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Year 2023, Volume: 44 Issue: 1, 224 - 228, 26.03.2023

Mustafa Ç. Korkmaz , Kadir Karakaya , Yunus Akdoğan , Yener Ünal

https://doi.org/10.17776/csj.1171453
Cited By: 2

Abstract

References

  • [1] Kumaraswamy, P., A generalized probability density function for double-bounded random processes , J. Hydrol., 46 (1980), 79-88.
  • [2] Gómez-Déniz, E., Sordo, M.A., Calderín-Ojeda, E., The log–lindley distribution as an alternative to the beta regression model with applications in insurance, Insurance Math. Econ., 54 (2014), 49-57.
  • [3] Mazucheli, J., Menezes, A.F.B., Chakraborty, S., On the one parameter unit-Lindley distribution and its associated regression model for proportion data, J. Appl. Stat., 46 (2019), 700-714.
  • [4] Korkmaz, M.Ç., Chesneau, C. On the unit burr-xii distribution with the quantile regression modeling and applications, Comput. Appl. Math., 40 (2021), 1-26.
  • [5] Korkmaz, M.Ç., Korkmaz, Z.S., The unit log–log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications, Journal of Applied Statistics, (2021) 1-20.
  • [6] Pham, H., A vtub-shaped hazard rate function with applications to system safety, Int. J. Reliab. Appl., 3 (2002), 1–16.
  • [7] Ferrari, S., Cribari-Neto, F., Beta regression for modelling rates and proportions, Journal of Applied Statistics, 31(7) (2004) 799–815.
  • [8] Mitnik, P.A., Baek, S., The Kumaraswamy distribution: Median-dispersion re-parameterizations for regression modeling and simulation-based estimation, Stat. Pap., 54 (2013) 177–192.
  • [9] Mazucheli, J., Menezes, A., Fernandes, L., de Oliveira, R., Ghitany, M., The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates, Journal of Applied Statistics, 47 (2020) 954–974.
  • [10] Kınacı, İ., Kuş, C., Karakaya, K., Akdoğan, Y., APT-Pareto Distribution and its Properties. Cumhuriyet Science Journal, (2019) 40 (2) 378-387.
  • [11] Karakaya, K., Tanış, C., Different methods of estimation for the one parameter Akash distribution, Cumhuriyet Science Journal, (2020) 41 (4) 944-950 .
  • [12] Tanış, C., Saraçoğlu, B., Kuş, C., Pekgör, A., Transmuted complementary exponential power distribution: properties and applications. Cumhuriyet Science Journal, (2020) 41 (2) 419-432.
  • [13] Hamedani, G.G., Korkmaz, M.Ç., Butt, N.S., Yousof, H.M., The Type I Quasi Lambert Family, Pakistan Journal of Statistics and Operation Research, 17(3) (2021) 545-558.
  • [14] Cheng, R.C.H., Amin, N.A.K., Maximum product of spacings estimation with application to the lognormal distribution, Math Report, (1979) 791.
  • [15] Dumonceaux, R., Antle, C.E., Discrimination between the log-normal and the Weibull distributions, Technometrics, 15(4) (1973) 923-926.
  • [16] Elgarhy, M., Exponentiated generalized Kumaraswamy distribution with applications, Annals of Data Science, 5(2) (2018) 273-292.

Parameters Estimation for the Unit log-log Distribution

Year 2023, Volume: 44 Issue: 1, 224 - 228, 26.03.2023

Mustafa Ç. Korkmaz , Kadir Karakaya , Yunus Akdoğan , Yener Ünal

https://doi.org/10.17776/csj.1171453
Cited By: 2

Abstract

In this paper, point estimation problem of two unknown parameters of the unit log-log distribution is examined. For point estimation, six methods of estimate such as maximum likelihood, maximum product spacing, Anderson-Darling, least squares, weighted least squares, and Cramer-von Mises are examined in detail. Extensive simulation experiments are conducted to compare the effectiveness of these estimators based on bias and mean squared errors. According to the simulation results, it is seen that all estimators performed well in terms of two criteria and take close values in case of large sample. Moreover, practical data applications are performed for all estimators. Results of the Kolmogorov-Smirnov statistics are reported for all estimators in practical applications.

