Araştırma Makalesi
BibTex RIS Kaynak Göster

Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications

Yıl 2025, Erken Görünüm, 1 - 1

Kadir Karakaya , Şule Sağlam

https://doi.org/10.35378/gujs.1549073

Öz

This study proposes the unit Gamma-Lindley distribution, a novel bounded statistical model that extends the flexibility of existing distributions for modeling data on the (0,1) interval. The proposed distribution is characterized, by closed-form expressions derived for its cumulative distribution, probability density, and hazard rate functions. Some statistical properties, including moments, order statistics, Bonferroni, Lorenz curves, entropy, etc. are examined. To estimate the unknown model parameters, several estimation methods are introduced and their performance is assessed through a Monte Carlo simulation experiment based on bias and mean square error criteria. A real data application focusing on firm management cost-effectiveness highlights the practical utility of the model, demonstrating its superior fit compared to current distributions, such as beta and Kumaraswamy. Furthermore, a novel regression model is developed based on the proposed distribution, with parameter estimation performed using the maximum likelihood method. The new regression model provides an alternative for analyzing bounded response variables. The findings contribute to the statistical literature by offering a flexible and comprehensive modeling framework for bounded data, with theoretical advancements and practical applicability.

Anahtar Kelimeler

Beta regression analysis Cost-effectiveness data Maximum likelihood estimation OECD Unit distribution

