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The Unit-transmuted Lindley Distribution with Applications

Year 2024, Volume: 45 Issue: 4, 803 - 810, 30.12.2024

Emrah Altun , Gholamhossein Hamedani , Abdullah Fazli

https://doi.org/10.17776/csj.1500898

Abstract

This paper introduces the unit-transmuted Lindley (unit-TL) distribution. The statistical properties of the unit-TL distribution defined between (0,1) are discussed in detail. Several estimation techniques are used to estimate the parameters of the unit-TL distribution. An analysis through simulation is carried out to evaluate the efficacy of the suggested model. Furthermore, a unique regression model is developed for bounded response variables based on the unit-TL distribution. To illustrate the importance of the suggested model in precisely describing restricted datasets, two distinct datasets are examined

Keywords

Proportion data Transmuted Lindley Least squares Simulation

References

  • [1] Papke L. E., Wooldridge J. M., Econometric methods for fractional response variables with an application to 401 (k) plan participation rates, Journal of applied econometrics, 11(6) (1996) 619-632.
  • [2] Topp C. W., Leone F. C., A family of J-shaped frequency functions, Journal of the American Statistical Association, 50(269) (1955) 209-219.
  • [3] Kumaraswamy P., A generalized probability density function for double-bounded random processes, Journal of Hydrology, 46(1-2) (1980) 79-88.
  • [4] Cordeiro G. M, de Castro M., A new family of generalized distributions, Journal of statistical computation and simulation, 81(7) (2011) 883-898.
  • [5] Mazucheli J., Menezes A. F., Dey S., The unit-Birnbaum-Saunders distribution with applications, Chilean Journal of Statistics (ChJS), 9(1) (2018) 47-57.
  • [6] Altun E., Hamedani G. G., The log-xgamma distribution with inference and application, Journal de la Societe Francaise de Statistique, 159(3) (2018) 40-55.
  • [7] Korkmaz M. C., Altun E., Alizadeh M., El-Morshedy M., The log exponential power distribution: Properties, estimations and quantile regression model, Mathematics, 9(21) (2021) 2634.
  • [8] Altun E., El-Morshedy, M., Eliwa M. S., A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models, Plos One, 16(1) (2021) e0245627.
  • [9] Altun E., The log-weighted exponential regression model: alternative to the beta regression model, Communications in Statistics-Theory and Methods, 50(10) (2021) 2306-2321.
  • [10] Altun E., Cordeiro G. M., The unit-improved second-degree Lindley distribution: inference and regression modeling, Computational Statistics, 35 (2020) 259-279.
  • [11] Korkmaz M. C., Altun E., Chesneau C., Yousof H. M., On the unit-Chen distribution with associated quantile regression and applications, Mathematica Slovaca, 72(3) (2022) 765-786.
  • [12] Korkmaz M. Ç., Leiva V., Martin-Barreiro C., The continuous Bernoulli distribution: Mathematical characterization, fractile regression, computational simulations, and applications. Fractal and Fractional, 7(5) (2023) 386.
  • [13] Mazucheli J., Korkmaz M.Ç., Menezes A.F., Leiva V., The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications. Soft Computing, 27(1) (2023) 279-295.
  • [14] Mazucheli J., Alves B., Korkmaz M.Ç. (2023). The Unit-Gompertz Quantile Regression Model for the Bounded Responses. Mathematica Slovaca, 73(4) (2023) 1039-1054.
  • [15] Ghitany, M. E., Atieh, B., Nadarajah, S., Lindley distribution and its application, Mathematics and computers in simulation, 78(4) (2008) 493-506.
  • [16] Merovci F., Transmuted lindley distribution, Int. J. Open Problems Compt. Math, 6(2) (2013) 63-72.
  • [17] Cox D. R., Snell E. J., A general definition of residuals, Journal of the Royal Statistical Society. Series B (Methodological), (1968) 248-275.
  • [18] Nadar M., Papadopoulos A., Kızılaslan F., Statistical analysis for Kumaraswamy’s distribution based on record data, Statistical Papers, 54(2) (2013) 355-369.
  • [19] Aarset A.S., How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36 (1987) 106-108.

