Abstract
In this paper, we are concerned with the situations, where sometimes value two is reported erroneously as one in relation to size biased generalized negative binomial distribution (SBGNBD) with probability ����. We have obtained the Maximum likelihood estimator and Bayes estimator under general entropy loss function. A simulated study is carried out to access the performance of the maximum likelihood estimators and Bayes estimators. Also comparison has been made between maximum likelihood estimator and Bayes estimator.
Highlights
IntroductionIt can be seen that variance is always greater than mean. This type of model was used to represent ‘accident-proneness’ by Greenwood and Yule (1920)
Pascal defined the negative binomial distribution as PP[XX = xx] mm + xx xx − θθxx (1 θθ)mm (1.1)xx = 0, 1, 2, ... ....Where 0 < θθ < 1, mm > 0The mean and variance of the distribution are given as EE(XX) = μμ1′
When the sampling mechanism selects units with probability proportional to some measure of the unit size, the resulting distribution is called size – biased. Such distributions arise in the life length and were studied by various authors. (see Gupta (1979, 1984), Gupta &
Summary
It can be seen that variance is always greater than mean. This type of model was used to represent ‘accident-proneness’ by Greenwood and Yule (1920). When the sampling mechanism selects units with probability proportional to some measure of the unit size, the resulting distribution is called size – biased. Such distributions arise in the life length and were studied by various authors. The resulting distribution of X based on (1.5) is called misclassified size-biased generalized negative binomial distribution (MSBGNBD), which can be written in the form. Under the different choice of the parameters of MSBGNBD, the graphs of the probability distribution are given below. This distribution is considered by Hassan and Ahmad (2009).
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