Kaynakça

  • [1] Mazucheli, J., Menezes, A.F.B., Fernandes, L. B., De Oliveira, R.P., and Ghitany, M.E., “The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics”, 47(6): 954-974, (2020). DOI: 10.1080/02664763.2019.1657813
  • [2] Bhatti, F. A., Ali, A., Hamedani, G., Korkmaz, M. Ç., and Ahmad, M. “The unit generalized log Burr XII distribution: Properties and applications”, AIMS Mathematics. (2021). DOI: 10.3934/math.2021592
  • [3] Ghitany, M. E., Mazucheli, J., Menezes, A. F. B., and Alqallaf, F., “The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval”, Communications in Statistics-Theory and Methods, 48(14): 3423-3438, (2019). DOI: 10.1080/03610926.2018.1476717
  • [4] Guerra, R. R., Pena-Ramirez, F. A., and Bourguignon, M., “The unit extended Weibull families of distributions and its applications”, Journal of Applied Statistics, 48(16): 3174-3192, (2021). DOI: 10.1080/02664763.2020.1796936
  • [5] Korkmaz, M.Ç., Leiva, V., and Martin-Barreiro, C., “The continuous Bernoulli distribution: Mathematical characterization, fractile regression, computational simulations, and applications” Fractal and Fractional, 7(5): 386, (2023). DOI: https://doi.org/10.3390/fractalfract7050386
  • [6] Korkmaz, M. Ç., Altun, E., Alizadeh, M., and El-Morshedy, M., “The log exponential-power distribution: Properties, estimations and quantile regression model”, Mathematics, 9(21): 2634, (2021). DOI: https://doi.org/10.3390/math9212634
  • [7] Korkmaz, M. Ç., Chesneau, C., and Korkmaz, Z. S. “The unit folded normal distribution: A new unit probability distribution with the estimation procedures, quantile regression modeling and educational attainment applications”, Journal of Reliability and Statistical Studies, 261-298, (2022). DOI: 10.13052/jrss0974-8024.15111
  • [8] Maya, R., Jodra, P., Irshad, M. R., and Krishna, A.,” The unit Muth distribution: Statistical properties and applications”, Ricerche di Matematica, 1-24, (2022). DOI: https://doi.org/10.1007/s11587-022-00703-7
  • [9] Mazucheli J, Menezes A.F., and Dey S.,” The unit-Birnbaum-Saunders distribution with applications”, Chilean Journal of Statistics, 9(1): 47-57, (2018).
  • [10] Mazucheli, J., Alves, B., Korkmaz, M. Ç., and Leiva, V., “Vasicek quantile and mean regression models for bounded data: New formulation, mathematical derivations, and numerical applications”, Mathematics, 10(9): 1389, (2022). DOI: https://doi.org/10.3390/ math10091389
  • [11] Mazucheli, J., Korkmaz, M. Ç., Menezes, A. F., and Leiva, V., “The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications”, Soft Computing, 27(1): 279-295, (2023). DOI: https://doi.org/10.1007/s00500-022-07278-3
  • [12] Mazucheli, J., Alves, B., and Korkmaz, M. Ç., “The Unit-Gompertz Quantile Regression Model for the Bounded Responses”, Mathematica Slovaca, 73(4): 1039-1054, (2023). DOI: https://doi.org/10.1515/ms-2023-0077
  • [13] Altun, E., and Cordeiro, G. M., “The unit-improved second-degree Lindley distribution: inference and regression modeling”, Computational Statistics, 35: 259-279, (2020). DOI: https://doi.org/10.1007/s00180-019-00921-y
  • [14] Korkmaz, M. C¸., Chesneau, C., and Korkmaz, Z. S., “Transmuted unit Rayleigh quantile regression model: Alternative to beta and Kumaraswamy quantile regression models”, University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, 83: 149-158, (2021).
  • [15 Ribeiro, T.F., Cordeiro, G.M., Pena-Ramirez, F.A., and Guerra, R.R., “A new quantile regression for the COVID-19 mortality rates in the United States”, Computational and Applied Mathematics, 40: 1-16, (2021). DOI: https://doi.org/10.1007/s40314-021-01553-z
  • [16] Abdi, M., Asgharzadeh, A., Bakouch, H. S., and Alipour, Z., “A new compound gamma and Lindley distribution with application to failure data”, Austrian Journal of Statistics, 48(3): 54-75, (2019). DOI: https://doi.org/10.17713/ajs.v48i3.843
  • [17] Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., “Spectral methods: evolution to complex geometries and applications to fluid dynamics”, Springer Science and Business Media, (2007).
  • [18] Bonferroni, C., Elmenti di statistica generale [elements of general statistics]. Firenze: Libreria Seber, (1930).
  • [19] Casella, G., Robert, C. P., and Wells, M. T., “Generalized accept-reject sampling schemes”, Lecture notes-monograph series, 342-347, (2004).
  • [20] Amigó, J. M., Balogh, S. G., and Hernández, S., “A brief review of generalized entropies”, Entropy, 20(11): 813, (2018). DOI: https://doi.org/10.3390/e20110813
  • [21] Kumaraswamy, P., “A generalized probability density function for double bounded random processes”, Journal of Hydrology, 46(1-2): 79-88, (1980). DOI: https://doi.org/10.1016/0022-1694(80)90036-0
  • [22] Korkmaz, M. C¸., and Chesneau, C., “On the unit Burr-XII distribution with the quantile regression modeling and applications”, Computational and Applied Mathematics, 40(1): 29, (2021). DOI: https://doi.org/10.1007/s40314-021-01418-5
  • [23] Abd El-Bar, A., Bakouch, H. S., and Chowdhury, S., “A new trigonometric distribution with bounded support and an application”, Revista de la Union Matematica Argentina, 62(2): 459-473, (2021). DOI: https://doi.org/10.33044/revuma.1872
  • [24] Gomez-Deniz, E., Sordo, M. A., and Calderin-Ojeda, E., “The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance”, Insurance: Mathematics and Economics, 54: 49-57, (2014). DOI: https://doi.org/10.1016/j.insmatheco.2013.10.017
  • [25] Jodra, P., and Jimenez-Gamero, M. D., “A quantile regression model for bounded responses based on the exponential-geometric distribution”, REVSTAT-Statistical Journal, 18(4): 415-436, (2020).

