Although the maximum likelihood estimation method based on progressively censored data has been studied extensively, traditionally the Newton-Raphson method has been used to obtain the estimates (Ng et al., 2002). As pointed out by Little and Rubin in 1983, the EM algorithm will converge reliably but rather slowly (as compared to the Newton-Raphson method) when the amount of information in the missing data is relatively large. Therefore, in this study, maximum likelihood estimates for the parameters of the Loglogistic distribution are obtained using the EM algorithm based on a progressive Type-II right censored sample. An illustrative example is also given.
In this paper, a new discrete distribution called Binomial-Discrete Lindley (BDL) distribution is proposed by compounding the binomial and discrete Lindley distributions. Some properties of the distribution are discussed including the moment generating function, moments and hazard rate function. The estimation of distribution parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the di¤erent estimates in terms of bias and mean square errors. Automobile claim data applications are also presented to see that the new distribution is useful in modelling data.
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