Distribution of Quadratic Forms

: A study is made of definite quadratic forms in both central and noncentral independent normal variates, and an application is given for each distribution. Two special cases of an indefinite quadratic form are discussed: the distribution of the difference between 2 independent chi-squares with different numbers of degrees of freedom, and the probability density function of an indefinite quadratic form when the latent roots of the matrix of the form are equal in pairs. Some inequalities are included for the distribution of a quadratic form in independent identically distributed variates, each of which is central normal or more general.