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Identifying common normal distributions

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  • Anthony Hayter

Abstract

Consider a one-way layout where random samples of data are available from k populations, where the distributions of the data from each population are considered to be completely unknown. This paper discusses a methodology for investigating whether it can be concluded that the k unknown distributions, or any subsets of these distributions, can be taken to be equal to a common normal distribution, and if so it is shown how to identify these common normal distributions. This is accomplished with an exact specified error rate by constructing confidence sets for the parameters of the common normal distributions using Kolmogorov’s (G. Ist. Ital. Attuari 4:83–91, 1933 ) procedure. The relationship of this methodology to standard tests of normality and to standard procedures for constructing confidence sets for the parameters of a normal distribution are discussed, together with its relationship to functional data analysis and other standard test procedures for data of this kind. Some examples of the implementation of the methodology are provided. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • Anthony Hayter, 2014. "Identifying common normal distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(1), pages 135-152, March.
    • Handle: RePEc:spr:testjl:v:23:y:2014:i:1:p:135-152
    DOI: 10.1007/s11749-013-0345-3
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    References listed on IDEAS

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    1. Mante, Claude & Yao, Anne-Francoise & Degiovanni, Claude, 2007. "Principal component analysis of measures, with special emphasis on grain-size curves," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4969-4983, June.
    2. Pedro Delicado, 2007. "Functional k-sample problem when data are density functions," Computational Statistics, Springer, vol. 22(3), pages 391-410, September.
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