Advertisement

Exact Likelihood Inference for an Exponential Parameter Under Progressive Hybrid Censoring Schemes

  • A. Childs
  • B. Chandrasekar
  • N. Balakrishnan
Part of the Statistics for Industry and Technology book series (SIT)

Abstract

The purpose of this chapter is to propose two types of progressive hybrid censoring schemes in life-testing experiments and develop exact inference for the mean of the exponential distribution. The exact distribution of the maximum likelihood estimator and an exact lower confidence bound for the mean lifetime are obtained under both types of progressive hybrid censoring schemes. Illustrative examples are finally presented.

Keywords and Phrases

Progressive censoring hybrid censoring life-testing exponential distribution maximum likelihood estimator conditional moment-generating function exact inference lower confidence bound truncated gamma density 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Balakrishnan, N. and Aggarwala, R. (2000). Progressive Censoring: Theory, Methods, and Applications, Birkhäuser, Boston.Google Scholar
  2. 2.
    Balakrishnan, N. and Basu, A. P. (Eds.) (1995). The Exponential Distribution: Theory, Methods and Applications, Gordon and Breach Science, Newark, N.J.zbMATHGoogle Scholar
  3. 3.
    Balakrishnan, N., Childs, A., and Chandrasekar, B (2002). An efficient computational method for moments of order statistics under progressive censoring, Statistics & Probability Letters, 60, 359–365.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Chen, S. and Bhattacharyya, G. K. (1988). Exact confidence bounds for an exponential parameter under hybrid censoring, Communications in Statistics—Theory and Methods, 17, 1857–1870.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Childs, A., Chandrasekar, B., Balakrishnan, N., and Kundu, D. (2003). Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution, Annals of the Institute of Statistical Mathematics, 55, 319–330.zbMATHMathSciNetGoogle Scholar
  6. 6.
    Epstein, B. (1954). Truncated life tests in the exponential case, Annals of Mathematical Statistics, 25, 555–564.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Nelson, W. (1982). Applied Life Data Analysis, John Wiley & Sons, New York.zbMATHCrossRefGoogle Scholar
  8. 8.
    Viveros, R. and Balakrishnan, N. (1994). Interval estimation of parameters of life from progressively censored data, Technometrics, 36, 84–91.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • A. Childs
    • 1
  • B. Chandrasekar
    • 2
  • N. Balakrishnan
    • 1
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Department of StatisticsLoyola CollegeChennaiIndia

Personalised recommendations