The McDonald exponentiated gamma distribution and its statistical properties

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Existing lifetime models like beta exponentiated gamma, Kumaraswamy exponentiated gamma, and exponentiated gamma have limitations.
• There is a need for more flexible and comprehensive lifetime distributions in statistical modeling.

Purpose of the Study:

• To propose a novel five-parameter lifetime model: the McDonald exponentiated gamma distribution.
• To provide a thorough mathematical investigation of the proposed distribution's properties.
• To explore parameter estimation methods for the new distribution.

Main Methods:

• Mathematical derivation of the moment generating function and rth moment.
• Application of maximum likelihood estimation for parameter estimation.
• Construction of the information matrix for statistical inference.

Main Results:

• The McDonald exponentiated gamma distribution is mathematically defined and its key properties are derived.
• The moment generating function and rth moment are obtained.
• Maximum likelihood estimators for the model parameters are discussed, along with the information matrix.

Conclusions:

• The McDonald exponentiated gamma distribution offers a flexible extension to existing gamma-based lifetime models.
• The derived mathematical properties and estimation methods provide a foundation for its application in statistical analysis.
• This new distribution has potential applications in reliability and survival analysis where complex lifetime behaviors are observed.