Ek Parametre İçermeyen Dönüşüm Tekniklerinin Karşılaştırılması ve İki Veri Seti Üzerinde Modellenmesi

Yıl 2024, Cilt: 14 Sayı: 3, 1444 – 1455, 15.09.2024

Hasan Hüseyin Gül

https://doi.org/10.31466/kfbd.1472795

Öz

İstatistik literatüründe, yeni dağılım elde etmek için bazı teknikler geliştirilmiştir. Geliştirilen bu teknikler, var olan dağılıma yeni bir veya birkaç parametre ekleyerek oluşturulmaktadır. Parametre eklemek esneklik bağlamında olumlu bir etki yaratırken, parametre tahmini ve diğer istatistiksel çıkarımlarda işlem zorluğunu da beraberinde getirmektedir. Bu noktada son yıllarda araştırmacılar tarafından ek parametre içermeyen yeni dağılım üretme teknikleri önerilmeye başlanmıştır. Bu çalışmada, Dinesh-Umesh-Sanjay (DUS), Logaritmik dönüşüm (LT) ve Kavya-Manoharan (KM) teknikleri ele alınmış ve bu tekniklerin önerilen üstel dağılım versiyonları (DUSE, LTE, KME) üzerinde durulmuştur. Bu dağılımların r. momentleri, moment çıkaran fonksiyonları ve quantile fonksiyonları gibi istatistiksel özellikleri ve en çok olabilirlik tahminleri incelenmiştir. Ayrıca iki veri seti üzerinde tekniklerin modelleme yetenekleri karşılaştırılmıştır. Sonuç olarak, KM tekniği kullanılarak önerilen KME dağılımının iki veri setini de daha iyi modellediği görülmüştür.

Anahtar Kelimeler

Dönüşüm Teknikleri, İstatistiksel Özellikler, En Çok Olabilirlik Tahmini, Üstel Dağılım

