Abstract
In this paper, a weighted version of the power Lomax distribution referred to the weighted power Lomax distribution, is introduced. The new distribution comprises the length biased and the area biased of the power Lomax distribution as new models as well as containing an existing model as the length biased Lomax distribution as special model. Essential distributional properties of the weighted power Lomax distribution are studied. Maximum likelihood and maximum product spacing methods are proposed for estimating the population parameters in cases of complete and Type-II censored samples. Asymptotic confidence intervals of the model parameters are obtained. A sample generation algorithm along with a Monte Carlo simulation study is provided to demonstrate the pattern of the estimates for different sample sizes. Finally, a real-life data set is analyzed as an illustration and its length biased distribution is compared with some other lifetime distributions.
Highlights
Weighted distributions (WDs)are handled in studies associated with reliability, biomedicine, meta-analysis, econometrics, survival analysis, renewal processes, physics, ecology and branching processes which are found in Zelen and Feinleib (1969), Patil and Ord (1976), Patil and Rao (1978), Gupta and Keating (1986), Oluyede
In view of the importance of the power Lo (PLo) distribution as well as the idea of the WD, we introduce a weighted version of the PLo distribution called the weighted PLo (WPLo) distribution
We give up with a numerical study to assess the attitude of the maximum likelihood (ML) and maximum product spacing (MPS) estimates of the WPLo distribution and their length biased version based on complete sample and type II censoring (TIIC) scheme
Summary
Weighted distributions (WDs)are handled in studies associated with reliability, biomedicine, meta-analysis, econometrics, survival analysis, renewal processes, physics, ecology and branching processes which are found in Zelen and Feinleib (1969), Patil and Ord (1976), Patil and Rao (1978), Gupta and Keating (1986), Oluyede (1999) and references therein These distributions arise in practice when observations from a sample are recorded with unequal probabilities. Weighted Power Lomax Distribution and its Length Biased Version: Properties and Estimation Based on Censored Samples problems (Corbellini et al (2010)) and reliability modelling and life testing (Hassan and Al-Ghamdi (2009) and Hassan et al (2016)).
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