A simple proof of the Gaussian correlation conjecture extended to multivariate gamma distributions

Hargé, G. (1999). A particular case of correlation inequality for the Gaussian measure. Ann. Probab

1951

Earlier work this paper cites.

Krishnamoorthy, A.S., and Parthasarathy, M. (1951). A multivariate gamma-type distribution. Ann. Math. Stat

1951

Earlier work this paper cites.

Khatri, C.G. (1967). On certain inequalities for normal distributions and their application to simultaneous confidence bounds, Ann. Math. Stat

1967

Earlier work this paper cites.

Šidák, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions, J. Amer. Statist. Assoc

1967

Earlier work this paper cites.

Das Gupta, S., Eaton, M. L., Olkin, I., Perlman, M., Savage, L.J., and Sobel, M. (1972). Inequalities on the probability content of convex regions for elliptically contoured distributions. Proc. Sixth Berkeley Symp. Math. Statist. Probab

1972

Earlier work this paper cites.

Pitt, L.D. (1977). A Gaussian correlation inequality for symmetric convex sets. Ann. Probab

1977

Cited alongside, same era.

Griffiths, R.C. (1984). Characterization of infinitely divisible multivariate gamma distributions, J. Multivariate Anal

1984

Cited alongside, same era.

Bapat, R.B. (1989). Infinite divisibility of multivariate gamma distributions and M-matrices, Sankhy a ¯ \bar{\rm{a}}

1989

Cited alongside, same era.

Royen, T. (1995). On some central and non-central multivariate chi-square distributions, Statist. Sinica

1995

Cited alongside, same era.

Schechtman, G., Schlumprecht, T., and Zinn, J. (1998). On the Gaussian measure of the intersection, Ann. Probab

1998

Cited alongside, same era.

Royen, T. (2007). Integral representations and approximations for multivariate gamma distributions, Ann. Inst. Statist. Math

2007

Later among the works it cites.

Memarian, Y. (2013). The Gaussian correlation conjecture proof, arXiv:1310. 8099v1 [mathPR]

2013

Later among the works it cites.

Qingyang, G. (2013). The Gaussian correlation inequality for symmetric convex sets, arXiv:1012.0676v4 [mathPR]

Original

2013

Later among the works it cites.

Royen, T. (2013). Some upper tail approximations for the distribution of the maximum of correlated chi-square or gamma random variables, Far East J. Theor. Statist

2013

Later among the works it cites.