On Exact Expressions for the Expected Values of Certain Normal Order Statistics On Exact Expressions for the Expected Values of Certain Normal Order Statistics

The expected values of normal order statistics have hitherto been expressed in terms of elementary functions just for samples of size n⩽5, their detailed computation for samples of size n>5 having been accomplished by methods of numerical integration. In this paper it is shown that by reducing a particular plane double integral to a convergent series, explicit expressions can be set out for the expected values of the order statistics of samples of size n⩽7 drawn from a unit normal parent.

The expected values of normal order statistics have hitherto been expressed in terms of elementary functions just for samples of size n⩽5, their detailed computation for samples of size n>5 having been accomplished by methods of numerical integration. In this paper it is shown that by reducing a particular plane double integral to a convergent series, explicit expressions can be set out for the expected values of the order statistics of samples of size n⩽7 drawn from a unit normal parent.