Keywords

Unit log-log distribution Estimation Monte Carlo simuation Kolmogrov-Smirnov statistic.

References

  • [1] Kumaraswamy, P., A generalized probability density function for double-bounded random processes , J. Hydrol., 46 (1980), 79-88.
  • [2] Gómez-Déniz, E., Sordo, M.A., Calderín-Ojeda, E., The log–lindley distribution as an alternative to the beta regression model with applications in insurance, Insurance Math. Econ., 54 (2014), 49-57.
  • [3] Mazucheli, J., Menezes, A.F.B., Chakraborty, S., On the one parameter unit-Lindley distribution and its associated regression model for proportion data, J. Appl. Stat., 46 (2019), 700-714.
  • [4] Korkmaz, M.Ç., Chesneau, C. On the unit burr-xii distribution with the quantile regression modeling and applications, Comput. Appl. Math., 40 (2021), 1-26.
  • [5] Korkmaz, M.Ç., Korkmaz, Z.S., The unit log–log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications, Journal of Applied Statistics, (2021) 1-20.
  • [6] Pham, H., A vtub-shaped hazard rate function with applications to system safety, Int. J. Reliab. Appl., 3 (2002), 1–16.
  • [7] Ferrari, S., Cribari-Neto, F., Beta regression for modelling rates and proportions, Journal of Applied Statistics, 31(7) (2004) 799–815.
  • [8] Mitnik, P.A., Baek, S., The Kumaraswamy distribution: Median-dispersion re-parameterizations for regression modeling and simulation-based estimation, Stat. Pap., 54 (2013) 177–192.
  • [9] Mazucheli, J., Menezes, A., Fernandes, L., de Oliveira, R., Ghitany, M., The unit-Weibull distribution as an alternative to the Kumaraswamy distribution for the modeling of quantiles conditional on covariates, Journal of Applied Statistics, 47 (2020) 954–974.
  • [10] Kınacı, İ., Kuş, C., Karakaya, K., Akdoğan, Y., APT-Pareto Distribution and its Properties. Cumhuriyet Science Journal, (2019) 40 (2) 378-387.
  • [11] Karakaya, K., Tanış, C., Different methods of estimation for the one parameter Akash distribution, Cumhuriyet Science Journal, (2020) 41 (4) 944-950 .
  • [12] Tanış, C., Saraçoğlu, B., Kuş, C., Pekgör, A., Transmuted complementary exponential power distribution: properties and applications. Cumhuriyet Science Journal, (2020) 41 (2) 419-432.
  • [13] Hamedani, G.G., Korkmaz, M.Ç., Butt, N.S., Yousof, H.M., The Type I Quasi Lambert Family, Pakistan Journal of Statistics and Operation Research, 17(3) (2021) 545-558.
  • [14] Cheng, R.C.H., Amin, N.A.K., Maximum product of spacings estimation with application to the lognormal distribution, Math Report, (1979) 791.
  • [15] Dumonceaux, R., Antle, C.E., Discrimination between the log-normal and the Weibull distributions, Technometrics, 15(4) (1973) 923-926.
  • [16] Elgarhy, M., Exponentiated generalized Kumaraswamy distribution with applications, Annals of Data Science, 5(2) (2018) 273-292.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Mustafa Ç. Korkmaz 0000-0003-3302-0705

Kadir Karakaya 0000-0002-0781-3587

Yunus Akdoğan 0000-0003-3520-7493

Yener Ünal 0000-0002-4796-8276

Publication Date March 26, 2023
Submission Date September 6, 2022
Acceptance Date January 11, 2023
Published in Issue Year 2023Volume: 44 Issue: 1

Cite

APA Korkmaz, M. Ç., Karakaya, K., Akdoğan, Y., Ünal, Y. (2023). Parameters Estimation for the Unit log-log Distribution. Cumhuriyet Science Journal, 44(1), 224-228. https://doi.org/10.17776/csj.1171453

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