Parameter estimation of the hybrid censored log-normal distribution

Abstract

The two most common censoring schemes used in life testing experiments are Type-I and Type-II censoring schemes. Hybrid censoring scheme is mixture of Type-I and Type-II censoring scheme. In this work we consider the estimation of parameters of log-normal distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method. It is observed that the maximum likelihood estimates can not be obtained in closed form. We obtain the maximum likelihood estimates of the unknown parameters using EM algorithm. We also propose approximate maximum likelihood estimates and these can be used as initial estimates for any iterative procedure. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. The method of obtaining optimum censoring scheme is discussed. One data set is analyzed for illustrative purposes.

Generalized inverted exponential distribution under hybrid censoring

“…It is clear that the optimum values cannot be obtained analytically, we need to find it numerically. The algorithm proposed by Dube et al [8] can be used for obtaining the optimum solution. For illustration, we consider an example with α = 1.5, λ = 1, C 1 = 15, C 2 = 30 and C 0 = 250.…”

“…Then the question arises, how do we choose the values of the decision parameters (n, r and T 0 ) of the experiment. In this work we choose the decision parameters of the life testing experiment such that the information on unknown parameters is maximum subject to some constraint using the idea of Dube et al [8]. In most of the practical situations, the obvious restrictions are on time and on the number of items used.…”

“…Also, in an industrial set-up, the management put some restrictions on cost. We use the cost function approach similar as in [19,23,8]. Let C 1 and C 2 be the cost per unit time and item respectively on the experiment.…”

“…Some early work on hybrid censoring can be found in [11,7,4]. Some recent studies on hybrid censoring have been carried out by many authors including Jeong et al [14], Gupta and Kundu [12], Childs et al [5], Kundu [16], Banerjee and Kundu [3], Kundu and Pradhan [18], Dube et al [8] and Balakrishnan and Kundu [2].…”

“…Recently, much attention has been given towards finding the optimal censoring schemes in the context of different censoring schemes. See for example, [26,30,16,29,18,8]. Finding the optimum censoring scheme is an important practical problem in many industrial applications.…”