Skip to main content
SpringerLink
Log in

Estimation Methods for the Generalized Inverted Exponential Distribution Under Type II Progressively Hybrid Censoring with Application to Spreading of Micro-Drops Data

  • Published:
Communications in Mathematics and Statistics Aims and scope Submit manuscript

Abstract

In this article, we consider the statistical inferences of the unknown parameters of a generalized inverted exponential distribution based on the Type II progressively hybrid censored sample. By applying the expectation–maximization (EM) algorithm, the maximum likelihood estimators are developed for estimating the unknown parameters. The observed Fisher information matrix is obtained using the missing information principle, and it can be used for constructing asymptotic confidence intervals. By applying the bootstrapping technique, the confidence intervals for the parameters are also derived. Bayesian estimates of the unknown parameters are obtained using the Lindley’s approximation. Monte Carlo simulations are implemented and observations are given. Finally, a real data set representing the spread factor of micro-drops is analyzed to illustrative purposes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Abouammoh, A.M., Alshingiti, A.M.: Reliability of generalized inverted exponential distribution. J. Stat. Comput. Simul. 79, 1301–1315 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Afify, W.M.: Theory and methods statistical inference using progressively hybrid censored data under exponentiated exponential distribution with binomial random removals. S. Afr. Stat. J. 45, 149–170 (2011)

    MathSciNet  Google Scholar 

  3. Balakrishnan, N., Kundu, D.: Hybrid censoring models, inferential results and applications. Comput. Stat. Data Anal. 57, 166–209 (2013)

    Article  MathSciNet  Google Scholar 

  4. Banerjee, A., Kundu, D.: Inference based on type-II hybrid censored data from a Weibull distribution. IEEE Trans. Reliab. 57, 369–378 (2008)

    Article  Google Scholar 

  5. Childs, A., Chandrasekhar, B., Balakrishnan, N., Kundu, D.: Exact inference based on type-I and type-II hybrid censored samples from the exponential distribution. Ann. Inst. Stat. Math. 55, 319–330 (2003)

    MathSciNet  MATH  Google Scholar 

  6. Dey, S., Pradhan, B.: Generalized inverted exponential distribution under hybrid censoring. Stat. Methodol. 18, 101–114 (2014)

    Article  MathSciNet  Google Scholar 

  7. Dey, S., Dey, T.: Generalized inverted exponential distribution: different methods of estimation. Am. J. Math. Manag. Sci. 33, 194–215 (2014)

    Google Scholar 

  8. Gupta, P.K., Singh, B.: Parameter estimation of Lindley distribution with hybrid censored data. Int. J. Syst. Assur. Eng. Manag. 1, 1–8 (2012)

    Google Scholar 

  9. Gürünlü Almaa, Ö., Arabi Belaghi, R.: On the estimation of the extreme value and normal distribution parameters based on progressive type-II hybrid-censored data. J. Stat. Comput. Simul. 86, 569–596 (2016)

    Article  MathSciNet  Google Scholar 

  10. Kang, C.W., Ng, H.W.: Splat morphology and spreading behavior due to oblique impact of droplets onto substrates in plasma spray coating process. Surface Coat. Technol. 200, 5462–5477 (2006)

    Article  Google Scholar 

  11. Krishna, H., Kumar, K.: Reliability estimation in generalized inverted exponential distribution with progressively type II censored sample. J. Stat. Comput. Simul. 83(6), 1007–1019 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kundu, D., Joarder, A.: Analysis of type-II progressively hybrid censored data. Comput. Stat. Data Anal. 50, 2509–2528 (2006a)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kundu, D., Joarder, A.: Analysis of type-II progressively hybrid censored competing risks data. J. Mod. Appl. Stat. Methods 5, 152–170 (2006b)

    Article  MATH  Google Scholar 

  14. Lindley, D.V.: Approximate Bayesian method. Trabajos de Estadistica 31, 223–245 (1980)

    Article  MathSciNet  Google Scholar 

  15. Louis, T.A.: Finding the observed information matrix when using the EM algorithm. J. R. Stat. Soc. Ser. B 44, 226–233 (1982)

    MathSciNet  MATH  Google Scholar 

  16. Panahi, H., Sayyareh, A.: Parameter estimation and prediction of order statistics for the Burr type XII distribution with type II censoring. J. Appl. Stat. 41, 215–232 (2014)

    Article  MathSciNet  Google Scholar 

  17. Panahi, H., Sayyareh, A.: Estimation and prediction for a unified hybrid-censored Burr type XII distribution. J. Stat. Comput. Simul. 86, 55–73 (2016)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Lahijan Branch, Islamic Azad University, Lahijan, Iran

    Hanieh Panahi

Authors
  1. Hanieh Panahi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hanieh Panahi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panahi, H. Estimation Methods for the Generalized Inverted Exponential Distribution Under Type II Progressively Hybrid Censoring with Application to Spreading of Micro-Drops Data. Commun. Math. Stat. 5, 159–174 (2017). https://doi.org/10.1007/s40304-017-0106-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40304-017-0106-9

Keywords

Mathematics Subject Classification

Search

Navigation