The Journal of the Indian Mathematical Society

M. L. Tiku

Abstract

A new set of orthogonal polynomials having non-central chi-square distribution as the weight function, is introduced. The distribution of the'one-way classification' variance-ratio under the assumption of nonzero block effects, is given in terms of these polynomials. Population cumulants of order greater than seven are ignored. The effect of non normality on the power of the test is illustrated by way of numerical examples and graphs.

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M. L. Tiku ¹

Affiliations
1 Indian Statistical Institute, Calcutta, IN

Abstract

An approximation to the sampling distribution of student's 't' in the case of a non-normal population was given by Gayen [4]. He started with the first four terms of a Gram-charlier series expansion of the probability density function of the population, thereby ignoring population cumulants of order greater than four and the square and higher powers of the fourth cumulant.

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