An Exponentiality Test of Fit Based on a Tail Characterization against Heavy and Light-Tailed Alternatives

Alex Karagrigoriou (), Ioannis Mavrogiannis, Georgia Papasotiriou and Ilia Vonta
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Alex Karagrigoriou: Lab of Statistics and Data Analysis, University of the Aegean, 83200 Karlovasi, Greece
Ioannis Mavrogiannis: M2P2, Centrale Méditerranée, 13013 Marseille, France
Georgia Papasotiriou: Department of Mathematics, National Technical University of Athens, 15780 Athens, Greece
Ilia Vonta: Department of Mathematics, National Technical University of Athens, 15780 Athens, Greece

Risks, 2023, vol. 11, issue 10, 1-22

Abstract: Log-concavity and log-convexity play a key role in various scientific fields, especially in those where the distinction between exponential and non-exponential distributions is necessary for inferential purposes. In the present study, we introduce a testing procedure for the tail part of a distribution which can be used for the distinction between exponential and non-exponential distributions. The conspiracy and catastrophe principles are initially used to establish a characterization of (the tail part of) the exponential distribution, which is one of the main contributions of the present work, leading the way for the construction of the new test of fit. The proposed test and its implementation are thoroughly discussed, and an extended simulation study has been undertaken to clarify issues related to its implementation and explore the extent of its capabilities. A real data case is also investigated.

Keywords: exponentiality test; tail characterization; log-concavity; log-convexity; extreme events; heavy-tailed distributions; light-tailed distributions (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2023
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