Goodness of Fit Statistics Based on the Spacings of Complete or Censored Samples

Summary A goodness‐of‐fit statistic Z is defined in terms of the spacings generated by the order statistics of a complete or a censored sample from a distribution of the type (l/s̀)f((x‐μ)/s̀), μ and s̀ unknown. The distribution of Z is studied, mostly through Monte Carlo methods. The power properties of Z for testing Exponential, Uniform, Normal, Gamma and Logistic distributions are discussed; Z is shown to be more powerful than the Smith & Bain (1976) correlation statistic, except for testing Uniform, Normal and Logistic (symmetric distributions) against symmetric alternatives. The statistic Z is generalized to test the goodness‐of‐fit from κ 2 independent complete or censored samples.