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Al-azhar University, Faculty of commerce, Statistics Department
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Al-azhar university , faculty of commerce,,statistics department
10.21608/cfdj.2025.435647.2401
المستخلص
This research investigates four distinct techniques for estimating parameters of the Gompertz Lomax (GL) distribution. It employs both full sample data and Maximum Likelihood Estimation (MLE) under two forms of censoring, denoted as type-I and type-II. The performance of these estimators is evaluated by analyzing their squared biases and variances using Monte Carlo simulation methods. Furthermore, the study offers a detailed examination of the distribution’s ordinary moments and its quantile function. The Lomax distribution—also known as the shifted Pareto or Pareto Type II—was originally introduced by Lomax in 1954 [11] to analyze patterns in business failure data. Since then, it has found widespread use across diverse domains, including economics (e.g., income and wealth disparity), engineering, healthcare, biological research, and survival analysis. This distribution can be described through multiple formulations. It represents a specific instance of the Pearson Type VI distribution and can also be interpreted as a hybrid of the exponential and gamma distributions. Despite its versatility, the Lomax model is not well-suited for datasets exhibiting non-monotonic hazard functions, such as those with bathtub-shaped or inverted bathtub failure rates—patterns frequently observed in biological and survival studies. Mathematically, the probability density function (PDF) of the Lomax distribution is defined using two parameters: the shape parameter α and the scale parameter β. There is a growing demand for generalized versions of the Lomax distribution across numerous practical disciplines. This study expands on earlier investigations within this field.
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