Year 2024, Volume: 45 Issue: 4, 803 - 810, 30.12.2024

Emrah Altun , Gholamhossein Hamedani , Abdullah Fazli

https://doi.org/10.17776/csj.1500898

Abstract

References

  • [1] Papke L. E., Wooldridge J. M., Econometric methods for fractional response variables with an application to 401 (k) plan participation rates, Journal of applied econometrics, 11(6) (1996) 619-632.
  • [2] Topp C. W., Leone F. C., A family of J-shaped frequency functions, Journal of the American Statistical Association, 50(269) (1955) 209-219.
  • [3] Kumaraswamy P., A generalized probability density function for double-bounded random processes, Journal of Hydrology, 46(1-2) (1980) 79-88.
  • [4] Cordeiro G. M, de Castro M., A new family of generalized distributions, Journal of statistical computation and simulation, 81(7) (2011) 883-898.
  • [5] Mazucheli J., Menezes A. F., Dey S., The unit-Birnbaum-Saunders distribution with applications, Chilean Journal of Statistics (ChJS), 9(1) (2018) 47-57.
  • [6] Altun E., Hamedani G. G., The log-xgamma distribution with inference and application, Journal de la Societe Francaise de Statistique, 159(3) (2018) 40-55.
  • [7] Korkmaz M. C., Altun E., Alizadeh M., El-Morshedy M., The log exponential power distribution: Properties, estimations and quantile regression model, Mathematics, 9(21) (2021) 2634.
  • [8] Altun E., El-Morshedy, M., Eliwa M. S., A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models, Plos One, 16(1) (2021) e0245627.
  • [9] Altun E., The log-weighted exponential regression model: alternative to the beta regression model, Communications in Statistics-Theory and Methods, 50(10) (2021) 2306-2321.
  • [10] Altun E., Cordeiro G. M., The unit-improved second-degree Lindley distribution: inference and regression modeling, Computational Statistics, 35 (2020) 259-279.
  • [11] Korkmaz M. C., Altun E., Chesneau C., Yousof H. M., On the unit-Chen distribution with associated quantile regression and applications, Mathematica Slovaca, 72(3) (2022) 765-786.
  • [12] Korkmaz M. Ç., Leiva V., Martin-Barreiro C., The continuous Bernoulli distribution: Mathematical characterization, fractile regression, computational simulations, and applications. Fractal and Fractional, 7(5) (2023) 386.
  • [13] Mazucheli J., Korkmaz M.Ç., Menezes A.F., Leiva V., The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications. Soft Computing, 27(1) (2023) 279-295.
  • [14] Mazucheli J., Alves B., Korkmaz M.Ç. (2023). The Unit-Gompertz Quantile Regression Model for the Bounded Responses. Mathematica Slovaca, 73(4) (2023) 1039-1054.
  • [15] Ghitany, M. E., Atieh, B., Nadarajah, S., Lindley distribution and its application, Mathematics and computers in simulation, 78(4) (2008) 493-506.
  • [16] Merovci F., Transmuted lindley distribution, Int. J. Open Problems Compt. Math, 6(2) (2013) 63-72.
  • [17] Cox D. R., Snell E. J., A general definition of residuals, Journal of the Royal Statistical Society. Series B (Methodological), (1968) 248-275.
  • [18] Nadar M., Papadopoulos A., Kızılaslan F., Statistical analysis for Kumaraswamy’s distribution based on record data, Statistical Papers, 54(2) (2013) 355-369.
  • [19] Aarset A.S., How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36 (1987) 106-108.
There are 19 citations in total.

Details

Primary Language English
Subjects Stochastic Analysis and Modelling
Journal Section Natural Sciences
Authors

Emrah Altun 0000-0001-5065-2523

Gholamhossein Hamedani 0000-0002-4435-8595

Abdullah Fazli 0009-0002-5365-0114

Publication Date December 30, 2024
Submission Date June 14, 2024
Acceptance Date October 15, 2024
Published in Issue Year 2024Volume: 45 Issue: 4

Cite

APA Altun, E., Hamedani, G., & Fazli, A. (2024). The Unit-transmuted Lindley Distribution with Applications. Cumhuriyet Science Journal, 45(4), 803-810. https://doi.org/10.17776/csj.1500898
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