Abstract
The Lomax distribution (Pareto Type-II) is widely applicable in reliability and life testing problems in engineering as well as in survival analysis as an alternative distribution. In this paper, Weighted Lomax distribution is proposed and studied. The density function and its behavior, moments, hazard and survival functions, mean residual life and reversed failure rate, extreme values distributions and order statistics are derived and studied. The parameters of this distribution are estimated by the method of moments and the maximum likelihood estimation method and the observed information matrix is derived. Moreover, simulation schemes are derived. Finally, an application of the model to a real data set is presented and compared with some other well-known distributions.
Highlights
Weighted distribution theory gives a unified approach to dealing with model specification and data interpretation problems
Weighted distributions occur frequently in studies related to reliability, survival analysis, analysis of family data, biomedicine, ecology and several other areas, see Stene (1981) and Oluyede and George (2002)
Statistical applications of weighted distributions related to human population and ecology can be found in Patil and Rao (1978)
Summary
Weighted distribution theory gives a unified approach to dealing with model specification and data interpretation problems. Weighted distributions occur frequently in studies related to reliability, survival analysis, analysis of family data, biomedicine, ecology and several other areas, see Stene (1981) and Oluyede and George (2002). Many authors have presented important results on weighted distributions, Rao (1965) introduced a unified concept of weighted distribution and identified various sampling situations that can modeled by weighted distributions. These situations occur when the recorded observations can not be considered as a random sample from the original distributions. Patil and Ord (1976) studied a size biased sampling and related invariant weighted distributions. Statistical applications of weighted distributions related to human population and ecology can be found in Patil and Rao (1978). Statistical applications of weighted distributions related to human population and ecology can be found in Patil and Rao (1978). Gupta and Tripathi (1996) studied the weighted version of the bivariate logarithmic series distribution, which has applications in many fields such as: ecology, social and behavioral sciences
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