Geodesic
Asymptotic Approximation of an Integral Involving the Normal Distribution*
Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 167-176

Voir la notice de l'article provenant de la source Cambridge University Press

An asymptotic approximation is obtained, as k → ∞, for the integral where Φ is the cumulative distribution function for a standard normal random variable, and L is a positive constant. The problem is motivated by a question in statistics, and an outline of'the application is given. Similar methods may be used to approximate other integrals involving the normal distribution.
DOI : 10.4153/CMB-1986-028-x
Mots-clés : 41A60, 62E20 
McClure, J. P. Asymptotic Approximation of an Integral Involving the Normal Distribution*. Canadian mathematical bulletin, Tome 29 (1986) no. 2, pp. 167-176. doi: 10.4153/CMB-1986-028-x
@article{10_4153_CMB_1986_028_x,
     author = {McClure, J. P.},
     title = {Asymptotic {Approximation} of an {Integral} {Involving} the {Normal} {Distribution*}},
     journal = {Canadian mathematical bulletin},
     pages = {167--176},
     year = {1986},
     volume = {29},
     number = {2},
     doi = {10.4153/CMB-1986-028-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-028-x/}
}
TY  - JOUR
AU  - McClure, J. P.
TI  - Asymptotic Approximation of an Integral Involving the Normal Distribution*
JO  - Canadian mathematical bulletin
PY  - 1986
SP  - 167
EP  - 176
VL  - 29
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-028-x/
DO  - 10.4153/CMB-1986-028-x
ID  - 10_4153_CMB_1986_028_x
ER  - 
%0 Journal Article
%A McClure, J. P.
%T Asymptotic Approximation of an Integral Involving the Normal Distribution*
%J Canadian mathematical bulletin
%D 1986
%P 167-176
%V 29
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-028-x/
%R 10.4153/CMB-1986-028-x
%F 10_4153_CMB_1986_028_x

[1] 1. Olver, F. W. J. Asymptotics and special functions, Academic Press, New York, 1974. Google Scholar

[2] 2. Tukey, J.W., Comparing individual means in the analysis of variance, Biometrics, 5 (1949), pp. 99–114. Google Scholar

[3] 3. Wong, R., A generalization of Watson's lemma, Ph.D. Thesis, University of Alberta, 1969. Google Scholar

Cité par Sources :