Öz
Bu makalede, log exponential-power dağılımının iki parametresini tahmin etmek için çeşitli tahmin yöntemleri araştırılmıştır. En çok olabilirlik, kuantil, en küçük kareler, ağırlıklandırılmış en küçük kareler, Anderson-Darling ve Cramer-von Mises tahmin yöntemleri detaylı olarak incelenmiştir. Bu tahmin edicilerin performanslarını değerlendirmek için Monte Carlo simülasyon deneyleri yapılmıştır. Ayrıca dört gerçek veri uygulaması gerçekleştirilmiş ve tüm tahmin ediciler Kolmogorov-Smirnov istatistiği sonuçları sunulmuştur.
Anahtar Kelimeler
Nokta tahmini Log exponential-power dağılımı En çok olabilirlik tahmini Gerçek veri uygulaması
Kaynakça
- Korkmaz, M.Ç., Altun, E., Alizadeh, M., El-Morshedy, M., The Log Exponential- Power Distribution: Properties, Estimations and Quantile Regression Model, Mathematics, 9 (21), 2634, 2021.
- Smith, R.M., Bain, L.J., An exponential power life-testing distribution, Communication in Statistics Theory Methods, 4, 469–481, 1975.
- Kumaraswamy, P., A generalized probability density function for double-bounded random processes, Journal of Hydrology, 46, 79–88, 1980.
- Kao, J.H., Computer methods for estimating Weibull parameters in reliability studies, IRE Transactions on Reliability and Quality Control, 13, 15-22, 1958.
- Dumonceaux, R., Antle, C.E., Discrimination between the log-normal and the Weibull distributions, Technometrics, 15 (4), 923-926, 1973.
- Balakrishnan, N., Cohen, A.C., Order Statistics & Inference: Estimation Methods, Elsevier, Amsterdam, The Netherlands, 2014.
- Alizadeh, M., Altun, E., Cordeiro, G.M., Rasekhi, M., The odd power Cauchy family of distributions: Properties, regression models and applications, Journal of Statistical Computation and Simulation, 88, 785–807, 2018.
- Elgarhy, M., Exponentiated generalized Kumaraswamy distribution with applications, Annals of Data Science, 5 (2), 273-292, 2018.
- Cordeiro, G.M., dos Santos Brito, R., The beta power distribution, Brazilian Journal Of Probability And Statistics, 26 (1), 88-112, 2012.
- Opone, F., Iwerumor, B., A new Marshall-Olkin extended family of distributions with bounded support, Gazi University Journal of Science, 34 (3), 899-914, 2021.
- Balogun, O.S., Iqbal, M.Z., Arshad, M.Z., Afify, A.Z., Oguntunde, P.E., A new generalization of Lehmann type-II distribution: Theory, simulation, and applications to survival and failure rate data, Scientific African, 12, e00790, 2021.
- Saraçoğlu, B., Tanış, C., A new statistical distribution: cubic rank transmuted Kumaraswamy distribution and its properties, Journal of the National Science Foundation of Sri Lanka, 46 (4), 505-518, 2018.
- Jamal, F., Chesneau, C., A new family of polyno-expo-trigonometric distributions with applications, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 22 (04), 1950027, 2019.
Öz
In this study, some estimation techniques are investigated to estimate two parameters of the log exponential-power distribution. The maximum likelihood, quantile, least squares, weighted least squares, Anderson-Darling, and Cramer-von Mises estimation methods are studied in detail. The efficiency of these estimators is validated through Monte Carlo simulation experiments. Also, four real data applications are performed and Kolmogorov-Smirnov statistic results for all estimators are presented.
Anahtar Kelimeler
Point estimation Log exponential-power distribution Maximum likelihood estimators Practical data application Nokta tahmini Log exponential-power dağılımı En çok olabilirlik tahmini Gerçek veri uygulaması.
Kaynakça
- Korkmaz, M.Ç., Altun, E., Alizadeh, M., El-Morshedy, M., The Log Exponential- Power Distribution: Properties, Estimations and Quantile Regression Model, Mathematics, 9 (21), 2634, 2021.
- Smith, R.M., Bain, L.J., An exponential power life-testing distribution, Communication in Statistics Theory Methods, 4, 469–481, 1975.
- Kumaraswamy, P., A generalized probability density function for double-bounded random processes, Journal of Hydrology, 46, 79–88, 1980.
- Kao, J.H., Computer methods for estimating Weibull parameters in reliability studies, IRE Transactions on Reliability and Quality Control, 13, 15-22, 1958.
- Dumonceaux, R., Antle, C.E., Discrimination between the log-normal and the Weibull distributions, Technometrics, 15 (4), 923-926, 1973.
- Balakrishnan, N., Cohen, A.C., Order Statistics & Inference: Estimation Methods, Elsevier, Amsterdam, The Netherlands, 2014.
- Alizadeh, M., Altun, E., Cordeiro, G.M., Rasekhi, M., The odd power Cauchy family of distributions: Properties, regression models and applications, Journal of Statistical Computation and Simulation, 88, 785–807, 2018.
- Elgarhy, M., Exponentiated generalized Kumaraswamy distribution with applications, Annals of Data Science, 5 (2), 273-292, 2018.
- Cordeiro, G.M., dos Santos Brito, R., The beta power distribution, Brazilian Journal Of Probability And Statistics, 26 (1), 88-112, 2012.
- Opone, F., Iwerumor, B., A new Marshall-Olkin extended family of distributions with bounded support, Gazi University Journal of Science, 34 (3), 899-914, 2021.
- Balogun, O.S., Iqbal, M.Z., Arshad, M.Z., Afify, A.Z., Oguntunde, P.E., A new generalization of Lehmann type-II distribution: Theory, simulation, and applications to survival and failure rate data, Scientific African, 12, e00790, 2021.
- Saraçoğlu, B., Tanış, C., A new statistical distribution: cubic rank transmuted Kumaraswamy distribution and its properties, Journal of the National Science Foundation of Sri Lanka, 46 (4), 505-518, 2018.
- Jamal, F., Chesneau, C., A new family of polyno-expo-trigonometric distributions with applications, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 22 (04), 1950027, 2019.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Gönderilme Tarihi | 14 Şubat 2022 |
| Kabul Tarihi | 28 Eylül 2022 |
| Yayımlanma Tarihi | 30 Aralık 2022 |
| DOI | https://doi.org/10.37094/adyujsci.1073616 |
| IZ | https://izlik.org/JA29RY55WU |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 12 Sayı: 2 |