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

  • Sam Hawala
  • Jane-Ling Wang


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 .


Sampling Plan Null Distribution Generalize Inverse Lifetime Data Composite Hypothesis 
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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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