Abstract
We study a three-parameter generalized Lomax distribution. Several structural and statistical properties such as quantiles, moments, order statistic and stochastic ordering have been investigated. Different estimators of unknown quantities of interest are derived from maximum likelihood and Bayesian approaches. We have computed Bayes estimators from the Tierney and Kadane method. Interval estimates are also discussed. Performance of all methods is compared using a simulation study. Illustrative discussion of a real data is presented as well. Finally, some concluding remarks are given.
Similar content being viewed by others
References
Abdul-Moniem I, Seham M (2015) Transmuted gompertz distribution. Comput Appl Math J 1(3):88–96
Andrews DF, Herzberg AM (2012) Data: a collection of problems from many fields for the student and research worker. Springer, Berlin
Azzalini A (1985) A class of distributions which includes the normal ones. Scand J Stat 12:171–178
Box GE, Cox DR (1964) An analysis of transformations. J R Stat Soc Ser B (Methodol) 26:211–252
Chen M-H, Shao Q-M (1999) Monte carlo estimation of bayesian credible and hpd intervals. J Comput Graph Stat 8(1):69–92
Elbatal I (2013) Kumaraswamy generalized linear failure rate distribution. Indian J Comput Appl Math 1:61–78
Gupta RD, Kundu D (1999) Theory & methods: generalized exponential distributions. Aust N Z J Stat 41(2):173–188
Gupta RD, Kundu D (2009a) Introduction of shape/skewness parameter(s) in a probability distribution. J Probab Stat Sci 7(2):153–171
Gupta RD, Kundu D (2009b) A new class of weighted exponential distributions. Statistics 43(6):621–634
Howlader HA, Hossain AM (2002) Bayesian survival estimation of pareto distribution of the second kind based on failure-censored data. Comput Stat Data Anal 38(3):301–314
Kundu D, Gupta AK (2014) On bivariate weibull-geometric distribution. J Multivar Anal 123:19–29
Mäkeläinen T, Schmidt K, Styan GP (1981) On the existence and uniqueness of the maximum likelihood estimate of a vector-valued parameter in fixed-size samples. Ann Stat 9(4):758–767
Rastogi MK, Tripathi YM (2013) Estimation using hybrid censored data from a twoparameter distribution with bathtub shape. Comput Stat Data Anal 67:268–281
Rodrigues J, Balakrishnan N, Cordeiro GM, de Castro M (2011) A unified view on lifetime distributions arising from selection mechanisms. Comput Stat Data Anal 55(12):3311–3319
Sarhan AM, Kundu D (2009) Generalized linear failure rate distribution. Commun Stat Theory Methods 38(5):642–660
Shaked M, Shanthikumar JG, Valdez-Torres JB (1994) Discrete probabilistic orderings in reliability theory. Stat Sin 4:567–579
Tierney L, Kadane JB (1986) Accurate approximations for posterior moments and marginal densities. J Am Stat Assoc 81(393):82–86
Xie M, Tang Y, Goh TN (2002) A modified weibull extension with bathtub-shaped failure rate function. Reliab Eng Syst Saf 76(3):279–285
Acknowledgements
We appreciate reviewers for encouraging comments which have led to substantial improvements in content and presentation of the paper. We thank the Editor for their constructive comments to improve our manuscript.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix
Appendix
1.1 Program for MLEs
Rights and permissions
About this article
Cite this article
Maurya, R.K., Tripathi, Y.M., Lodhi, C. et al. On a generalized Lomax distribution. Int J Syst Assur Eng Manag 10, 1091–1104 (2019). https://doi.org/10.1007/s13198-019-00839-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13198-019-00839-0