Kaynakça

  • Abu El Azm, W. S., Almetwally, E. M., Naji AL-Aziz, S., El-Bagoury, A. A. A. H., Alharbi, R., and Abo-Kasem, O. E. (2021). A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID‐19 Data. Computational Intelligence and Neuroscience, 2021(1), 5918511.
  • Adeyinka, F. S. (2019). On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application. Budapest International Research in Exact Sciences (BirEx) Journal, 1(3), 34-42.
  • Adetunji, A. A. (2023). Transmuted Ailamujia distribution with applications to lifetime observations. Asian Journal of Probability and Statistics, 21(1), 1-11.
  • Ahmad, K., Ahmad, S. P., and Ahmed, A. (2015). Structural properties of transmuted Weibull distribution. Journal of Modern Applied Statistical Methods, 14(2), 13.
  • Akkanphudit, T. (2023). Generalized DUS Transformed Garima Distribution: Properties, Simulations and Applications. Lobachevskii Journal of Mathematics, 44(2), 803-814.
  • Al-Babtain, A. A., Elbatal, I., Chesneau, C., and Jamal, F. (2020). The transmuted Muth generated class of distributions with applications. Symmetry, 12(10), 1677.
  • Alrashidi, A., and Ragab, I. E. (2023). Generalized Dinesh–Umesh–Sanjay generalized exponential distribution with application to engineering data. AIP Advances, 13(11).
  • Badr, M. M., Elbatal, I., Jamal, F., Chesneau, C., and Elgarhy, M. (2020). The transmuted odd Fréchet-G family of distributions: Theory and applications. Mathematics, 8(6), 958.
  • Balaswamy, S. (2018). Transmuted Half Normal Distribution. Int. J. Sci. Res. in Mathematical and Statistical Sciences, 5(4).
  • Chakraborty, A., Rana, S., and Maiti, S. I. (2024). Transmuted Shifted Lindley Distribution: Characterizations, Classical and Bayesian Estimation with Applications. Annals of Data Science, 1-28.
  • Corderio, G. M., Ortega, E. M., and da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1), 1-27.
  • Efron, B. (1988). Logistic Resgression, Survavial Analysis, and the Kaplan-Meier Curve. Journal of the American Statistical Association, 83, 414-425.
  • Elbatal, I., Alghamdi, S. M., Jamal, F., Khan, S., Almetwally, E. M., and Elgarhy, M. (2023). Kavya-Manoharan Weibull-G family of distributions: Statistical inference under progressive type-II censoring scheme. Advances and Applications in Statistics, 87(2), 191-223.
  • Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modelling failure time data by Lehman alternatives. Communications in Statistics-Theory and Methods, 27(4),887-904.
  • Gül, H. H., Acıtaş, Ş., Bayrak, H., and Şenoğlu, B. (2023). DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(1), 42-50.
  • Haq M. A., Butt, N. S., Usman, R. M., and Fattah, A. A. (2016). Transmuted power function distribution. Gazi University Journal of Science, 29(1), 177-185.
  • Hassan, O. H. M., Elbatal, I., Al-Nefaie, A. H., and Elgarhy, M. (2022). On the Kavya–Manoharan–Burr X Model: Estimations under Ranked Set Sampling and Applications. Journal of Risk and Financial Management, 16(1), 19.
  • Hassan, M. K., and Aslam, M. (2023). DUS-neutrosophic multivariate inverse Weibull distribution: properties and applications. Complex & Intelligent Systems, 9(5), 5679-5691.
  • Irshad, M. R., Chesneau, C., Nitin, S. L., Shibu, D. S., and Maya, R. (2021). The generalized DUS transformed log-normal distribution and its applications to cancer and heart transplant datasets. Mathematics, 9(23), 3113.
  • Karakaya, K., Kınacı, İ., Kuş, C., and Akdoğan, Y. (2021). On the DUS-Kumaraswamy distribution. Istatistik Journal of The Turkish Statistical Association, 13(1), 29-38.
  • Kaushik, A., and Nigam, U. (2022). GDUS-Modified Topp-Leone Distribution: A New Distribution with Increasing, Decreasing, and Bathtub Hazard Functions. Journal of Reliability and Statistical Studies, 299-324.
  • Kavya, P., and Manoharan, M. (2021). Some parsimonious models for lifetimes and applications. Journal of Statistical Computation and Simulation, 1-16.
  • Khan, M. S., Robert, K., and Irene, L. H. (2016). Transmuted Gompertz distribution: Properties and estimation. Pak. J. Statist, 32(3), 161-182.
  • Khan, M. I., and Mustafa, A. (2023). Powered Inverse Rayleigh Distribution Using DUS Transformation. International Journal of Analysis and Applications, 21, 61-61.
  • Kumar, D., Singh, U., and Singh, S. K. (2015). A method of proposing new distribution and its application to Bladder cancer patients data. J. Stat. Appl. Pro. Lett, 2(3),235-245.
  • Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
  • Maurya, S. K., Kaushik, A., Singh, R. K., Singh, S. K., and Singh, U. (2016). A new method of proposing distribution and its application to real data. Imperial Journal of Interdisciplinary Research, 2(6), 1331-1338.
  • Maurya, S. K., Kaushik, A., Singh, S. K., and Singh, U. (2017). A new class of distribution having decreasing, increasing, and bathtub-shaped failure rate. Communications in Statistics-Theory and Methods, 46(20),10359-10372.
  • Nadarajah, S., and Kotz, S. (2006). The exponentiated type distributions. Acta Applicandae Mathematica, 96(2), 97-111.
  • Onyekwere, C. K., Okoro, C. N., Obulezi, O. J., Udofia, E. M., and Anabike, I. C. (2022). Modification of Shanker distribution using quadratic rank transmutation map. Journal of Xidian University, 16(8), 179-198.
  • Sabri, S. R. M., and Adetunji, A. A. (2024). On the Poisson-transmuted exponential distribution and its application to frequency of claim in actuarial science. Statistics in Transition, 25(2), 103-120.
  • Samuel, A. F., and Kehinde, O. A. (2019). A study on transmuted half logistic distribution: Properties and application. International Journal of Statistical Distributions and Applications, 5(3), 54.
  • Shafiq, A., Sindhu, T. N., Riaz, M. B., Hassan, M. K., and Abushal, T. A. (2024). A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling. Heliyon, 10(9).
  • Shaw, W. T., and Buckley, I. R. (2007). The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions. Submitted, Feb, 7, 64.
  • Tanış, C. (2022). Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications. Ricerche di Matematica, 71(2), 777-802.
  • Xı, Y., Lu, H., and Liang, F. (2024). On a New Transmuted Three-Parameter Lindley Distribution and Its Applications. Sains Malaysiana, 53(6), 1427-1440.

