A Gull Alpha Power Weibull distribution with applications to real and simulated data

Area of Science:

• Statistics
• Probability Theory

Background:

• Survival analysis and reliability engineering frequently encounter data with complex hazard rate behaviors.
• Existing distributions may not adequately capture both monotonic and non-monotonic hazard rate functions.

Purpose of the Study:

• To introduce a new flexible distribution family, the Gull Alpha Power Family of Distributions (GAPF).
• To propose a specific case, the Gull Alpha Power Weibull (GAPW) distribution, utilizing the Weibull distribution as a baseline.
• To demonstrate the utility of GAPF and GAPW in modeling diverse hazard rate behaviors.

Main Methods:

• Derivation of the general Gull Alpha Power Family of Distributions (GAPF).
• Specification of the Gull Alpha Power Weibull (GAPW) distribution as a special case.
• Mathematical derivation of key statistical properties for the proposed distributions.
• Parameter estimation using the Maximum Likelihood Estimation (MLE) method.

Main Results:

• The proposed GAPF and its special case GAPW can model both monotonic and non-monotonic hazard rates.
• Statistical properties of the new distributions were successfully derived.
• The Maximum Likelihood Estimation method provided effective parameter estimation.
• The distributions showed practical applicability on real-world lifetime data and simulated datasets.

Conclusions:

• The Gull Alpha Power Family of Distributions (GAPF), particularly the GAPW distribution, offers a valuable and flexible tool for survival analysis and reliability engineering.
• The proposed distributions are capable of modeling complex hazard rate functions, addressing limitations of existing models.
• Empirical validation using real and simulated data supports the practical utility and effectiveness of the new distribution family.