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On the Joint Distribution of Placement Statistics under Progressive Censoring and Applications to Precedence Test

Author

Listed:
  • N. Balakrishnan

    (University of Texas at San Antonio)

  • Ram C. Tripathi

    (University of Texas at San Antonio)

  • Nandini Kannan

    (University of Texas at San Antonio)

Abstract

In reliability and survival analysis, comparison of two or more populations is an important problem. For example, while comparing a treatment group with a control group, one may be interested in determining whether the observations in the treatment group have a longer lifetime than those from the control group, that is, whether the treatment is effective or not. In such a studym it would be extremenly valuable to make a decision based on early failures. In this paper, we consider independent progressively Type-II censored random samples from two populations with cumulative distribution function's (cdf) F(.) and G(.) respectively, and discuss a precedence test for testing the equality of the two distributions based on placements. For this purpose, we derive the joint distribution of the first l placement statistics from the progressively censored sample from F(.). We then derive the exact null distribution of the precedence test statistic which is simply the sum of the placements. We provide the rejection regions for fixed levels of significance and various sample sizes and different progressive censoring schemes.

Suggested Citation

  • N. Balakrishnan & Ram C. Tripathi & Nandini Kannan, 2007. "On the Joint Distribution of Placement Statistics under Progressive Censoring and Applications to Precedence Test," Working Papers 0009, College of Business, University of Texas at San Antonio.
    • Handle: RePEc:tsa:wpaper:0035mss
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    File URL: http://interim.business.utsa.edu/wps/MSS/0009MSS-213-2007.pdf
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    Citations

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    Cited by:

    1. N. Balakrishnan & Ram C. Tripathi & Nandini Kannan & H. K. T. Ng, 2008. "Precedence-type Test based on Progressively Censored Samples," Working Papers 0054, College of Business, University of Texas at San Antonio.
    2. Minghe Sun, 2008. "A Tabu Search Heuristic Procedure for the Capacitated Facility Location Problem," Working Papers 0050, College of Business, University of Texas at San Antonio.
    3. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.

    More about this item

    Keywords

    Progressove Type-II censoring; placements; precedence and exceedance statistics; nonparametric tests of homogeneity; Wilcoxon rank-sum test.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    Statistics

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