Comparison of Additional Parameter-Free Transformation Techniques and Modelling on Two Data Sets

Yıl 2024, Cilt: 14 Sayı: 3, 1444 – 1455, 15.09.2024

Hasan Hüseyin Gül

https://doi.org/10.31466/kfbd.1472795

Öz

In the statistics literature, some techniques have been developed to obtain new distributions. These techniques are created by adding one or more parameters to the existing distribution. While adding parameters creates a positive effect in terms of flexibility, it also brings processing difficulties in parameter estimation and other statistical inferences. At this point, new distribution generation techniques without additional parameters have been proposed by researchers in recent years. In this study, Dinesh-Umesh-Sanjay (DUS), Logarithmic transformation (LT) and Kavya-Manoharan (KM) techniques are discussed and the proposed exponential distribution versions of these techniques (DUSE, LTE, KME) are examined. Statistical properties of these distributions such as r. moments, moment generating functions, quantile functions and maximum likelihood estimates are analysed. In addition, the modelling capabilities of the techniques are compared on two data sets. As a result, it was found that the KME distribution proposed using the KM technique modelled both data sets better.

Anahtar Kelimeler

Transformation techniques, Statistical properties, Maximum likelihood estimation, Exponential distribution

Kaynakça

  • Abu El Azm, W. S., Almetwally, E. M., Naji AL-Aziz, S., El-Bagoury, A. A. A. H., Alharbi, R., and Abo-Kasem, O. E. (2021). A New Transmuted Generalized Lomax Distribution: Properties and Applications to COVID‐19 Data. Computational Intelligence and Neuroscience, 2021(1), 5918511.
  • Adeyinka, F. S. (2019). On the Performance of Transmuted Logistic Distribution: Statistical Properties and Application. Budapest International Research in Exact Sciences (BirEx) Journal, 1(3), 34-42.
  • Adetunji, A. A. (2023). Transmuted Ailamujia distribution with applications to lifetime observations. Asian Journal of Probability and Statistics, 21(1), 1-11.
  • Ahmad, K., Ahmad, S. P., and Ahmed, A. (2015). Structural properties of transmuted Weibull distribution. Journal of Modern Applied Statistical Methods, 14(2), 13.
  • Akkanphudit, T. (2023). Generalized DUS Transformed Garima Distribution: Properties, Simulations and Applications. Lobachevskii Journal of Mathematics, 44(2), 803-814.
  • Al-Babtain, A. A., Elbatal, I., Chesneau, C., and Jamal, F. (2020). The transmuted Muth generated class of distributions with applications. Symmetry, 12(10), 1677.
  • Alrashidi, A., and Ragab, I. E. (2023). Generalized Dinesh–Umesh–Sanjay generalized exponential distribution with application to engineering data. AIP Advances, 13(11).
  • Badr, M. M., Elbatal, I., Jamal, F., Chesneau, C., and Elgarhy, M. (2020). The transmuted odd Fréchet-G family of distributions: Theory and applications. Mathematics, 8(6), 958.
  • Balaswamy, S. (2018). Transmuted Half Normal Distribution. Int. J. Sci. Res. in Mathematical and Statistical Sciences, 5(4).
  • Chakraborty, A., Rana, S., and Maiti, S. I. (2024). Transmuted Shifted Lindley Distribution: Characterizations, Classical and Bayesian Estimation with Applications. Annals of Data Science, 1-28.
  • Corderio, G. M., Ortega, E. M., and da Cunha, D. C. (2013). The exponentiated generalized class of distributions. Journal of Data Science, 11(1), 1-27.
  • Efron, B. (1988). Logistic Resgression, Survavial Analysis, and the Kaplan-Meier Curve. Journal of the American Statistical Association, 83, 414-425.
  • Elbatal, I., Alghamdi, S. M., Jamal, F., Khan, S., Almetwally, E. M., and Elgarhy, M. (2023). Kavya-Manoharan Weibull-G family of distributions: Statistical inference under progressive type-II censoring scheme. Advances and Applications in Statistics, 87(2), 191-223.
  • Gupta, R. C., Gupta, P. L., and Gupta, R. D. (1998). Modelling failure time data by Lehman alternatives. Communications in Statistics-Theory and Methods, 27(4),887-904.
  • Gül, H. H., Acıtaş, Ş., Bayrak, H., and Şenoğlu, B. (2023). DUS Inverse Weibull Distribution and Parameter Estimation in Regression Model. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(1), 42-50.
  • Haq M. A., Butt, N. S., Usman, R. M., and Fattah, A. A. (2016). Transmuted power function distribution. Gazi University Journal of Science, 29(1), 177-185.
