inference, Communications in Statistics-Theory and Methods, Communications in Statistics-Simulation and Computation, Journal of Statistical Computation and Simulation, Journal of Statistical Distributions and Applications, Journal of Statistical Theory and Applications. He is reviewer of more than 55 national and international statistical journals. Dr. Tahir’s research interests include distribution theory, generalized classes of distributions, survival and lifetime data analysis, methods of estimation, and construction of experimental designs.

Muhammad Mansoor, Department of Statistics, Government Sadiq Egerton College, Bahawalpur, Pakistan

Muhammad Mansoor is Assistant Professor of Statistics at the Department of Statistics, Government Sadiq Egerton Graduate College, Bahawalpur, Pakistan. His current research focuses on generalizing statistical distributions arising from the hazard function. Other research areas include statistical inference of probability models, computational statistics, and regression analysis.

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Published

2021-08-23

How to Cite

Ali, S. ., Dey, S. ., Tahir, M. H. ., & Mansoor, M. . (2021). The Poisson Nadarajah-Haghighi Distribution: Different Methods of Estimation. Journal of Reliability and Statistical Studies, 14(02), 415–450. https://doi.org/10.13052/jrss0974-8024.1423

Issue

2021: Vol 14 Iss 2

Section

Articles