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BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 69 Sayı: 2, 995 - 1012, 31.12.2020

Omid Kharazmi Ali Saadatinik G.g Hamedani

https://doi.org/10.31801/cfsuasmas.614578

Öz

Kaynakça

  • Ababneh, M., Ebrahem, M. A. H., Designing degradation experiments using a Weibull distribution, Journal of Statistics and Management Systems, 21(6) (2018), 971-983.
  • Alzaatreh, A., Lee, C., Famoye, F., A new method for generating families of continuous distributions, Metron, 71(1)(2013), 63-79.
  • Aarset, M. V., How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36(1) (1987), 106-108.
  • Efron, B., Tibshirani, R. J., An introduction to the bootstrap, CRC press, 1994.
  • Glänzel, W., A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Reidel, Dordrecht, Vol. B, (1987), 75--84.
  • Glänzel, W., Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21 (4) (1990), 613--618.
  • Hamedani, G.G., On certain generalized gamma convolution distributions II, Technical Report No. 484, MSCS, Marquette University, 2013.
  • Lee, E. T., Wang, J., Statistical methods for survival data analysis, (Vol. 476), John Wiley & Sons, 2003. Lindley, D.V., Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society Series B, 20 (1958), 102-107.
  • Murthy, D. P., Xie, M., Jiang, R., Weibull models, (Vol. 505). John Wiley & Sons, 2004.
  • Nadarajah, S., Bakouch, H. S., Tahmasbi, R., A generalized Lindley distribution, Sankhya B, 73 (2) (2011), 331-359.
  • Samuel, B. R., Balamurali, S., Aslam, M., Designing of repetitive group sampling plan under truncated life test based on generalized inverted exponential distribution, Journal of Statistics and Management Systems, 21(6) (2018), 955-970. Zeghdoudi, H., Nedjar, S., Gamma Lindley distribution and its application, Journal of Applied Probability and Statistics, 11 (1) (2015), 1-11.
  • Zakerzadeh, H., Dolati, A., Generalized Lindley distribution, Journal of Mathematical Extension, 3 (2) (2009), 13-25.

A new generalized-upper record values-G family of lifetime distributions

Yıl 2020, Cilt: 69 Sayı: 2, 995 - 1012, 31.12.2020

Omid Kharazmi Ali Saadatinik G.g Hamedani

https://doi.org/10.31801/cfsuasmas.614578

Öz

A new family of lifetime distributions is introduced via distribution of the upper record values, the well-known concept in survival analysis and reliability engineering. Some important properties of the proposed model including quantile function, hazard function, order statistics are obtained in a general setting. A special case of this new family is proposed by considering the exponential and Weibull distribution as the parent distributions. In addition estimating unknown parameters of specialized distribution is examined from the perspective of the traditional statistics. A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, one example of real data set is studied; point and interval estimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority of the proposed model in terms of the parent exponential distribution over other known distributions is shown via the example of real observations.

Anahtar Kelimeler

Upper record value order statistics maximum likelihood estimation bootstrap Weibull distribution

Kaynakça

  • Ababneh, M., Ebrahem, M. A. H., Designing degradation experiments using a Weibull distribution, Journal of Statistics and Management Systems, 21(6) (2018), 971-983.
  • Alzaatreh, A., Lee, C., Famoye, F., A new method for generating families of continuous distributions, Metron, 71(1)(2013), 63-79.
  • Aarset, M. V., How to identify a bathtub hazard rate, IEEE Transactions on Reliability, 36(1) (1987), 106-108.
  • Efron, B., Tibshirani, R. J., An introduction to the bootstrap, CRC press, 1994.
  • Glänzel, W., A characterization theorem based on truncated moments and its application to some distribution families, Mathematical Statistics and Probability Theory (Bad Tatzmannsdorf, 1986), Reidel, Dordrecht, Vol. B, (1987), 75--84.
  • Glänzel, W., Some consequences of a characterization theorem based on truncated moments, Statistics: A Journal of Theoretical and Applied Statistics, 21 (4) (1990), 613--618.
  • Hamedani, G.G., On certain generalized gamma convolution distributions II, Technical Report No. 484, MSCS, Marquette University, 2013.
  • Lee, E. T., Wang, J., Statistical methods for survival data analysis, (Vol. 476), John Wiley & Sons, 2003. Lindley, D.V., Fiducial distributions and Bayes theorem, Journal of the Royal Statistical Society Series B, 20 (1958), 102-107.
  • Murthy, D. P., Xie, M., Jiang, R., Weibull models, (Vol. 505). John Wiley & Sons, 2004.
  • Nadarajah, S., Bakouch, H. S., Tahmasbi, R., A generalized Lindley distribution, Sankhya B, 73 (2) (2011), 331-359.
  • Samuel, B. R., Balamurali, S., Aslam, M., Designing of repetitive group sampling plan under truncated life test based on generalized inverted exponential distribution, Journal of Statistics and Management Systems, 21(6) (2018), 955-970. Zeghdoudi, H., Nedjar, S., Gamma Lindley distribution and its application, Journal of Applied Probability and Statistics, 11 (1) (2015), 1-11.
  • Zakerzadeh, H., Dolati, A., Generalized Lindley distribution, Journal of Mathematical Extension, 3 (2) (2009), 13-25.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik, Uygulamalı Matematik
Bölüm Research Article
Yazarlar

Omid Kharazmi 0000-0001-6557-3852

Ali Saadatinik Bu kişi benim 0000-0002-1839-5667

G.g Hamedani 0000-0001-7976-1088

Yayımlanma Tarihi 31 Aralık 2020
Gönderilme Tarihi 3 Eylül 2019
Kabul Tarihi 27 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 69 Sayı: 2

Kaynak Göster

APA Kharazmi, O., Saadatinik, A., & Hamedani, G. (2020). A new generalized-upper record values-G family of lifetime distributions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 995-1012. https://doi.org/10.31801/cfsuasmas.614578
AMA Kharazmi O, Saadatinik A, Hamedani G. A new generalized-upper record values-G family of lifetime distributions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Aralık 2020;69(2):995-1012. doi:10.31801/cfsuasmas.614578
Chicago Kharazmi, Omid, Ali Saadatinik, ve G.g Hamedani. “A New Generalized-Upper Record Values-G Family of Lifetime Distributions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, sy. 2 (Aralık 2020): 995-1012. https://doi.org/10.31801/cfsuasmas.614578.
EndNote Kharazmi O, Saadatinik A, Hamedani G (01 Aralık 2020) A new generalized-upper record values-G family of lifetime distributions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 995–1012.
IEEE O. Kharazmi, A. Saadatinik, ve G. Hamedani, “A new generalized-upper record values-G family of lifetime distributions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 69, sy. 2, ss. 995–1012, 2020, doi: 10.31801/cfsuasmas.614578.
ISNAD Kharazmi, Omid vd. “A New Generalized-Upper Record Values-G Family of Lifetime Distributions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (Aralık 2020), 995-1012. https://doi.org/10.31801/cfsuasmas.614578.
JAMA Kharazmi O, Saadatinik A, Hamedani G. A new generalized-upper record values-G family of lifetime distributions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:995–1012.
MLA Kharazmi, Omid vd. “A New Generalized-Upper Record Values-G Family of Lifetime Distributions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 69, sy. 2, 2020, ss. 995-1012, doi:10.31801/cfsuasmas.614578.
Vancouver Kharazmi O, Saadatinik A, Hamedani G. A new generalized-upper record values-G family of lifetime distributions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):995-1012.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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