New Modified Generalized Inverted Exponential Distribution and Its Applications

Area of Science:

• Statistics
• Probability Theory
• Mathematical Modeling

Background:

• The need for flexible statistical distributions in data analysis.
• Limitations of existing distributions in capturing complex data patterns.

Purpose of the Study:

• To introduce and define a novel three-parameter statistical model: the New Modified Generalized Inverted Exponential (MGIE) distribution.
• To derive key statistical properties of the MGIE distribution, including its quantile function, median, moments, mode, mean deviation, harmonic mean, reliability, hazard and odds functions, and Rényi entropy.
• To investigate parameter estimation for the MGIE distribution using the maximum likelihood estimation method.

Main Methods:

• Theoretical derivation of statistical characteristics for the proposed MGIE distribution.
• Application of the maximum likelihood estimation (MLE) technique for parameter estimation.
• Monte Carlo simulation study to evaluate the performance and behavior of the MGIE distribution's parameters.
• Validation using three real-world data sets.

Main Results:

• The paper successfully defines the New Modified Generalized Inverted Exponential (MGIE) distribution and derives its comprehensive statistical properties.
• Maximum likelihood estimators for the MGIE distribution parameters were obtained.
• Simulation results demonstrated the practical behavior of the MGIE distribution's parameters.
• Application to real data sets confirmed the utility and importance of the proposed MGIE distribution.

Conclusions:

• The New Modified Generalized Inverted Exponential (MGIE) distribution is a statistically sound and flexible model.
• The proposed distribution and its associated estimation methods are effective for analyzing real-world data.
• The MGIE distribution offers a valuable addition to the repertoire of statistical distributions for applied researchers.