IJPAM: Volume 52, No. 2 (2009)

INFERENCE AND PREDICTION FOR A GENERALIZED
EXPONENTIAL DISTRIBUTION BASED ON
THE $k$-TH LOWER RECORDS

Iwona Malinowska$^1$, Dominik Szynal$^2$
$^1$Department of Mathematics
Lublin University of Technology
38a, Nadbystrzycka, Lublin, 20-618, POLAND
e-mail: [email protected]
$^2$Institute of Mathematics
Maria Curie-Sk\lodowska University
1, Pl. M. Curie-Sk\lodowskiej, Lublin, 20-031, POLAND
e-mail: [email protected]


Abstract.The minimum variance unbiased estimator (MVU estimator), the maximum likelihood estimator (ML estimator) and the Bayesian estimator for the parameter of the generalized exponential distribution are obtained based on $k$-th lower record values. The Bayes estimators are obtained using the symmetric loss functions: squared error, squared log error and Kullback-Leibler divergence type loss function (KLD) and the asymmetric loss functions: LINEX, General Entropy and Modified General Entropy (MGE) loss function. Interval prediction for future $k$-th lower record values is also presented from a Bayesian point of view. Numerical computations are given to illustrate these procedures.

Received: March 3, 2009

AMS Subject Classification: 62F10, 62F15, 62G32

Key Words and Phrases: generalized exponential distribution, minimum variance estimators, maximum likelihood estimators, Bayes estimators, $k$-th record values, LINEX loss function, general entropy loss function, modified general entropy, Kullback-Leibler divergence, prediction

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 2