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Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama

Year 2022, Volume: 22 Issue: 2, 307 - 314, 30.04.2022
https://doi.org/10.35414/akufemubid.1068310

Abstract

Bu çalışmada yeni bir dağılım olan üç parametreli Odd genelleştirilmiş yarı lojistik Weibull-Rayleigh (OGYLW-R) dağılımı tanıtılmıştır. Dağılımın elde edilmesinde, Chipepa vd. (2020) tarafından önerilen yeni dağılım ailesi olarak Odd genelleştirilmiş yarı lojistik Weibul-genelleştirilmiş (OGYLW-G) dağılım ailesi kullanılmıştır. Elde edilen dağılımın olasılık yoğunluk, dağılım, hazard, yaşam ve kantil fonksiyonları, momentleri, çarpıklık, basıklık katsayıları ve sıralı istatistiklerini içeren temel istatistiksel özellikleri elde edilmiştir. Dağılımın parametre tahmini en çok olabilirlik tahmin yöntemi ile bulunmuştur. Önerilen dağılımın literatürdeki dağılımlardan üstünlüğünü göstermek için gerçek veri setine uygulanmış ve OGYLW-R dağılımının kesilmiş Weibull-Rayleigh dağılımının uyumu ile karşılaştırılmıştır. OGHLW-R dağılımının veriye daha uyumlu olduğu görülmüştür. Çarpıklık katsayısına göre dağılımın sola çarpık, basıklık katsayısına göre ise normal dağılıma göre daha basık olduğu görülmüştür.

References

  • Ben-Israel, A., 1966. A Newton-Raphson method for the solution of systems of equations. Journal of Mathematical Analysis and Applications, 15(2), 243-252.
  • Afify, A.Z., Altun, E., Alizadeh, M., Ozel, G. and Hamedani, G.G., 2017. The Odd Exponentiated Half-Logistic-G Family: properties, characterizations and applications. Chilean Journal of Statistics, 8(2), 65-91.
  • Al-Noor, N.H. and Assi, N.K., 2020. Rayleigh-Rayleigh distribution: properties and applications. Journal of Physics: Conference Series 1591, doi:10.1088/1742-6596/1591/1/012038.
  • Balakrishnan, N., 1985. Order statistics from the half logistic distribution. Journal of Statistical Computation and Simulation, 20(4), 287-309.
  • Bourguignon, M., Silva, R. B. And Cordeiro, G. M., 2014. The Weibull-G family of probability distributions. Journal of Data Science, 12(1), 53-68.
  • Chipepa, F., Oluyede, B. and Makubate, B., 2020. The odd generalized half-logistic Weibull-G family of distributions: properties and applications. Journal of Statistical Modelling: Theory and Applications, 1(1), 65-89.
  • Cordeiro, G. M., Alizadeh, M. and Diniz Marinho, P. R. 2016. The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, 86(4), 707-728.
  • Khalifa, E.H., Ramadan, A.D. and El-Desouky, B.S., 2021. Statistical inference of truncated weibull-rayleigh distribution: its properties and applications. Open Journal of Modelling and Simulation, 9, 281-298.
  • Korkmaz, M.Ç., Alizadeh, M. and Yousof, H.M., 2018. The generalized odd weibull generated family of distributions: statistical properties and applications. Pakistan Journal of Statistics and Operation Research, 3, 541-556.
  • Luguterah, A., 2016. Odd generalized exponential rayleigh distribution, advances and applications in statistics. Advances and Applications in Statistics, 48(1), 33-48.
  • Mansoor, M., Tahir, M.H., Gauss M. Cordeiro, G.M., Alzaatreh, A. and Zubair, M., 2017. A new family of distributions to analyze lifetime data. Journal of Statistical Theory and Applications, 16(4), 490–507.
  • Marinho P.R.D, Silva R.B., Bourguignon M., Cordeiro G.M. and Nadarajah S. 2019. AdequacyModel: An R package for probability distributions and general purpose optimization. PLoS ONE 14(8): e0221487. https://doi.org/10.1371/journal.pone.0221487.
  • Nadarajah, S., and Rocha, R. 2016. Newdistns: An R package for new families of distributions. Journal of Statistical Software, 69(10), 1-32, doi:10.18637/jss.v069.i10.
  • Ozel, G. And Çakmakyapan, S., 2015. A new distribution and application on the lifetime data. World Academy of Science, Engineering and Technology, 9(7), 420-423.
  • Tekin, S. and Özel, G., 2020. Alfa Güç Burr-XII Dağılımı ve Bir Uygulama. Nicel Bilimler Dergisi, 2(1), 33-46.
  • İnternet kaynakları 1-https://www.R-project.org/. (04.02.2022)

Odd Generalized Half-Logistic Weibull Rayleigh Distribution: Properties and an Application

Year 2022, Volume: 22 Issue: 2, 307 - 314, 30.04.2022
https://doi.org/10.35414/akufemubid.1068310

Abstract

In this study, a new three-parameter Odd generalized semi-logistic Weibull-Rayleigh (OGYLW-R) distribution is introduced. In obtaining the distribution, Chipepa et al. (2020), the Odd generalized semi-logistic Weibul-generalized (OGYLW-G) distribution family was used as the new distribution family. Basic statistical properties of the obtained distribution including probability density, distribution, hazard, survival and quantile functions, moments, skewness, kurtosis coefficients, and ordinal statistics are obtained. The parameter estimation of the distribution was found using the maximum likelihood estimation method. To show the superiority of the proposed distribution over the distributions in the literature, it was applied to the real data set and the OGYLW-R distribution was compared with the fit of the truncated Weibull-Rayleigh distribution. It was seen that the OGHLW-R distribution was more compatible with the data. According to the skewness coefficient, it was observed that the distribution was skewed to the left, and according to the kurtosis coefficient, it was more flattened than the normal distribution.

