The Simultaneous Distribution of Mean and Standard Deviation in Small Samples
Allen T. Craig · The Annals of Mathematical Statistics · 1932
If, however. the parent population is other than the normal type. thlere appears to be little known regarding the form of FKX, s). In the present paper, we propose to determine the simultaneous frequeney function of the arithmetic mean and standard deviation ;i1 samples of small numbers of items selected at random from a rather arbitrary universe. For convenience, we shall classify frequeiicy distributions according as the range of the independenit variable is (oo ), 0 ' ) or (e,4a)a< We shall further aissume that the total area under the distribution function is unity. 2. The simultaneous distributioin of x and s in samples of ni 2. Let f(x), -wx < oo be the fiequency unction of the variable x Let x, and xz be two independentl erved values of X . write