IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i10p1648-d418504.html
   My bibliography  Save this article

A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods

Author

Listed:
  • Mohamed Aboraya

    (Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University, Damietta 34519, Egypt)

  • Haitham M. Yousof

    (Department of Statistics, Mathematics and Insurance, Benha University, Banha 13513, Egypt)

  • G.G. Hamedani

    (Department of Mathematical and Statistical Sciences, Marquette University, Milwaukee, WI 53201-1881, USA)

  • Mohamed Ibrahim

    (Department of Applied Statistics and Insurance, Faculty of Commerce, Damietta University, Damietta 34519, Egypt)

Abstract

In this work, we propose and study a new family of discrete distributions. Many useful mathematical properties, such as ordinary moments, moment generating function, cumulant generating function, probability generating function, central moment, and dispersion index are derived. Some special discrete versions are presented. A certain special case is discussed graphically and numerically. The hazard rate function of the new class can be “decreasing”, “upside down”, “increasing”, and “decreasing-constant-increasing (U-shape)”. Some useful characterization results based on the conditional expectation of certain function of the random variable and in terms of the hazard function are derived and presented. Bayesian and non-Bayesian methods of estimation are considered. The Bayesian estimation procedure under the squared error loss function is discussed. Markov chain Monte Carlo simulation studies for comparing non-Bayesian and Bayesian estimations are performed using the Gibbs sampler and Metropolis–Hastings algorithm. Four applications to real data sets are employed for comparing the Bayesian and non-Bayesian methods. The importance and flexibility of the new discrete class is illustrated by means of four real data applications.

Suggested Citation

  • Mohamed Aboraya & Haitham M. Yousof & G.G. Hamedani & Mohamed Ibrahim, 2020. "A New Family of Discrete Distributions with Mathematical Properties, Characterizations, Bayesian and Non-Bayesian Estimation Methods," Mathematics, MDPI, vol. 8(10), pages 1-25, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1648-:d:418504
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/10/1648/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/10/1648/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bebbington, Mark & Lai, Chin-Diew & Wellington, Morgan & Zitikis, RiÄ ardas, 2012. "The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 37-44.
    2. Mahdi Rasekhi & Mohammad Mehdi Saber & Haitham M. Yousof, 2020. "Bayesian and classical inference of reliability in multicomponent stress-strength under the generalized logistic model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(21), pages 5114-5125, September.
    3. Li Cai, 2010. "Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis," Journal of Educational and Behavioral Statistics, , vol. 35(3), pages 307-335, June.
    4. M. El-Morshedy & M. S. Eliwa & H. Nagy, 2020. "A new two-parameter exponentiated discrete Lindley distribution: properties, estimation and applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(2), pages 354-375, January.
    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. Mohamed Ibrahim & M. Masoom Ali & Haitham M. Yousof, 2023. "The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods," Annals of Data Science, Springer, vol. 10(4), pages 1069-1106, August.
    2. Manal M. Yousef & Amal S. Hassan & Abdullah H. Al-Nefaie & Ehab M. Almetwally & Hisham M. Almongy, 2022. "Bayesian Estimation Using MCMC Method of System Reliability for Inverted Topp–Leone Distribution Based on Ranked Set Sampling," Mathematics, MDPI, vol. 10(17), pages 1-26, August.

