Probability functions for the modulus and angle of the normal complex variate

This paper deals mainly with various ‘distribution functions’ and ‘cumulative distribution functions’ pertaining to the modulus and to the angle of the ‘normal’ complex variate, for the case where the mean value of this variate is zero. Also, for auxiliary uses chiefly, the distribution function pertaining to the reciprocal of the modulus is included. For all of these various probability functions the paper derives convenient general formulas, and for four of the functions it supplies comprehensive sets of curves; furthur, it gives a table of computed values of the cumulative distribution function for the modulus, serving to verify the values computed by a different method in an earlier paper by the same author.¹