5.3 Qui-quadrado

5.3.2 Qui-quadrado bivariada

(Kotz, Balakrishnan, and Johnson 2000, 451) (Gunst and Webster 1973) (Amos and Bulgren 1972)

let (q,,q2) ~iv%’(ab,, c) denote that the random ldariab!es q, am! q 2 have a hivariate Chi-square distribution, where a = degrees of freedom of rhe marginai Chi-square distribution of ql, 6 = &,geesof fr~edorni;f the rnargica! CEi-square distribution ofqz, c = number of non-zero canonical correlations between the underlying nmmz! vectors of qi and qi.

5.3.3 Qui-quadrado multivariada (Jensen)

(Kotz, Balakrishnan, and Johnson 2000, 471)

“The joint distribution of \(Y_1,\ldots,Y_k\) can be regarded as a multivariate chi-squared or, more generally (allowing \(\nu\) and the \(p_j\)’s to take fractional values), a multivariate gamma distribution.” (Kotz, Balakrishnan, and Johnson 2000, 474)

5.3.4 Qui-quadrado multivariada não centralizada

(Kotz, Balakrishnan, and Johnson 2000, 475)


Amos, DE, and WG Bulgren. 1972. “Computation of a Multivariate f Distribution.” Mathematics of Computation 26 (117): 255–64. https://www.ams.org/journals/mcom/1972-26-117/S0025-5718-1972-0298881-9/S0025-5718-1972-0298881-9.pdf.
Gunst, Richard F, and John T Webster. 1973. “Density Functions of the Bivariate Chi-Square Distribution.” Journal of Statistical Computation and Simulation 2 (3): 275–88. http://dx.doi.org/10.1080/00949657308810052.
Kotz, Samuel, N Balakrishnan, and Norman L Johnson. 2000. “Continuous Multivariate Distributions. Vol. 1. Models and Applications.” Wiley-Interscience, New York.