Work

Anderson-Darling and Watson tests for the geometric distribution with estimated probability of success

Year: 2024

Type: article

Abstract: This paper introduces two new goodness-of-fit tests for the geometric distribution based on discrete adaptations of the Watson W2 and Anderson-Darling A2 statistics, where the probability of success is unknown. Although these tests are widely applied to continuous distributions, their application in discrete models has been relatively unexplored. Our study addresses this need by developing a robust statistical framework specifically for discrete distributions, particularly the geometric distribution. We provide extensive tables of asymptotic critical values for these tests and demonstrate their practical relevance through a financial case study. Specifically, we apply these tests to analyze price runs derived from daily time series of NASDAQ, DJIA, Nikkei 225, and the Mexican IPC indices, covering the period from January 1, 2015, to December 31, 2022. This work broadens the range of available tools for assessing goodness-of-fit in discrete models, which are essential for applications in finance and beyond. The Python programs developed for this paper are available to the academic community.

Source: PLoS ONE

DOI: 10.1371/journal.pone.0315855

Authors: Héctor Francisco Coronel-Brizio, Alejandro Raúl Hernández-Montoya, Manuel Enrique Rodríguez-Achach, Horacio Tapia-McClung, Juan Evangelista Trinidad-Segovia

Institutions: Universidad Veracruzana, Universidad Marista de Mérida, University of Almería

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,290

Funders: Consejo Nacional de Ciencia y Tecnología, Ministerio de Ciencia e Innovación