DOI: 10.12688/f1000research.172479.1 ISSN: 2046-1402

New Extension of Inverse Burr-X Distribution: Structural Properties, Simulations, and Applications (Carbon Fibers and Leukemia Patient Data)

Qasim Husain, Alaa Dedaa, Nooruldeen A. Noori
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Abstract* This paper presents a new statistical distribution, the Enhanced Gompertz Inverse Burr-X (EGIBX) distribution, which combines the properties of the Enhanced Gompertz family with those of the base Inverse Burr-X distribution. The general form of the probability density function (pdf ) and cumulative distribution function (CDF) are presented, along with other basic functions such as hazard and survival. Some mathematical properties of EGIBX are analyzed, including instantaneous values, skewness, and kurtosis, and the probabilistic behavior of functions is studied. Monte Carlo simulation is used to evaluate the performance of three parameter estimation methods and compare their effectiveness in small and large samples. The distribution is applied to real data, including breaking stress of carbon fibers (in GPa) and data from 40 leukemia patients from a Ministry of Health hospital in KSA. The efficiency and flexibility of EGIBX are verified by comparing the proposed distribution with six other distributions, proving its efficiency and superiority. This superiority was measured using four information criteria (AIC, BIC, CAIC, HQIC) and four Goodness-of-Fit measures. The outcomes indicated that the designed distribution maintains a robust degree of flexibility in its statistical representation and provides a greater accuracy of fit relative to the other competing distributions.

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