KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2019 / Cilt: 48 - Sayı: 3

The power-linear hazard rate distribution and estimation of its parameters under progressively type-II censoring

Bahman TARVİRDİZADE
Nader NEMATOLLAHİ
Sayfa
818–844
Yayın Tarihi
2019-06-15
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, a Monte Carlo simulation study is conducted to investigate and compare the performance of different types of estimators presented in this paper.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we introduce a class of distributions which generalizes the power hazard rate distribution and is obtained by combining the linear and power hazard rate functions.
📊
Temel Bulgular & Veri:This class of distributions, which is called the power-linear hazard rate distribution, is simple and flexible and contains some important lifetime distributions.
💡
Sonuç & Katkı:Finally, a Monte Carlo simulation study is conducted to investigate and compare the performance of different types of estimators presented in this paper.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Bayes estimation · Bootstrap confidence intervals · EM algorithm

Abstract

In this paper, we introduce a class of distributions which generalizes the power hazard rate distribution and is obtained by combining the linear and power hazard rate functions. This class of distributions, which is called the power-linear hazard rate distribution, is simple and flexible and contains some important lifetime distributions. The maximum likelihood estimators of the parameters using the Newton-Raphson (NR) and the expectation-maximization (EM) algorithms and the Bayes estimators of the parameters under squared error loss (SEL), linear-exponential (LINEX) and Stein loss functions are obtained based on progressively type-II censored sample. Also, we obtain the asymptotic confidence interval and some bootstrap confidence intervals and construct the HPD credible interval for the parameters. A real data set is analyzed and observed that the present hazard rate distribution can provide a better fit than other three-parameter distributions. Finally, a Monte Carlo simulation study is conducted to investigate and compare the performance of different types of estimators presented in this paper.

🔖

Bu Makaleye Atıf Yap

TARVİRDİZADE, B., NEMATOLLAHİ, N. (2019). The power-linear hazard rate distribution and estimation of its parameters under progressively type-II censoring. Hacettepe Journal of Mathematics and Statistics, Cilt: 48 - Sayı: 3, 818–844. https://ajindex.com/articles/669369

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. Akdam, N., Kinaci, I. and Saracoglu, B. Statistical inference of stress-strength reliability for the exponential power distribution based on progressive type-II censored samples, Hacettepe Journal of Mathematics and Statistics 46, 239–253, 2017.
  2. Bain, L. Analysis for the linear failure-rate life testing distribution, Technometrics 15, 551– 559, 1974.
  3. Balakrishnan, N. and Aggarwala, R. Progressive Censoring, Theory, Methods and Applica- tions, Birkhauser, Boston, 2000.
  4. Balakrishnan, N. and Sandhu, R.A. A simple simulation algorithm for generating progres- sively type-II generated samples, American Statistician 49, 229–230, 1995.
  5. Chen, M.H. and Shao, Q.M. Monte Carlo estimation of Bayesian credible and HPD inter- vals, Journal of Computational and Graphical Statistics 8, 69–92, 1999.
  6. Cohen, A.C. Progressively censored samples in life testing, Technometrics 5, 327–339, 1963.
  7. Cordeiro G.M., Ortega, E.M. and Popovic, B.V. The gamma-linear failure rate distribution: theory and applications, Journal of Statistical Computation and Simulation 84, 2408–2426, 2014.
  8. Dempster, A.P., Laird, N.M. and Rubin, D.B. Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Statist. Soc. Ser. B 39, 1–38, 1977.
  9. Efron, B. and Tibshirani, R.J. An Introduction to the Bootstrap, Chapman and Hall, New York, 1993.
  10. Gelfand, A.E. and Smith, A.F.M. Sampling-based approaches to calculating marginal den- sities, Journal of the American Statistical Association 85, 398–409, 1990.
  11. Ghitany, M.E. and Kotz, S. Reliability properties of extended linear failure rate distributions, Probability in the Engineering and Informational Sciences 21, 441–450, 2007.
  12. Jiang, H., Xie, M. and Tang, L.C. On MLEs of the parameters of a modified Weibull distribution for progressively type-II censored samples, Journal of Applied Statistics 37, 617–627, 2010.
  13. Kinaci, I. Estimation of $P(Y Kus, C. and Kaya, M.F. Estimation of parameters of the loglogistic distribution based on progressive censoring using the EM algorithm, Hacettepe Journal of Mathematics and Sta- tistics 35, 203–211, 2006.
  14. Lin, C.T., Wu. S.J.S. and Balakrishnan, N. Parameter estimation for the linear hazard rate distribution based on records and inter-record times, Communications in Statistics–Theory and Methods 32, 729–748, 2003.
  15. Lin, C.T., Wu. S.J.S. and Balakrishnan, N. Monte Carlo methods for Bayesian inference on the linear hazard rate distribution, Communications in Statistics–Simulation and Com- putation 35, 575–590, 2006. Linhar