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On the Distribution of the Ratio of the ith Observation in an Ordered Sample from a Normal Population to an Independent Estimate of the Standard Deviation
This paper deals with the distribution of any observation, $x_i$, in an ordered sample of size $n$ from a normal population with zero mean and unit standard deviation. The distribution has been developed as a series of Gamma functions, and has been used to obtain the distribution of $q_i = …