%0 Journal Article
%T On Parameters Estimation of Lomax Distribution under General Progressive Censoring
%A Bander Al-Zahrani
%A Mashail Al-Sobhi
%J Journal of Quality and Reliability Engineering
%D 2013
%R 10.1155/2013/431541
%X We consider the estimation problem of the probability for Lomax distribution based on general progressive censored data. The maximum likelihood estimator and Bayes estimators are obtained using the symmetric and asymmetric balanced loss functions. The Markov chain Monte Carlo (MCMC) methods are used to accomplish some complex calculations. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation study. 1. Introduction The Lomax distribution, also called ¡°Pareto type II¡± distribution is a particular case of the generalized Pareto distribution (GPD). The Lomax distribution has been used in the literature in a number of ways. For example, it has been extensively used for reliability modelling and life testing; see, for example, Balkema and de Haan [1]. It also has been used as an alternative to the exponential distribution when the data are heavy tailed; see Bryson [2]. Ahsanullah [3] studied the record values of Lomax distribution. Balakrishnan and Ahsanullah [4] introduced some recurrence relations between the moments of record values from Lomax distribution. The order statistics from nonidentical right-truncated Lomax random variables have been studied by Childs et al. [5]. Also, the Lomax model has been studied, from a Bayesian point of view, by many authors; see, for example, Arnold et al. [6] and El-Din et al. [7]. Howlader and Hossain [8] presented Bayesian estimation of the survival function of the Lomax distribution. Ghitany et al. [9] considered Marshall-Olkin approach and extended Lomax distribution. Cramer and Schmiedt [10] considered progressively type-II censored competing risks data from Lomax distribution. The Lomax distribution has applications in economics, actuarial modelling, queuing problems and biological sciences; for details, we refer to Johnson et al. [11]. A positive random variable is said to have the Lomax distribution, abbreviated as , if it has the probability density function (pdf) Here, and are the shape and the scale parameters, respectively. The survival function (sf) associated with (1) is Further probabilistic properties of this distribution are given, for example, in Arnold [12]. This paper is concerned with the problem of estimating for Lomax based on general progressive censored data. The reliability of a component during a given period of time is defined as the probability that its strength exceeds the stress , and symbolically we write . We assume and to be independent, and each follows a Lomax distribution. A good overview on estimating can be found in the monograph of Kotz
%U http://www.hindawi.com/journals/jqre/2013/431541/