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 $ X_
{ii}, j= 1,···, m_i, i= 1,···, k, $ be a set of independent random variables and let $ F_i (x) $ be
the probability distribution function of $ X_ {ii} $. The set of admissible hypotheses
designates that each $ F_i $ belongs to some class of distribution functions $\Omega $.

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¿-sample problem, when expressed formally is stated as follows: Let Xu, j=
I,•*·, mt, i= 1,···, k, be a set of independent random variables and let Ft (x) be the probability
distribution function of. The set of admissible hypotheses designates that each Ft belongs to
some class of distribution functions Ω. The hypothesis to be tested, say H0,»[Kcifies that F {is …