article · Journal of Radiation Research and Applied Sciences
Counting data plays a vital role across real-world transactions, requiring statistical models to interpret patterns and extract useful insights. A new statistical tool called the Poisson quasi-XLindley distribution offers a novel two-parameter discrete framework for analysing such information. The mathematical characteristics of this model have been examined in detail, covering its mode, moments, survival and hazard functions, dispersion behaviour, order statistics, and Shannon entropy. To calibrate the model, parameters are estimated using the maximum likelihood approach, with the performance of these estimators confirmed through simulation studies. The distribution has been tested on two practical datasets alongside the introduction and application of a corresponding count regression model.
Real-world observations often involve count data, which requires accurate mathematical distributions to understand risks, failure rates, and trends. By offering a flexible new model with proven mathematical properties, analysts can more reliably interpret complex datasets where standard models may fall short.
This work represents early-stage theoretical and applied statistical research. It provides data analysts and quantitative researchers with an additional tool for modelling count data and regression relationships, though the abstract does not indicate a specific commercial product or direct industry application pathway.
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In real-world transactions, counting data plays a crucial role. To gain a deeper understanding of this data and extract important information, statistical analysis, and modeling are necessary. This paper introduces the Poisson quasi-XLindley distribution, a novel two-parameter discrete distribution. Various mathematical characteristics of this discrete model are investigated, including mode, survival, and hazard functions, the shape of the probability mass function and failure rate (hazard function), moments, dispersion behavior, order statistics, and Shannon entropy. The parameters are estimated using the maximum likelihood approach. A simulation study is conducted to evaluate the effectiveness of the derived maximum likelihood estimators. The proposed distribution is applied to two practical datasets. Additionally, a count regression model is introduced for this distribution and applied.
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DOI: 10.1016/j.jrras.2024.100874
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