Discriminating between the generalized Rayleigh and Weibull distributions: Some comparative studies

ABSTRACT

The generalized Rayleigh distribution was introduced and studied quite effectively in the literature. The closeness and separation between the distributions are extremely important for analyzing any lifetime data. In this spirit, both the generalized Rayleigh and Weibull distributions can be used for analyzing skewed datasets. In this article, we compare these two distributions based on the Fisher information measures and use it for discrimination purposes. It is evident that the Fisher information measures play an important role in separating between the distributions. The total information measures and the variances of the different percentile estimators are computed and presented. A real life dataset is analyzed for illustration purposes and a numerical comparison study is performed to assess our procedures in separating between these two distributions.

KEYWORDS:

• Generalized Rayleigh distribution
• Information measure matrix
• Percentiles
• Weibull distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62F10
• 62E25

Acknowledgment

The authors are thankful to the referees for their valuable suggestions on the previous version of this article.