Cubic rank transmuted generalized Gompertz distribution: properties and applications

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• Existing lifetime distributions, such as generalized Gompertz and its modified versions, have limitations.
• There is a need for alternative distributions with desirable statistical properties for modeling.
• The cubic rank transmutation family provides a framework for developing new distributions.

Purpose of the Study:

• To introduce and characterize a new lifetime distribution.
• To explore its statistical properties, including hazard function, moments, and quantile function.
• To investigate parameter estimation methods and compare their performance.

Main Methods:

• The new distribution is derived as a special case of the cubic rank transmuted family.
• Key statistical properties are mathematically derived.
• Three distinct parameter estimation techniques are discussed and evaluated using Monte Carlo simulations.

Main Results:

• The proposed distribution exhibits useful characteristic properties.
• Monte Carlo simulations assess the performance of different estimation methods based on mean square errors and biases.
• The distribution's applicability is demonstrated through three real-world data analyses.

Conclusions:

• The newly proposed lifetime distribution serves as a viable alternative to existing models.
• The study provides a thorough analysis of its properties and estimation methods.
• The distribution shows practical relevance and usefulness in applied statistical modeling.