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Abstract. In this paper a new method for estimating the value of an improper integral by a finite sum is introduced. In particular, the method is applied to the Chi-Square integral and proves to be of some value in estimating the value of this integral for values equal or greater than .9. | I. Introduction. The problem of computing the area, Qix2\v), under the right tail of a chi-square distribution is quite important and occurs often in applications. For an even number, v, of degrees of freedom, the computation of Qix2\v) is straightforward (although quite lengthy if v is large). For v not an even integer, one must use an approximation such as asymptotic or series expansion, normal approximation, or numerical integration. It is well known that most relevant series expansions [1], [5] converge very slowly, often requiring a large number of terms in order to be accurate to only a few significant digits. If only a few significant digits are needed, one can use an asymptotic expansion, but the number of terms used in the series is a function of x2 and v; i.e., an approximation using a fixed number of terms from an asymptotic expansion generally has an acceptable accuracy over a limited range of values for x2 and v.In this paper a simple approximation for Qix2\Y is developed, and in the process, some new methods for developing approximations are presented. The approximation given here is quite useful for computation on digital computers and for hand calculations when only 3 to 4D accuracy is needed and if Qix2\Y á .1.

In this paper a new method for estimating the value of an improper integral by a finite sum is introduced. In particular, the method is applied to the Chi-Square integral and proves to be of some value in estimating the value of this integral for values equal or greater than .9. |