Let X and Y be two random variables; then the exact distribution of the ratio is derived when X and Y are independent Bessel function random variables.
Soient X et Y deux variables aléatoires ; on en déduit la valeur du rapport dans le cas où X et Y sont des variables aléatoires dont les densités de probabilités sont de type Bessel.
Accepted:
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@article{CRMATH_2006__343_8_531_0, author = {Nadarajah, Saralees and Kotz, Samuel}, title = {The {Bessel} ratio distribution}, journal = {Comptes Rendus. Math\'ematique}, pages = {531--534}, publisher = {Elsevier}, volume = {343}, number = {8}, year = {2006}, doi = {10.1016/j.crma.2006.09.031}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2006.09.031/} }
TY - JOUR AU - Nadarajah, Saralees AU - Kotz, Samuel TI - The Bessel ratio distribution JO - Comptes Rendus. Mathématique PY - 2006 SP - 531 EP - 534 VL - 343 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.09.031/ DO - 10.1016/j.crma.2006.09.031 LA - en ID - CRMATH_2006__343_8_531_0 ER -
Nadarajah, Saralees; Kotz, Samuel. The Bessel ratio distribution. Comptes Rendus. Mathématique, Volume 343 (2006) no. 8, pp. 531-534. doi : 10.1016/j.crma.2006.09.031. http://www.numdam.org/articles/10.1016/j.crma.2006.09.031/
[1] The use of McKay's Bessel function curves for graduating frequency distributions, Sankhyā, Volume 6 (1942), pp. 175-182
[2] Exact moments of a ratio of two positive quadratic forms in normal variables, Communications in Statistics—Theory and Methods, Volume 12 (1983), pp. 675-679
[3] Table of Integrals, Series, and Products, Academic Press, San Diego, 2000
[4] The Laplace Distribution and Generalizations: A Revisit with Applications to Communications, Economics, Engineering and Finance, Birkhäuser, Boston, 2001
[5] Distribution of the ratio of the mean square successive difference to the variance, Annals of Mathematical Statistics, Volume 12 (1941), pp. 367-395
[6] The exact density function of the ratio of two dependent linear combinations of chi-square variable, Annals of the Institute of Statistical Mathematics, Volume 46 (1994), pp. 557-571
[7] Integrals and Series, vols. 1–3, Gordon and Breach Science Publishers, Amsterdam, 1986
[8] Testing equality between sets of coefficients after a preliminary test for equality of disturbance variances in two linear regressions, Journal of Econometrics, Volume 31 (1986), pp. 67-80
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