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Some new techniques for the evaluation of improper integrals of the first kind are presented. The importance of these approximations for some distribution functions is noted. In an illustrative application, the transformations are employed to yield a new approximating formula for Mills' Ratio. The results are compared to other expressions of comparable complexity. The potential of the transformations, in the field of mathematical statistics is discussed.
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Gray et al. (1968) studied this question.
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