Abstract
AbstractSuppose that in a random sample of size n from a population with probability density function f(x), the order statistics are X(1) < X(2) < … < X(n). It is proved that a necessary and sufficient condition for f(x) to be the density function of the power function distribution is that the statistics X(r)/X(s) and X(t) (1 ≤ r < s < t ≤ n) are independent.
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