A General Approach to Derive Chi-Square Type of Goodness-of-Fit Tests for Lifetime Data

  • Sam Hawala
  • Jane-Ling Wang
Chapter

Abstract

Pearson’s original chi-square test for goodness-of-fit has been extended and generalized in various ways to test the composite hypothesis of a certain parametric family {F (x; θ): θ ∈ Θ}. We illustrate in this paper that, for lifetime data that are subject to incomplete observation, a unified approach is available to derive general chi-square tests for parametric families, regardless of the sampling plan for such incomplete data. Let be a nonparametric estimate of the target distribution function F, and let be any parametric estimate of the true parameter under the null hypothesis. The general test statistic is a quadratic form of the estimated sample process evaluated at r points (called cell boundaries) of the xs. A unified large sample theory is available for such test statistics, and one tractable test is recommended. Several applications are discussed involving various choices of .

Keywords

Sampling Plan Null Distribution Generalize Inverse Lifetime Data Composite Hypothesis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • Sam Hawala
    • 1
  • Jane-Ling Wang
    • 2
  1. 1.Department of MathematicsUniversity of St. ThomasSt. PaulUSA
  2. 2.Division of StatisticsUniversity of CaliforniaDavisUSA

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