Daniels, H. E. Tail probability approximations. (English) Zbl 0614.62016 Int. Stat. Rev. 55, 37-48 (1987). This paper is a very interesting and clear review on two explicit approximations for the tail probability of a sample mean. The Edgeworth type expansion gives an asymptotic expansion in powers of \(n^{-1/2}\) when \(\bar x-E(X)=O(n^{-1/2})\). For large deviations it can be further reduced to an expansion whose terms decrease by a factor \(n^{-1}.\) A recent approach, due to R. Lugannani and S. Rice [Adv. Appl. Probab. 12, 475-490 (1980; Zbl 0425.60042)] is based on an extension of the saddlepoint technique. It yields an asymptotic expansion whose terms decrease in order by a factor \(n^{-1}\) over the whole range of \(\bar x.\) The novelty of the paper is that it covers the case of lattice variables. Reviewer: J.G.Szekely Cited in 4 ReviewsCited in 106 Documents MSC: 62E20 Asymptotic distribution theory in statistics Keywords:survey paper; saddlepoint approximation; approximations for the tail probability of a sample mean; Edgeworth type expansion; asymptotic expansion; large deviations; lattice variables Citations:Zbl 0425.60042 PDFBibTeX XMLCite \textit{H. E. Daniels}, Int. Stat. Rev. 55, 37--48 (1987; Zbl 0614.62016) Full Text: DOI