Dans cette Note, on résout un problème, posé depuis 1936, sur la distribution exacte du produit de variables aléatoires normales corrélées. Comme résultat supplémentaire, on déduit la distribution exacte de la moyenne du produit de variables aléatoires normales corrélées.
We solve a problem that has remained unsolved since 1936 – the exact distribution of the product of two correlated normal random variables. As a by-product, we derive the exact distribution of the mean of the product of correlated normal random variables.
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@article{CRMATH_2016__354_2_201_0, author = {Nadarajah, Saralees and Pog\'any, Tibor K.}, title = {On the distribution of the product of correlated normal random variables}, journal = {Comptes Rendus. Math\'ematique}, pages = {201--204}, publisher = {Elsevier}, volume = {354}, number = {2}, year = {2016}, doi = {10.1016/j.crma.2015.10.019}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2015.10.019/} }
TY - JOUR AU - Nadarajah, Saralees AU - Pogány, Tibor K. TI - On the distribution of the product of correlated normal random variables JO - Comptes Rendus. Mathématique PY - 2016 SP - 201 EP - 204 VL - 354 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.10.019/ DO - 10.1016/j.crma.2015.10.019 LA - en ID - CRMATH_2016__354_2_201_0 ER -
%0 Journal Article %A Nadarajah, Saralees %A Pogány, Tibor K. %T On the distribution of the product of correlated normal random variables %J Comptes Rendus. Mathématique %D 2016 %P 201-204 %V 354 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.10.019/ %R 10.1016/j.crma.2015.10.019 %G en %F CRMATH_2016__354_2_201_0
Nadarajah, Saralees; Pogány, Tibor K. On the distribution of the product of correlated normal random variables. Comptes Rendus. Mathématique, Tome 354 (2016) no. 2, pp. 201-204. doi : 10.1016/j.crma.2015.10.019. http://www.numdam.org/articles/10.1016/j.crma.2015.10.019/
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