    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. Mohamed Ibrahim & M. Masoom Ali & Haitham M. Yousof, 2023. "The Discrete Analogue of the Weibull G Family: Properties, Different Applications, Bayesian and Non-Bayesian Estimation Methods," Annals of Data Science, Springer, vol. 10(4), pages 1069-1106, August.
    2. Walid Emam & Yusra Tashkandy & G.G. Hamedani & Mohamed Abdelhamed Shehab & Mohamed Ibrahim & Haitham M. Yousof, 2023. "A Novel Discrete Generator with Modeling Engineering, Agricultural and Medical Count and Zero-Inflated Real Data with Bayesian, and Non-Bayesian Inference," Mathematics, MDPI, vol. 11(5), pages 1-28, February.
    3. M. S. Eliwa & Ziyad Ali Alhussain & M. El-Morshedy, 2020. "Discrete Gompertz-G Family of Distributions for Over- and Under-Dispersed Data with Properties, Estimation, and Applications," Mathematics, MDPI, vol. 8(3), pages 1-26, March.
    4. Mohamed S. Eliwa & Mahmoud El-Morshedy & Haitham M. Yousof, 2022. "A Discrete Exponential Generalized-G Family of Distributions: Properties with Bayesian and Non-Bayesian Estimators to Model Medical, Engineering and Agriculture Data," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
    5. Luo, Nanyu & Ji, Feng & Han, Yuting & He, Jinbo & Zhang, Xiaoya, 2024. "Fitting item response theory models using deep learning computational frameworks," OSF Preprints tjxab, Center for Open Science.
    6. Sijia Huang & Li Cai, 2024. "Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 311-341, June.
    7. Alessandro Barbiero & Asmerilda Hitaj, 2024. "Discrete half-logistic distributions with applications in reliability and risk analysis," Annals of Operations Research, Springer, vol. 340(1), pages 27-57, September.
    8. Irshad, M.R. & Jodrá, P. & Krishna, A. & Maya, R., 2023. "On the discrete analogue of the Teissier distribution and its associated INAR(1) process," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 227-245.
    9. Radhakumari Maya & Christophe Chesneau & Anuresha Krishna & Muhammed Rasheed Irshad, 2022. "Poisson Extended Exponential Distribution with Associated INAR(1) Process and Applications," Stats, MDPI, vol. 5(3), pages 1-18, August.
    10. Harold Doran, 2023. "A Collection of Numerical Recipes Useful for Building Scalable Psychometric Applications," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 37-69, February.
    11. Guibing, Gao & Wenhui, Yue & Wenchu, Ou & Hao, Tang, 2018. "Vulnerability evaluation method applied to manufacturing systems," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 255-265.
    12. Andrea Svicher & Letizia Palazzeschi & Alessio Gori & Annamaria Di Fabio, 2022. "The Gratitude Resentment and Appreciation Test-Revised Short (GRAT-RS): A Multidimensional Item Response Theory Analysis in Italian Workers," IJERPH, MDPI, vol. 19(24), pages 1-10, December.
    13. Hanan Haj Ahmad, 2024. "The Efficiency of Hazard Rate Preservation Method for Generating Discrete Rayleigh–Lindley Distribution," Mathematics, MDPI, vol. 12(8), pages 1-17, April.
    14. Cosimo Magazzino & Marco Mele, 2022. "A Dynamic Factor and Neural Networks Analysis of the Co-movement of Public Revenues in the EMU," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 8(2), pages 289-338, July.
    15. Hanan Haj Ahmad & Dina A. Ramadan & Ehab M. Almetwally, 2024. "Evaluating the Discrete Generalized Rayleigh Distribution: Statistical Inferences and Applications to Real Data Analysis," Mathematics, MDPI, vol. 12(2), pages 1-23, January.
    16. Motonori Oka & Kensuke Okada, 2023. "Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational Inference," Psychometrika, Springer;The Psychometric Society, vol. 88(1), pages 302-331, March.
    17. Lemonte, Artur J., 2013. "A new exponential-type distribution with constant, decreasing, increasing, upside-down bathtub and bathtub-shaped failure rate function," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 149-170.
    18. Shaul K. Bar-Lev & Ad Ridder, 2022. "The Large Arcsine Exponential Dispersion Model—Properties and Applications to Count Data and Insurance Risk," Mathematics, MDPI, vol. 10(19), pages 1-25, October.
    19. Giannelis, Alexandros & Willoughby, Emily A. & Corley, Robin & Hopfer, Christian & Hewitt, John K. & Iacono, William G. & Anderson, Jacob & Rustichini, Aldo & Vrieze, Scott I. & McGue, Matt & Lee, Jam, 2023. "The association between saving disposition and financial distress: A genetically informed approach," Journal of Economic Psychology, Elsevier, vol. 96(C).
    20. Heon-Jae Jeong & Hsun-Hsiang Liao & Su Ha Han & Wui-Chiang Lee, 2020. "An Application of Item Response Theory to Scoring Patient Safety Culture Survey Data," IJERPH, MDPI, vol. 17(3), pages 1-10, January.

    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:gam:jmathe:v:8:y:2020:i:10:p:1648-:d:418504. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.