  • Hassan, O. H. M., Elbatal, I., Al-Nefaie, A. H., and Elgarhy, M. (2022). On the Kavya–Manoharan–Burr X Model: Estimations under Ranked Set Sampling and Applications. Journal of Risk and Financial Management, 16(1), 19.
  • Hassan, M. K., and Aslam, M. (2023). DUS-neutrosophic multivariate inverse Weibull distribution: properties and applications. Complex & Intelligent Systems, 9(5), 5679-5691.
  • Irshad, M. R., Chesneau, C., Nitin, S. L., Shibu, D. S., and Maya, R. (2021). The generalized DUS transformed log-normal distribution and its applications to cancer and heart transplant datasets. Mathematics, 9(23), 3113.
  • Karakaya, K., Kınacı, İ., Kuş, C., and Akdoğan, Y. (2021). On the DUS-Kumaraswamy distribution. Istatistik Journal of The Turkish Statistical Association, 13(1), 29-38.
  • Kaushik, A., and Nigam, U. (2022). GDUS-Modified Topp-Leone Distribution: A New Distribution with Increasing, Decreasing, and Bathtub Hazard Functions. Journal of Reliability and Statistical Studies, 299-324.
  • Kavya, P., and Manoharan, M. (2021). Some parsimonious models for lifetimes and applications. Journal of Statistical Computation and Simulation, 1-16.
  • Khan, M. S., Robert, K., and Irene, L. H. (2016). Transmuted Gompertz distribution: Properties and estimation. Pak. J. Statist, 32(3), 161-182.
  • Khan, M. I., and Mustafa, A. (2023). Powered Inverse Rayleigh Distribution Using DUS Transformation. International Journal of Analysis and Applications, 21, 61-61.
  • Kumar, D., Singh, U., and Singh, S. K. (2015). A method of proposing new distribution and its application to Bladder cancer patients data. J. Stat. Appl. Pro. Lett, 2(3),235-245.
  • Lawless, J. F. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
  • Maurya, S. K., Kaushik, A., Singh, R. K., Singh, S. K., and Singh, U. (2016). A new method of proposing distribution and its application to real data. Imperial Journal of Interdisciplinary Research, 2(6), 1331-1338.
  • Maurya, S. K., Kaushik, A., Singh, S. K., and Singh, U. (2017). A new class of distribution having decreasing, increasing, and bathtub-shaped failure rate. Communications in Statistics-Theory and Methods, 46(20),10359-10372.
  • Nadarajah, S., and Kotz, S. (2006). The exponentiated type distributions. Acta Applicandae Mathematica, 96(2), 97-111.
  • Onyekwere, C. K., Okoro, C. N., Obulezi, O. J., Udofia, E. M., and Anabike, I. C. (2022). Modification of Shanker distribution using quadratic rank transmutation map. Journal of Xidian University, 16(8), 179-198.
  • Sabri, S. R. M., and Adetunji, A. A. (2024). On the Poisson-transmuted exponential distribution and its application to frequency of claim in actuarial science. Statistics in Transition, 25(2), 103-120.
  • Samuel, A. F., and Kehinde, O. A. (2019). A study on transmuted half logistic distribution: Properties and application. International Journal of Statistical Distributions and Applications, 5(3), 54.
  • Shafiq, A., Sindhu, T. N., Riaz, M. B., Hassan, M. K., and Abushal, T. A. (2024). A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling. Heliyon, 10(9).
  • Shaw, W. T., and Buckley, I. R. (2007). The alchemy of probability distributions: Beyond gram-charlier & cornish-fisher expansions, and skew-normal or kurtotic-normal distributions. Submitted, Feb, 7, 64.
  • Tanış, C. (2022). Transmuted lower record type inverse rayleigh distribution: estimation, characterizations and applications. Ricerche di Matematica, 71(2), 777-802.
  • Xı, Y., Lu, H., and Liang, F. (2024). On a New Transmuted Three-Parameter Lindley Distribution and Its Applications. Sains Malaysiana, 53(6), 1427-1440.

Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Yazılım Mühendisliği (Diğer)
BölümMakaleler
Yazarlar

Hasan Hüseyin Gül GİRESUN ÜNİVERSİTESİ, FEN-EDEBİYAT FAKÜLTESİ 0000-0001-9905-8605 Türkiye

Yayımlanma Tarihi15 Eylül 2024
Gönderilme Tarihi24 Nisan 2024
Kabul Tarihi14 Ağustos 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 14 Sayı: 3

Kaynak Göster

APAGül, H. H. (2024). Ek Parametre İçermeyen Dönüşüm Tekniklerinin Karşılaştırılması ve İki Veri Seti Üzerinde Modellenmesi. Karadeniz Fen Bilimleri Dergisi, 14(3), 1444-1455. https://doi.org/10.31466/kfbd.1472795

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