Bayesian Analysis of Record Statistics Based on Generalized Inverted Exponential Model

Amal S. Hassan, Marwa Abd-Allah, Heba F. Nagy


In some situations, only observations that are more extreme than the current extreme value are recorded. This kind of data is called record values which have many applications in a lot of fields. In this paper, the Bayesian estimators using squared error and LINEX loss functions for the generalized inverted exponential distribution parameters are considered depending on upper record values and upper record ranked set sampling. The Bayes estimates and credible intervals are derived by considering the independent gamma priors for the parameters. The Markov Chain Monte Carlo (MCMC) method is developed due to the lack of explicit forms for the Bayes estimates. A Simulation study is implemented to compute and compare the performance of estimators in both sampling schemes with respect to relative absolute biases, estimated risks and the width of credible intervals.


upper record ranked set sample; Bayesian estimator; squared error (SE) loss function; linear exponential (LINEX) loss function; Markov Chain Monte Carlo

Full Text:



K. N. Chandler, “The distribution and frequency of record values,†Journal of the Royal Statistical Society, vol. 14(2), pp. 220-228, 1952.

H. N. Nagaraja, “Record values and related statistics - a review,†Communications in Statistics - Theory and Methods, vol. 17(7), pp. 2223-2238, 1988.

B. C. Arnold, N. Balakrishnan, and H. N. Nagaraja, Records, ser. Wiley series in probability and statistics, Canada: John Wiley & Sons, Inc., 1998.

M. Ahsanullah and V. B. Nevzorov, Records via probability theory, ser. Atlantis studies in probability and statistics, Tampa, USA: Atlantis Press, 2015, vol. 6.

M. Salehi and J. Ahmadi, “Record ranked set sampling scheme,†Metron, vol. 72(3), pp. 351-365, 2014.

M. A. M. Ali Mousa, Z. F. Jaheen and A. A. Ahmad, “Bayesian estimation, prediction and characterization for the Gumbel model based on records,†Statistics: A Journal of Theoretical and Applied Statistics, vol. 36(1), pp. 65-74, 2002.

Z. F. Jaheen, “A Bayesian analysis of record statistics from the Gompertz model,†Applied Mathematics and Computation, vol. 145( 2-3), pp. 307-320, 2003.

M. Doostparast and J. Ahmadi, “Statistical analysis for geometric distribution based on records,†Computers & Mathematics with Applications, vol. 52(6-7), pp. 905-916, 2006.

A. A. Soliman and F. M. Al-Aboud, “Bayesian inference using record values from Rayleigh model with application,†European Journal of Operational Research, vol. 185(2), pp. 659-672, 2008.

A. Baklizi, “Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution,†Computational Statistics & Data Analysis, vol. 52(7), pp. 3468-3473, 2008.

M. D. Habib, A. M. Abd-Elfattah and M. A. Selim, “Bayesian and Non-Bayesian estimation for exponentiated-Weibull distribution based on record values,†The Egyptian Statistical Journal, vol. 54(2), pp. 47-59, 2010.

M. Nadar and A. S. Papadopoulos, “Bayesian analysis for the Burr type XII distribution based on record values,†STATISTICA, vol. 71(4), pp. 421-435, 2011.

M. Doostparast, M. G. Akbari and N. Balakrishna, “Bayesian analysis for the two-parameter Pareto distribution based on record values and times,†Journal of Statistical Computation and Simulation, vol. 81(11), pp. 1393-1403, 2011.

S. Dey and T. Dey, “Bayesian estimation of the parameter and reliability of a Rayleigh distribution using records,†Model Assisted Statistics and Applications, vol. 7(2012), pp. 81–90, 2012.

F. Kızılaslan and M. Nadar, “Classical and Bayesian analysis for the generalized exponential distribution based on record values and times,†Bilim ve Teknoloji Dergisi B-Teorik Bilim, vol. 2, pp. 111-120, 2013.

S. Dey, T. Dey, M. Salehi and J. Ahmadi, “Bayesian inference of generalized exponential distribution based on lower record values,†American Journal of Mathematical and Management Sciences, vol. 32(1), pp. 1-18, 2015.

R. M. El-Sagheer, “Bayesian estimation based on record values from exponentiated Weibull distribution: An Markov Chain Monte Carlo approach,†American Journal of Theoretical and Applied Statistics, vol. 4(1), pp. 26-32, 2015.

J. I. Seo and Y. Kim, “Bayesian inference on extreme value distribution using upper record values,†Communications in Statistics - Theory and Methods, vol. 46(15), pp. 7751-7768, 2016.

S. Dey, T. Dey, and D. J. Luckett, “Statistical inference for the generalized inverted exponential distribution based on upper record values,†Mathematics and Computers in Simulation, vol. 120, pp. 64-78, 2016.

Z. Khoshkhoo Amiri and S. M. T. K. MirMostafaee. “Estimation of the shape parameter of the weighted exponential distribution under the record ranked set sampling plan,†in Proc. Second Seminar on Reliability Theory and its applications, 2016, p. 115.

S. K. Singh, U. Singh and M. Kumar, “Estimation of parameters of generalized inverted exponential distribution for progressive type-II censored sample with binomial removals,†Journal of Probability and Statistics, vol. 2013, pp. 1-12, 2013.

A. M. Abouammoh and A. M. Alshingiti, “Reliability estimation of generalized inverted exponential distribution,†Journal of Statistical Computation and Simulation, vol. 79(11), pp. 1301-1315, 2009.



Published by INSIGHT - Indonesian Society for Knowledge and Human Development