Statistical Analysis Based on Adaptive Progressive Hybrid Censored Data From Lomax Distribution

  • Amal Helu The University of Jordan
  • Hani Samawi Georgia Southern University
Keywords: Lomax distribution; maximum likelihood; Lindley’s approximation; adaptive progressive censoring.


In this article, we consider statistical inferences about the unknown parameters of the Lomax distribution basedon the Adaptive Type-II Progressive Hybrid censoring scheme, this scheme can save both the total test time and the cost induced by the failure of the units and increases the efficiency of statistical analysis. The estimation of the parameters is derived using the maximum likelihood (MLE) and the Bayesian procedures. The Bayesian estimators are obtained based on the symmetric and asymmetric loss functions. There are no explicit forms for the Bayesian estimators, therefore, we propose Lindley’s approximation method to compute the Bayesian estimators. A comparison between these estimators is provided by using extensive simulation. A real-life data example is provided to illustrate our proposed estimators.


Arnold, B.C., The pareto distributions, International Co-operative publishing house, Fairland, MD., 1983.

Balakrishnan, N., & Asgharzadeh, A., Inference for the scaled half-logistic distribution based on progressively Type-II censored samples, Communications in Statistics-Theory and Methods, 34(1), 73-87, 2005.

Balakrishnan, N., & Cramer, E., The art of progressive censoring, New York: Springer, 2014.

Basu, A. P., & Ebrahimi, N., Bayesian approach to life testing and reliability estimation using asymmetric loss function, Journal of statistical planning and inference, 29(1-2), 21-31, 1991.

Bryson, M.C., Heavy-tailed distributions: properties and tests, Technometrics. 16, 61-68, 1974.

Calabria, R. and Pulcini, G., Point estimation under asymmetric loss functions for left-truncated exponential samples, Communications in Statistics Theory and Methods, 25, 585-600, 1996.

Chahkandi, M., and Ganjali, M, On some lifetime distributions with decreasing failure rate, Comput. Statist. Data Anal, 53, 4433-4440, 2009.

Chen, S., & Gui, W., Statistical analysis of a lifetime distribution with a bathtub-shaped failure rate function under adaptive progressive type-II censoring, Mathematics, 8(5), 670, 2020.

Childs, A., Balakrishnan, N. and Moshref, M., Order statistics from non-identical right-truncated Lomax random variables with applications, Statistical Papers, 42, 187-206, 2001.

Cui, W., Yan, Z., & Peng, X., Statistical Analysis for Constant-Stress Accelerated Life Test With Weibull Distribution Under Adaptive Type-II Hybrid Censored Data, IEEE Access, 7, 165336-165344, 2019.

Feynman, R.P., Mr. Feynman goes to Washigton. Engineering and science. California Institute of Technology, Pasadena, CA, 6-22,1987.

David, H. A., & Nagaraja, H. N., Order statistics, third edition, Wiley: New York, NY., 2003.

Elfattah, A., Alaboud, F. and Alharby, A., On Sample Size Estimation For Lomax Disrtibution, Australian Journal of Basic and Applied Sciences, 4, 373-378, 2007.

El-Sherpieny, E. S. A., Almetwally, E. M., & Muhammed, H. Z., Progressive Type-II hybrid censored schemes based on maximum product spacing with application to Power Lomax distribution, Physica A: Statistical Mechanics and its Applications, 553, 124251, 2020.

Helu, A., & Samawi, H., On Marginal Distributions under Progressive Type II Censoring: Similarity/Dissimilarity Properties, Open Journal of Statistics, 7(4), 633-644, 2017.

Helu, A., Samawi, H., Rochani, H., Yin, J., & Vogel, R., Kernel density estimation based on progressive type-II censoring, Journal of the Korean Statistical Society, 49(2), 475-498, 2020.

Helu, A., Samawi, H., & Raqab, M. Z., Estimation on Lomax progressive censoring using the EM algorithm, Journal of Statistical Computation and Simulation, 85(5), 1035-1052, 2015.

Howlader, and H. Hossain, A., Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data, Computational statistics and data analysis, 38, 301-314, 2002.

Kohansal, A., & Shoaee, S., Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data, Statistical Papers, 1-51. 2019.

Kundu, D., & Joarder, A., Analysis of Type-II progressively hybrid censored data, Computational Statistics & Data Analysis, 50(10), 2509-2528, 2006.

Lindley, D. V., Approximate bayesian methods, Trabajos de estad´ıstica y de investigacion operativa, 31(1), 223-245, 1980. ´

Lomax, K., Business failures. Another example of the analysis of failure data, J. Amer. Statist. Assoc. 49, 847-852. 1954.

Nassar, M., Abo-Kasem, O., Zhang, C., & Dey, S., Analysis of Weibull distribution under adaptive type-II progressive hybrid censoring scheme, Journal of the Indian Society for Probability and Statistics, 19(1), 25-65, 2018.

Ng, Hon Keung Tony, Debasis Kundu, and Ping Shing Chan, Statistical analysis of exponential lifetimes under an adaptive Type-II, progressive censoring scheme.” Naval Research Logistics (NRL) 56, no. 8: 687-698, 2009.

Norstrom, J. G., The use of precautionary loss functions in risk analysis, IEEE Transactions on reliability, 45(3), 400-403, 1996.

Panahi, H., Estimation methods for the generalized inverted exponential distribution under type ii progressively hybrid censoring with application to spreading of micro-drops data, Communications in Mathematics and Statistics, 5(2), 159-174, 2017.

Panahi, H., & Asadi, S., On adaptive progressive hybrid censored Burr type III distribution: application to the nano droplet dispersion data, Quality Technology & Quantitative Management, 18(2), 179-201, 2021.

Simpson J., Use of the gamma distribution in single-cloud rainfall analysis, MonthlyWeather Rev., 100:309–312, 1972.

Varian, H. R., A Bayesian approach to real estate assessment, Studies in Bayesian econometric and statistics in Honor of Leonard J. Savage, 195-208, 1975.

Wang, L., Inference for Weibull competing risks data under generalized progressive hybrid censoring, IEEE Transactions on Reliability, 67(3), 998-1007, 2018.

Yan, Z., & Wang, N., Statistical analysis based on adaptive progressive hybrid censored sample from alpha power generalized exponential distribution, IEEE Access, 8, 54691-54697, 2020.

Ye, Z. S., Chan, P. S., Xie, M., & Ng, H. K. T. Statistical inference for the extreme value distribution under adaptive Type-II progressive censoring schemes, Journal of Statistical Computation and Simulation, 84(5), 1099-1114, 2014.

Zellner, A., On assessing prior distributions and Bayesian regression analysis with g-prior distributions, Bayesian inference and decision techniques, 1986.

Zheng, G., & Shi, Y. M., Statistical analysis in constant-stress accelerated life tests for generalized exponential distribution based on adaptive type-II progressive hybrid censored data, Chinese Journal of Applied Probability and Statistics, 29(4), 363-80, 2013.

How to Cite
Helu, A., & Hani Samawi. (2021). Statistical Analysis Based on Adaptive Progressive Hybrid Censored Data From Lomax Distribution. Statistics, Optimization & Information Computing, 9(4), 789-808.
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