A problem which occurs frequently in statistical analysis is that of deciding whether several samples should be regarded as coming from the same population. This problem, usually referred to as the k-sample problem, when expressed formally is stated as follows: Let Xᵢᵢ , j = 1, · · · , mᵢ, i = 1, · · · , k, be a set of independent random variables and let Fᵢ(x) be the probability distribution function of Xᵢᵢ . The set of admissible hypotheses designates that each Fᵢ belongs to some class of distribution functions Ω.
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Madan L. Puri (1965) studied this question.
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