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On General Exponential Weight Functions and Variation Phenomenon

Author

Listed:
  • Célestin C. Kokonendji

    (Université Bourgogne Franche-Comté, UFR Sciences et Techniques)

  • Aboubacar Y. Touré

    (Université Bourgogne Franche-Comté, UFR Sciences et Techniques)

  • Rahma Abid

    (University of Sfax
    and University Paris-Dauphine Tunis)

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.

Suggested Citation

  • Célestin C. Kokonendji & Aboubacar Y. Touré & Rahma Abid, 2022. "On General Exponential Weight Functions and Variation Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 924-940, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00226-z
    DOI: 10.1007/s13171-020-00226-z
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    References listed on IDEAS

    as
    1. Roy, Shongkour & Adnan, Mian Arif Shams, 2012. "Wrapped weighted exponential distributions," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 77-83.
    2. Shaul K. Bar-Lev, 2020. "Independent, Tough Identical Results: The Class of Tweedie on Power Variance Functions and the Class of Bar-Lev and Enis on Reproducible Natural Exponential Families," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-30, January.
    3. Filippo Domma & Francesca Condino & Božidar V. Popović, 2017. "A new generalized weighted Weibull distribution with decreasing, increasing, upside-down bathtub, N-shape and M-shape hazard rate," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(16), pages 2978-2993, December.
    4. Abid, Rahma & Kokonendji, Célestin C. & Masmoudi, Afif, 2019. "Geometric dispersion models with real quadratic v-functions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 197-204.
    5. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
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    Cited by:

    1. Marcelo Bourguignon & Célestin C. Kokonendji, 2024. "Coherent indexes for shifted count and semicontinuous models," Statistical Papers, Springer, vol. 65(8), pages 5253-5271, October.
    2. Shaul K. Bar-Lev & Apostolos Batsidis & Jochen Einbeck & Xu Liu & Panpan Ren, 2023. "Cumulant-Based Goodness-of-Fit Tests for the Tweedie, Bar-Lev and Enis Class of Distributions," Mathematics, MDPI, vol. 11(7), pages 1-20, March.

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