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1980•Australian Journal of StatisticsRequires access

GOODNESS OF FIT STATISTICS BASED ON THE SPACINGS OF COMPLETE OR CENSORED SAMPLES

MOTI L. TIKU

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Goodness of fit, Statistics, Mathematics, Statistic, Order statistic, Logistic regression, Monte Carlo method, Logistic distribution

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