Yıl 2025, Erken Görünüm, 1 - 1

Kadir Karakaya , Şule Sağlam

https://doi.org/10.35378/gujs.1549073

Öz

Kaynakça

  • [1] Mazucheli, J., Menezes, A.F.B., Fernandes, L. B., De Oliveira, R.P., and Ghitany, M.E., “The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates. Journal of Applied Statistics”, 47(6): 954-974, (2020). DOI: 10.1080/02664763.2019.1657813
  • [2] Bhatti, F. A., Ali, A., Hamedani, G., Korkmaz, M. Ç., and Ahmad, M. “The unit generalized log Burr XII distribution: Properties and applications”, AIMS Mathematics. (2021). DOI: 10.3934/math.2021592
  • [3] Ghitany, M. E., Mazucheli, J., Menezes, A. F. B., and Alqallaf, F., “The unit-inverse Gaussian distribution: A new alternative to two-parameter distributions on the unit interval”, Communications in Statistics-Theory and Methods, 48(14): 3423-3438, (2019). DOI: 10.1080/03610926.2018.1476717
  • [4] Guerra, R. R., Pena-Ramirez, F. A., and Bourguignon, M., “The unit extended Weibull families of distributions and its applications”, Journal of Applied Statistics, 48(16): 3174-3192, (2021). DOI: 10.1080/02664763.2020.1796936
  • [5] Korkmaz, M.Ç., Leiva, V., and Martin-Barreiro, C., “The continuous Bernoulli distribution: Mathematical characterization, fractile regression, computational simulations, and applications” Fractal and Fractional, 7(5): 386, (2023). DOI: https://doi.org/10.3390/fractalfract7050386
  • [6] Korkmaz, M. Ç., Altun, E., Alizadeh, M., and El-Morshedy, M., “The log exponential-power distribution: Properties, estimations and quantile regression model”, Mathematics, 9(21): 2634, (2021). DOI: https://doi.org/10.3390/math9212634
  • [7] Korkmaz, M. Ç., Chesneau, C., and Korkmaz, Z. S. “The unit folded normal distribution: A new unit probability distribution with the estimation procedures, quantile regression modeling and educational attainment applications”, Journal of Reliability and Statistical Studies, 261-298, (2022). DOI: 10.13052/jrss0974-8024.15111
  • [8] Maya, R., Jodra, P., Irshad, M. R., and Krishna, A.,” The unit Muth distribution: Statistical properties and applications”, Ricerche di Matematica, 1-24, (2022). DOI: https://doi.org/10.1007/s11587-022-00703-7
  • [9] Mazucheli J, Menezes A.F., and Dey S.,” The unit-Birnbaum-Saunders distribution with applications”, Chilean Journal of Statistics, 9(1): 47-57, (2018).
  • [10] Mazucheli, J., Alves, B., Korkmaz, M. Ç., and Leiva, V., “Vasicek quantile and mean regression models for bounded data: New formulation, mathematical derivations, and numerical applications”, Mathematics, 10(9): 1389, (2022). DOI: https://doi.org/10.3390/ math10091389
  • [11] Mazucheli, J., Korkmaz, M. Ç., Menezes, A. F., and Leiva, V., “The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications”, Soft Computing, 27(1): 279-295, (2023). DOI: https://doi.org/10.1007/s00500-022-07278-3
  • [12] Mazucheli, J., Alves, B., and Korkmaz, M. Ç., “The Unit-Gompertz Quantile Regression Model for the Bounded Responses”, Mathematica Slovaca, 73(4): 1039-1054, (2023). DOI: https://doi.org/10.1515/ms-2023-0077
  • [13] Altun, E., and Cordeiro, G. M., “The unit-improved second-degree Lindley distribution: inference and regression modeling”, Computational Statistics, 35: 259-279, (2020). DOI: https://doi.org/10.1007/s00180-019-00921-y
  • [14] Korkmaz, M. C¸., Chesneau, C., and Korkmaz, Z. S., “Transmuted unit Rayleigh quantile regression model: Alternative to beta and Kumaraswamy quantile regression models”, University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, 83: 149-158, (2021).
  • [15 Ribeiro, T.F., Cordeiro, G.M., Pena-Ramirez, F.A., and Guerra, R.R., “A new quantile regression for the COVID-19 mortality rates in the United States”, Computational and Applied Mathematics, 40: 1-16, (2021). DOI: https://doi.org/10.1007/s40314-021-01553-z
  • [16] Abdi, M., Asgharzadeh, A., Bakouch, H. S., and Alipour, Z., “A new compound gamma and Lindley distribution with application to failure data”, Austrian Journal of Statistics, 48(3): 54-75, (2019). DOI: https://doi.org/10.17713/ajs.v48i3.843
  • [17] Canuto, C., Hussaini, M. Y., Quarteroni, A., and Zang, T. A., “Spectral methods: evolution to complex geometries and applications to fluid dynamics”, Springer Science and Business Media, (2007).
  • [18] Bonferroni, C., Elmenti di statistica generale [elements of general statistics]. Firenze: Libreria Seber, (1930).
  • [19] Casella, G., Robert, C. P., and Wells, M. T., “Generalized accept-reject sampling schemes”, Lecture notes-monograph series, 342-347, (2004).
  • [20] Amigó, J. M., Balogh, S. G., and Hernández, S., “A brief review of generalized entropies”, Entropy, 20(11): 813, (2018). DOI: https://doi.org/10.3390/e20110813
  • [21] Kumaraswamy, P., “A generalized probability density function for double bounded random processes”, Journal of Hydrology, 46(1-2): 79-88, (1980). DOI: https://doi.org/10.1016/0022-1694(80)90036-0
  • [22] Korkmaz, M. C¸., and Chesneau, C., “On the unit Burr-XII distribution with the quantile regression modeling and applications”, Computational and Applied Mathematics, 40(1): 29, (2021). DOI: https://doi.org/10.1007/s40314-021-01418-5
  • [23] Abd El-Bar, A., Bakouch, H. S., and Chowdhury, S., “A new trigonometric distribution with bounded support and an application”, Revista de la Union Matematica Argentina, 62(2): 459-473, (2021). DOI: https://doi.org/10.33044/revuma.1872
  • [24] Gomez-Deniz, E., Sordo, M. A., and Calderin-Ojeda, E., “The Log–Lindley distribution as an alternative to the beta regression model with applications in insurance”, Insurance: Mathematics and Economics, 54: 49-57, (2014). DOI: https://doi.org/10.1016/j.insmatheco.2013.10.017
  • [25] Jodra, P., and Jimenez-Gamero, M. D., “A quantile regression model for bounded responses based on the exponential-geometric distribution”, REVSTAT-Statistical Journal, 18(4): 415-436, (2020).
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistiksel Teori, Uygulamalı İstatistik
Bölüm Research Article
Yazarlar

