Bayesian Analysis for Two Parameter Lomax Distribution Under Different Loss Functions
DOI:
https://doi.org/10.26713/cma.v13i1.1679Keywords:
Lomax distribution, Informative priors, Entropy loss function, Precautionary loss function, R softwareAbstract
Statistical analysis via Bayesian approach is a common practice applied to draw inference about unknown parameter(s) and reliability characteristics of the probability distribution. The article include Bayesian inference of unknown shape parameter of two-parameter Lomax distribution. An attempt has been made to obtain Bayes estimators by using extension of Jeffrey’s prior and Gamma prior under Entropy loss function and Precautionary loss function. Comparison has been made by using mean square error through simulation study with varying sample sizes.
Downloads
References
A. M. Abd-Elfattah and A. H. Alharbey, Estimation of Lomax parameters based on generalized probability weighted moment, The Journal of King Abdulaziz University: Science 22 (2010), 171 – 184, DOI: 10.4197/Sci.22-2.13.
A. Afaq, S. P. Ahmad and A. Ahmed, Bayesian Analysis of shape parameter of Lomax distribution under different loss functions, International Journal of Statistics and Mathematics 2 (2015), 55 – 65, DOI: 10.18576/jsapl/030105.
H. S. Al-Kutubi, on comparison estimation procedures for parameter and survival function, Iraqi Journal of Statistical Science 9 (2005), 1 – 14.
M. Aslam, An application of prior predictive distribution to elicit the prior density, Journal of Statistics Theory and Application 2 (2003), 183 – 197.
A. B. Atkinson and A. J. Harrison, Distribution of Personal Wealth in Britain, Cambridge University Press, Cambridge (1978).
R. Calabria and G. Pulcini, An engineering approach to Bayes estimation for the Weibull distribution, Microelectronics Reliability 34 (1994), 789 – 802, DOI: 10.1016/0026-2714(94)90004-3.
M. Chahkandi and M. Ganjali, On some lifetime distributions with decreasing failure rate, Journal of Computational Statistics and Data Analysis 53 (2009), 4433 – 4440, DOI: 10.1016/j.csda.2009.06.016.
P. H. Garthwaite and J. M. Dickey, Elicitation of prior distributions for variable-selection problems in regression, Annals of Statistics 20 (1992), 1697 – 1719, URL: https://www.jstor.org/stable/2242364.
A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari and D. Rubin, Bayesian Data Analysis, 3rd edition, Chapman and Hall/CRC, New York (2014), URL: https://statisticalsupportandresearch.files.wordpress.com/2017/11/bayesian_data_analysis.pdf.
W. Glänzel, On some new bibliometric applications of statistics related to the h-index, Scientometrics 77 (2008), 187 – 196, DOI: 10.1007/s11192-007-1989-0.
C. M. Harris, The Pareto distribution as a queue service discipline, Operations Research 16 (1968), 307 – 313, DOI: 10.1287/opre.16.2.307.
H. S. Lomax, Business failures: Another example of the analysis of failure data, Journal of the American Statistical Association 49 (1954), 847 – 852, DOI: 10.1080/01621459.1954.10501239.
P. Nasiri and S. Hosseini, Statistical inferences for Lomax distribution based on record values (Bayesian and Classical), Journal of Modern Applied Statistical Methods 11 (2012), 179 – 189, DOI: 10.22237/jmasm/1335845640.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.