An asymptotic expression is given for the probability integral of range for samples from a symmetrical unimodal population. Its accuracy is investigated for the case of a normal parent population and ...

In this article, we derive a series expansion of the multivariate normal probability integrals based on Fourier series. The basic idea is to transform the limits of each integral from hi to ∞ to be ...

REFERRING to Prof. H. C. Plummer's letter on “An Approximation to the Probability Integral,” published in NATURE of October 25, the following alternative way of ...

THE probability integral can be represented by the simple approximation over such a range (t<3) as to make the approximation useful to the statistician and others whose problems do not require great ...