## The Annals of Mathematical Statistics

### On the Distribution of $2 \times 2$ Random Normal Determinants

W. L. Nicholson

#### Abstract

The c.d.f. of a $2 \times 2$ random determinant with mutually independent normally distributed entries is derived as an infinite series. Error functions that bound the tail of this series facilitate numerical calculation. Conditions are imposed on four variable quadratic forms for this distribution to apply. A normal approximation to the distribution is suggested.

#### Article information

Source
Ann. Math. Statist., Volume 29, Number 2 (1958), 575-580.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706634

Digital Object Identifier
doi:10.1214/aoms/1177706634

Mathematical Reviews number (MathSciNet)
MR93844

Zentralblatt MATH identifier
0092.35802

JSTOR
links.jstor.org

#### Citation

Nicholson, W. L. On the Distribution of $2 \times 2$ Random Normal Determinants. Ann. Math. Statist. 29 (1958), no. 2, 575--580. doi:10.1214/aoms/1177706634. https://projecteuclid.org/euclid.aoms/1177706634