Inference Based on k-Record Values from Generalized Exponential Distribution


  • Manoj Chacko University of Kerala
  • Laji Muraleedharan University of Kerala



k-record values, Bayesian estimation, MCMC method, Prediction interval


In this paper, the lower k-record values arising from a two parameter generalized exponential distribution is considered. The maximum likelihood estimators for the shape parameter and scale parameter are obtained. The Bayes estimates of the parameters are also developed by using Markov chain Monte Carlo method under symmetric and asymmetric loss functions. Finally, a simulation study is performed to find the performance of different estimators developed in this paper.


J. AHMADI, M. DOOSTPARAST (2006). Bayesian estimation and prediction for some life distributions based on record values. Statistical Papers, 47, pp. 373–392.

J. AHMADI, M. DOOSTPARAST (2005). Estimation and prediction in a two parameter exponential distribution based on k-record values under LINEX loss function. Communications in Statistics - Theory and Methods, 34, pp. 795–805.

J. AHMADI, M. DOOSTPARAST (2008). Statistical inference based on k-records. Mashhad Research Journal of Mathematical Sciences, 1, pp. 67–82.

M. AHSANULLAH (1995). Record Statistics. Nova Science Publishers, New York.

B. C. ARNOLD, N. BALAKRISHNAN, H. N. NAGARAJA (1998). Records. Wiley, New York.

N. BALAKRISHNAN, P. S. CHAN (1998). On the normal record values and associated inference. Statistics and Probability Letters , 39, pp. 73–80.

M. CHACKO, S. M. MARY (2013a). Estimation and prediction based on k-record values from normal distribution. Statistica, 73, no. 4, pp. 505–516.

M. CHACKO, S. M. MARY (2013b). Concomitants of k-record values arising from Morgenstern family of distributions and its applications in parameter estimation. Statistical Papers, 54, pp. 21–46.

K. N. CHANDLER (1952). The distribution and frequency of record values. Journal of the Royal Statistical Society: Series B, 14, pp. 220–228.

S. CHIB, E. GREENBERG (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49, pp. 327–335.

W. DZIUBDZIELA, B. KOPOCINSKI (1976). Limiting properties of the k-th record values. Zastosowania Matematyki, 15, pp. 187–190.

R. D. GUPTA, D. KUNDU (1999). Generalizd exponential distribution. Australian and New Zealand Journal of Statistics, 41, pp. 173–188.

F. KIZILASLAN, M.NADAR (2015). Estimation with the generalized exponential distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation, 85, pp. 978–999.

M. T. MADI, M. Z. RAQAB (2007). Bayesian prediction of rainfall records using the generalized exponential distribution. Environmetrics, 18, pp. 541-549.

S. M.MARY, M. CHACKO (2010). Estimation of parameters of uniform distribution based on k-record values. Calcutta Statistical Association Bulletin, 62, pp. 143–158.

I. MALINOWSKA, D. SZYNAL (2004). On a family of Bayesian estimators and predictors for Gumbel model based on the k-th lower records. Applied Mathematics, 31, pp. 107–115.

J. PAUL, P. Y. THOMAS (2015). On generalized upper(k) record values from Weibull distribution. Statistica, 75, no. 3, pp. 313–330.

M. RAQAB (2002). Inference for generalized exponential distribution based on record statistics. Journal of Statistical Planning and Inference, 104, pp. 339–350.

G. O. ROBERTS, J. S. ROSENTHAL (2009). Examples of adaptive MCMC. Journal of Computational and Graphical Statistics, 18, pp. 349–367.

K. S. SULTAN, M. E.MOSHREF,A.CHILDS (2002).Record values from generalized power function distribution and associated inference. Journal of Applied Statistical Science, 11, pp. 143–156.




How to Cite

Chacko, M., & Muraleedharan, L. (2018). Inference Based on k-Record Values from Generalized Exponential Distribution. Statistica, 78(1), 37–56.