Ahmad Aijaz , S. Qurat ul Ain , Ahmad Afaq , Rajnee Tripathi

© A. Aijaz, S. Qurat ul Ain, A. Afaq, R. Tripathi. Article available under the CC BY-SA 4.0 licence


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In this paper, a new Poisson area-biased Ailamujia distribution has been formulated to analyse count data. It was created by combining two distributions: the Poisson and areabiased Ailamujia distributions, using the compounding technique. Several distributional properties of the formulated distribution were studied. Its ageing characteristics were determined and expressed explicitly. A variety of diagrams were used to demonstrate the characteristics of the probability mass function (pmf) and the cumulative distribution function (cdf). The parameter of the developed model was estimated by employing the maximum likelihood estimation approach. Finally, two data sets were used to demonstrate the effectiveness of the investigated distribution.


compound technique, Poisson distribution, area-biased Ailamujia distribution, reliability analysis, order statistics, maximum likelihood estimator.


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