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On General Exponential Weight Functions and Variation Phenomenon

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Abstract

General weighted exponential distributions including modified exponential ones are widely used with great ability in statistical applications, particularly in reliability. In this paper, we investigate full exponential weight functions and their extensions from any nonnegative continuous reference weighted distribution. Several properties and their connections with the recent variation phenomenon are then established. In particular, characterizations, weightening operations and dual distributions are set forward. Illustrative examples and concluding remarks are extensively discussed.

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Acknowledgments

This paper is dedicated to Professor Gérard Letac for his 80th birthday. We sincerely thank the Associate Editor and two anonymous referees for their positive and valuable comments.

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Authors and Affiliations

  1. Laboratoire de Mathématiques de Besançon UMR 6623 CNRS-UFC, Université Bourgogne Franche-Comté, UFR Sciences et Techniques, 16 route de Gray, 25030, Besançon, France

    Célestin C. Kokonendji & Aboubacar Y. Touré

  2. Laboratory of Probability and Statistics, University of Sfax, Soukra road B.P. 1171, 3038, Sfax, Tunisia

    Rahma Abid

  3. and University Paris-Dauphine Tunis, Tunis, Tunisia

    Rahma Abid

Authors
  1. Célestin C. Kokonendji
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  2. Aboubacar Y. Touré
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  3. Rahma Abid
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Correspondence to Aboubacar Y. Touré.

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Kokonendji, C.C., Touré, A.Y. & Abid, R. On General Exponential Weight Functions and Variation Phenomenon. Sankhya A 84, 924–940 (2022). https://doi.org/10.1007/s13171-020-00226-z

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