A novel unit-asymmetric distribution based on correlated Fréchet random variables

2025/01/01 by Roberto Vila, Vila, Roberto, Felipe Quintino +1 · 1 citation
Mathematics · #60E05 #62Exx #62Fxx #Applications (stat.AP) #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Distribution Estimation and Applications

paper · pdf · doi:10.48550/arxiv.2501.00970

openalex publication_date 2025/01/01 · openalex created_date 2025/01/04 · openalex updated_date 2026/07/28

Abstract

In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type W=X₁/(X₁+X₂), where (X₁, X₂)^\top follows a bivariate extreme distribution with Fréchet margins, that is, X₁ and X₂ are two correlated Fréchet random variables. Some mathematical properties such as identifiability, symmetry, stochastic representation, characterization as a ratio, moments, stress-strength probability, quantiles, and the maximum likelihood method are rigorously analyzed. Two applications of the ratio distribution are discussed.

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