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Unit-Gompertz Distribution with Applications

Author

Listed:
  • Josmar Mazucheli

    (Departamento de Estatística, Universidade Estadual de Maringá)

  • André Felipe Menezes

    (Departamento de Estatística, Universidade Estadual de Maringá)

  • Sanku Dey

    (Department of Statistics, St. Anthony’s College, Shillong)

Abstract

The transformed family of distributions are sometimes very useful to explore additional properties of the phenomenons which non-transformed (baseline) family of distributions cannot. In this paper, we introduce a new transformed model, called the unit-Gompertz (UG) distribution which exhibit right-skewed (unimodal) and reversed-J shaped density while the hazard rate has constant, increasing, upside-down bathtub and then bathtub shaped hazard rate. Some statistical properties of this new distribution are presented and discussed. Maximum likelihood estimation for the parameters that index UG distribution are derived along with their corresponding asymptotic standard errors. Monte Carlo simulations are conducted to investigate the bias, root mean squared error of the maximum likelihood estimators as well as the coverage probability. Finally, the potentiality of the model is presented and compared with three others distributions using two real data sets.

Suggested Citation

  • Josmar Mazucheli & André Felipe Menezes & Sanku Dey, 2019. "Unit-Gompertz Distribution with Applications," Statistica, Department of Statistics, University of Bologna, vol. 79(1), pages 25-43.
    • Handle: RePEc:bot:rivsta:v:79:y:2019:i:1:p:25-43
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    Citations

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    Cited by:

    1. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Muhammad H. Tahir & Aqib Ali & Muhammad Zubair & Sania Anam, 2020. "Some New Facts about the Unit-Rayleigh Distribution with Applications," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    2. Muhammad Aslam & Mehreen Afzaal & M. Ishaq Bhatti, 2021. "A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 101-119, December.
    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. Aslam Muhammad & Afzaal Mehreen & Ishaq Bhatti M., 2021. "A study on exponentiated Gompertz distribution under Bayesian discipline using informative priors," Statistics in Transition New Series, Polish Statistical Association, vol. 22(4), pages 101-119, December.
    5. Mustafa Ç. Korkmaz & Emrah Altun & Morad Alizadeh & M. El-Morshedy, 2021. "The Log Exponential-Power Distribution: Properties, Estimations and Quantile Regression Model," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
    6. Shama, M.S. & Dey, Sanku & Altun, Emrah & Afify, Ahmed Z., 2022. "The Gamma–Gompertz distribution: Theory and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 689-712.
    7. Muhammad Ahsan ul Haq & Sharqa Hashmi & Khaoula Aidi & Pedro Luiz Ramos & Francisco Louzada, 2023. "Unit Modified Burr-III Distribution: Estimation, Characterizations and Validation Test," Annals of Data Science, Springer, vol. 10(2), pages 415-440, April.
    8. Rashad A. R. Bantan & Christophe Chesneau & Farrukh Jamal & Mohammed Elgarhy & Waleed Almutiry & Amani Abdullah Alahmadi, 2021. "Study of a Modified Kumaraswamy Distribution," Mathematics, MDPI, vol. 9(21), pages 1-26, November.

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