References

  • Ben-Israel, A., 1966. A Newton-Raphson method for the solution of systems of equations. Journal of Mathematical Analysis and Applications, 15(2), 243-252.
  • Afify, A.Z., Altun, E., Alizadeh, M., Ozel, G. and Hamedani, G.G., 2017. The Odd Exponentiated Half-Logistic-G Family: properties, characterizations and applications. Chilean Journal of Statistics, 8(2), 65-91.
  • Al-Noor, N.H. and Assi, N.K., 2020. Rayleigh-Rayleigh distribution: properties and applications. Journal of Physics: Conference Series 1591, doi:10.1088/1742-6596/1591/1/012038.
  • Balakrishnan, N., 1985. Order statistics from the half logistic distribution. Journal of Statistical Computation and Simulation, 20(4), 287-309.
  • Bourguignon, M., Silva, R. B. And Cordeiro, G. M., 2014. The Weibull-G family of probability distributions. Journal of Data Science, 12(1), 53-68.
  • Chipepa, F., Oluyede, B. and Makubate, B., 2020. The odd generalized half-logistic Weibull-G family of distributions: properties and applications. Journal of Statistical Modelling: Theory and Applications, 1(1), 65-89.
  • Cordeiro, G. M., Alizadeh, M. and Diniz Marinho, P. R. 2016. The type I half-logistic family of distributions. Journal of Statistical Computation and Simulation, 86(4), 707-728.
  • Khalifa, E.H., Ramadan, A.D. and El-Desouky, B.S., 2021. Statistical inference of truncated weibull-rayleigh distribution: its properties and applications. Open Journal of Modelling and Simulation, 9, 281-298.
  • Korkmaz, M.Ç., Alizadeh, M. and Yousof, H.M., 2018. The generalized odd weibull generated family of distributions: statistical properties and applications. Pakistan Journal of Statistics and Operation Research, 3, 541-556.
  • Luguterah, A., 2016. Odd generalized exponential rayleigh distribution, advances and applications in statistics. Advances and Applications in Statistics, 48(1), 33-48.
  • Mansoor, M., Tahir, M.H., Gauss M. Cordeiro, G.M., Alzaatreh, A. and Zubair, M., 2017. A new family of distributions to analyze lifetime data. Journal of Statistical Theory and Applications, 16(4), 490–507.
  • Marinho P.R.D, Silva R.B., Bourguignon M., Cordeiro G.M. and Nadarajah S. 2019. AdequacyModel: An R package for probability distributions and general purpose optimization. PLoS ONE 14(8): e0221487. https://doi.org/10.1371/journal.pone.0221487.
  • Nadarajah, S., and Rocha, R. 2016. Newdistns: An R package for new families of distributions. Journal of Statistical Software, 69(10), 1-32, doi:10.18637/jss.v069.i10.
  • Ozel, G. And Çakmakyapan, S., 2015. A new distribution and application on the lifetime data. World Academy of Science, Engineering and Technology, 9(7), 420-423.
  • Tekin, S. and Özel, G., 2020. Alfa Güç Burr-XII Dağılımı ve Bir Uygulama. Nicel Bilimler Dergisi, 2(1), 33-46.
  • İnternet kaynakları 1-https://www.R-project.org/. (04.02.2022)
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Applied Mathematics
Journal Section Articles
Authors

Ceren Ünal 0000-0002-9357-1771

Gamze Özel 0000-0003-3886-3074

Publication Date April 30, 2022
Submission Date February 4, 2022
Published in Issue Year 2022 Volume: 22 Issue: 2

Cite

APA Ünal, C., & Özel, G. (2022). Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 22(2), 307-314. https://doi.org/10.35414/akufemubid.1068310
AMA Ünal C, Özel G. Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. April 2022;22(2):307-314. doi:10.35414/akufemubid.1068310
Chicago Ünal, Ceren, and Gamze Özel. “Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri Ve Bir Uygulama”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22, no. 2 (April 2022): 307-14. https://doi.org/10.35414/akufemubid.1068310.
EndNote Ünal C, Özel G (April 1, 2022) Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22 2 307–314.
IEEE C. Ünal and G. Özel, “Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 22, no. 2, pp. 307–314, 2022, doi: 10.35414/akufemubid.1068310.
ISNAD Ünal, Ceren - Özel, Gamze. “Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri Ve Bir Uygulama”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22/2 (April 2022), 307-314. https://doi.org/10.35414/akufemubid.1068310.
JAMA Ünal C, Özel G. Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22:307–314.
MLA Ünal, Ceren and Gamze Özel. “Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri Ve Bir Uygulama”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 22, no. 2, 2022, pp. 307-14, doi:10.35414/akufemubid.1068310.
Vancouver Ünal C, Özel G. Odd Genelleştirilmiş Yarı Lojistik Weibull-Rayleigh Dağılımı: Özellikleri ve Bir Uygulama. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22(2):307-14.