Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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NEW EXPRESSIONS FOR REPEATED LOWER TAIL INTEGRALS OF THE NORMAL DISTRIBUTION

  • Withers, Christopher S. (Applied Mathematics Group, Industrial Research Limited Lower Hutt) ;
  • Nadarajah, Saralees (School of Mathematics, University of Manchester)
  • Published : 2007.09.30
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Abstract

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

Keywords

References

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