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Yıl 2023, Cilt: 44 Sayı: 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

Öz

Kaynakça

  • [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

Yıl 2023, Cilt: 44 Sayı: 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

Öz

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.

Anahtar Kelimeler

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

Kaynakça

  • [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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İstatistik
Bölüm Natural Sciences
Yazarlar

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

Yayımlanma Tarihi 26 Mart 2023
Gönderilme Tarihi 6 Eylül 2022
Kabul Tarihi 11 Ocak 2023
Yayımlandığı Sayı Yıl 2023Cilt: 44 Sayı: 1

Kaynak Göster

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

Cited By

New Circular Distribution with an Application to Biology
Cumhuriyet Science Journal
https://doi.org/10.17776/csj.1316115
Estimation and Optimal Censoring Plan for a New Unit Log-Log Model via Improved Adaptive Progressively Censored Data
Axioms
https://doi.org/10.3390/axioms13030152
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