Correction to: The Weibull Fréchet distribution and its applications.

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The Weibull Fréchet distribution, a four-parameter lifetime model, was introduced by Afify et al. (2016).
• The original study contained inaccuracies in the log-likelihood function and score vector components.

Purpose of the Study:

• To identify and rectify errors in the mathematical formulation of the Weibull Fréchet distribution.
• To provide accurate log-likelihood and score vector components for the Weibull Fréchet distribution.

Main Methods:

• Comparative analysis of the original formulation with established statistical principles.
• Derivation and presentation of corrected equations for the log-likelihood function.
• Derivation and presentation of corrected equations for the score vector components.

Main Results:

• Specific errors in the log-likelihood function presented by Afify et al. were identified.
• Mistakes in the components of the score vector were pinpointed.
• Corrected expressions for both the log-likelihood and score vector were derived.

Conclusions:

• The corrected formulation enhances the reliability and applicability of the Weibull Fréchet distribution.
• Accurate statistical components are crucial for the proper application of lifetime models.
• This note provides a revised foundation for future research utilizing the Weibull Fréchet distribution.