Kadir Karakaya 0000-0002-0781-3587

Şule Sağlam 0000-0002-1851-8217

Erken Görünüm Tarihi 26 Nisan 2025
Yayımlanma Tarihi
Gönderilme Tarihi 12 Eylül 2024
Kabul Tarihi 13 Şubat 2025
Yayımlandığı Sayı Yıl 2025 Erken Görünüm

Kaynak Göster

APA Karakaya, K., & Sağlam, Ş. (2025). Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications. Gazi University Journal of Science1-1. https://doi.org/10.35378/gujs.1549073
AMA Karakaya K, Sağlam Ş. Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications. Gazi University Journal of Science. Published online 01 Nisan 2025:1-1. doi:10.35378/gujs.1549073
Chicago Karakaya, Kadir, ve Şule Sağlam. “Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications”. Gazi University Journal of Science, Nisan (Nisan 2025), 1-1. https://doi.org/10.35378/gujs.1549073.
EndNote Karakaya K, Sağlam Ş (01 Nisan 2025) Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications. Gazi University Journal of Science 1–1.
IEEE K. Karakaya ve Ş. Sağlam, “Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications”, Gazi University Journal of Science, ss. 1–1, Nisan 2025, doi: 10.35378/gujs.1549073.
ISNAD Karakaya, Kadir - Sağlam, Şule. “Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications”. Gazi University Journal of Science. Nisan 2025. 1-1. https://doi.org/10.35378/gujs.1549073.
JAMA Karakaya K, Sağlam Ş. Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications. Gazi University Journal of Science. 2025;:1–1.
MLA Karakaya, Kadir ve Şule Sağlam. “Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications”. Gazi University Journal of Science, 2025, ss. 1-1, doi:10.35378/gujs.1549073.
Vancouver Karakaya K, Sağlam Ş. Unit Gamma-Lindley Distribution: Properties, Estimation, Regression Analysis, and Practical Applications. Gazi University Journal of Science. 2025:1-.