The distribution and properties of a weighted sum of chi squares
F. C. Delaney, Alan H. Feiveson · NASA Technical Reports Server (NASA) · 1968
A study of some of the properties of a weighted sum of chi-square random variables is presented.Derivations of approximations to the distribution of this sum and an evaluation of the Welch approximation for the distribution of the test statistic in the Behrens-Fisher Problem a r e included.The study indicates that if equal sample sizes a r e selected, the Welch approximation to the Behrens-Fisher Problem may be safely used, even for sample s i z e s as small as 5. ' a 2 variances@ 2(t), @ 2(t), . . .characteristic functions for the random variables Z 2 , Nj 2 , and N. J so forth Z @(-I X 2 (4 standard normal cumulative distribution function (c.d. f. ) chi-square distribution with n degrees of freedom v Behrens-Fisher statistic