IDEAS home Printed from https://ideas.repec.org/a/spr/alstar/v104y2020i1d10.1007_s10182-019-00350-8.html
   My bibliography  Save this article

Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon

Author

Listed:
  • Rahma Abid

    (University of Sfax)

  • Célestin C. Kokonendji

    (Université Bourgogne Franche-Comté)

  • Afif Masmoudi

    (University of Sfax)

Abstract

We introduce a new class of regression models based on the geometric Tweedie models (GTMs) for analyzing both continuous and semicontinuous data, similar to the recent and standard Tweedie regression models. We also present a phenomenon of variation with respect to the equi-varied exponential distribution, where variance is equal to the squared mean. The corresponding power v-functions which characterize the GTMs, obtained in turn by exponential-Tweedie mixture, are transformed into variance to use the conventional generalized linear models. The real power parameter of GTMs works as an automatic distribution selection such for asymmetric Laplace, geometric-compound-Poisson-gamma and geometric-Mittag-Leffler. The classification of all power v-functions reveals only two border count distributions, namely geometric and geometric-Poisson. We establish practical properties, into the GTMs, of zero-mass and variation phenomena, also in connection with some reliability measures. Simulation studies show that the proposed model highlights asymptotic unbiased and consistent estimators, despite the general over-variation. We illustrate two applications, under- and over-varied, on real datasets to a time to failure and time to repair in reliability; one of which has positive values with many achievements in zeros. We finally make concluding remarks, including future directions.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:alstar:v:104:y:2020:i:1:d:10.1007_s10182-019-00350-8
    DOI: 10.1007/s10182-019-00350-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10182-019-00350-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10182-019-00350-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bent Jørgensen & Sven Jesper Knudsen, 2004. "Parameter Orthogonality and Bias Adjustment for Estimating Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 93-114, March.
    2. Maria Iwińska & Magdalena Szymkowiak, 2016. "Characterizations of the exponential distribution by Pascal compound," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(1), pages 63-70, January.
    3. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    4. Jay M. Ver Hoef, 2012. "Who Invented the Delta Method?," The American Statistician, Taylor & Francis Journals, vol. 66(2), pages 124-127, May.
    5. Maria Iwińska & Magdalena Szymkowiak, 2017. "Characterizations of distributions through selected functions of reliability theory," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 69-74, January.
    6. 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.
    7. Kokonendji, Célestin C. & Puig, Pedro, 2018. "Fisher dispersion index for multivariate count distributions: A review and a new proposal," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 180-193.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.
    2. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    3. 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.
    4. Célestin C. Kokonendji & Sobom M. Somé, 2021. "Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics," Stats, MDPI, vol. 4(1), pages 1-22, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    2. Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.
    3. Aurélien Saussay & Misato Sato, 2018. "The Impacts of Energy Prices on Industrial Foreign Investment Location: Evidence from Global Firm Level Data," Working Papers hal-03475473, HAL.
    4. Dennis D. Boos & Jason A. Osborne, 2015. "Assessing Variability of Complex Descriptive Statistics in Monte Carlo Studies Using Resampling Methods," International Statistical Review, International Statistical Institute, vol. 83(2), pages 228-238, August.
    5. Agahi, Hamzeh & Khalili, Monavar, 2020. "Truncated Mittag-Leffler distribution and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    6. Christoph, Gerd & Schreiber, Karina, 2000. "Scaled Sibuya distribution and discrete self-decomposability," Statistics & Probability Letters, Elsevier, vol. 48(2), pages 181-187, June.
    7. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2006. "Vector Multiplicative Error Models: Representation and Inference," NBER Technical Working Papers 0331, National Bureau of Economic Research, Inc.
    8. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.
    9. Emad-Eldin Aly & Nadjib Bouzar, 2000. "On Geometric Infinite Divisibility and Stability," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(4), pages 790-799, December.
    10. Levy, Edmond, 2021. "On the density for sums of independent Mittag-Leffler variates with common order," Statistics & Probability Letters, Elsevier, vol. 179(C).
    11. Subrata Chakraborty & S. H. Ong, 2017. "Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-17, December.
    12. Julian Ramirez-Villegas & Andrew J. Challinor, 2016. "Towards a genotypic adaptation strategy for Indian groundnut cultivation using an ensemble of crop simulations," Climatic Change, Springer, vol. 138(1), pages 223-238, September.
    13. Kozubowski, Tomasz J., 2005. "A note on self-decomposability of stable process subordinated to self-decomposable subordinator," Statistics & Probability Letters, Elsevier, vol. 74(1), pages 89-91, August.
    14. Stefano Cabras & María Castellanos & Erlis Ruli, 2014. "A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models," METRON, Springer;Sapienza Università di Roma, vol. 72(2), pages 153-167, August.
    15. Mohamed Kayid & Mansour Shrahili, 2023. "Characterization Results on Lifetime Distributions by Scaled Reliability Measures Using Completeness Property in Functional Analysis," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    16. K. K. Kataria & P. Vellaisamy, 2019. "On Distributions of Certain State-Dependent Fractional Point Processes," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1554-1580, September.
    17. Rudan Wang & Bruce Morley & Javier Ordóñez, 2016. "The Taylor Rule, Wealth Effects and the Exchange Rate," Review of International Economics, Wiley Blackwell, vol. 24(2), pages 282-301, May.
    18. 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.
    19. Maria Victoria Ibañez & Marina Martínez-Garcia & Amelia Simó, 2021. "A Review of Spatiotemporal Models for Count Data in R Packages. A Case Study of COVID-19 Data," Mathematics, MDPI, vol. 9(13), pages 1-23, July.
    20. Cirillo, Pasquale & Hüsler, Jürg, 2009. "An urn approach to generalized extreme shock models," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 969-976, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:alstar:v:104:y:2020:i:1:d:10.1007_s10182-019-00350-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.