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The use of statistical distributions to model life phenomena has received a great deal of attention in various sciences. Recent studies have shown the possibility of statistical distributions in data modeling in applied sciences, especially in environmental sciences. Among them is the inverse Weibull distribution, which is one of the most common statistical models that can be used very effectively in modeling data in the health, engineering, and environmental fields, as well as other fields. This study proposes to present a new generalization for the inverse Weibull distribution, where two new parameters are added to the basic distribution according to the Odd Lomax-G family so that the new generalization is more modern and flexible with real-world data. It is called the Odd Lomax Inverse Weibull (LoIW) distribution. The OLIW distribution comes with an expansion of its pdf and CDF functions by using binomial series, exponential, and Logarithm expansions with many statistical properties such as (Rényi entropy, moments, skewness, kurtosis with the moments generating function (mgf), ordered statistics, as well as the Quantile function), and the four distribution parameters are estimated using the maximum likelihood function (MLEs). To ensure the robustness of the proposed model, a practical application is conducted using the R language on two different types of real data and compared with many other statistical models.
Khalaf et al. (Fri,) studied this question.