Abstract
In this paper we define the Mid-Truncated Burr XII distribution and derive some of its statistical properties such as moments, moment generating function, characteristic function, likelihood function, etc. We have also obtained the recurrence relations for single and product moments of order statistics in a random sample of size n drawn from Mid-Truncated Burr XII distribution. Further, the characterization of mid truncated distribution using conditional moments has been given.
Highlights
Many authors like Malik [10], Balakrishnan and Joshi [1], Balakrishnan et al [2], Saran and Pushkarna [17, 18, 19], etc. have obtained several results for the single and product moments of order statistics from the un-truncated, left truncated, right truncated and doubly truncated distributions
Mohie El-Din et al [11] have obtained moment generating functions of order statistics from doubly truncated exponential distribution in terms of hypergeometric function. They have derived some recurrence relations between these moment generating functions.The truncated distributions are quite effectively used where a random variable is restricted to be observed on some range and these situations are common in various fields
We propose to consider the mid-truncated Burr distribution (MTBD) (Type XII) with three parameters, which contains, as special sub models, mid-truncated Weibull distribution, mid-truncated exponential distribution, mid-truncated log-logistic distribution, among others
Summary
Many authors like Malik [10], Balakrishnan and Joshi [1], Balakrishnan et al [2], Saran and Pushkarna [17, 18, 19], etc. have obtained several results for the single and product moments of order statistics from the un-truncated, left truncated, right truncated and doubly truncated distributions. Mohie El-Din and Sultan [12] have obtained recurrence relations for moments of order statistics from doubly truncated continuous distributions They have presented some applications of their results. Mohie El-Din et al [11] have obtained moment generating functions of order statistics from doubly truncated exponential distribution in terms of hypergeometric function They have derived some recurrence relations between these moment generating functions.The truncated distributions are quite effectively used where a random variable is restricted to be observed on some range and these situations are common in various fields. After the stationary phase the most bacterial cells will die because of the exclusion of nutrients and lead to accumulation of waste products In such live models mid-truncated distributions are quite effectively used where the random variable is restricted. Due to the flexibility of the considered distribution in accommodating different forms of risk function, this MTBD is appropriate for a variety of problems modelling lifetime data
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