Bravais Distribution

< Back to Probability Distribution List

The Bravais distribution is another name for the bivariate normal distribution, (also sometimes called the bivariate Gaussian or Bivariate Laplace–Gauss distribution).

Teugels & Sundt lists the Bravais distribution as the probability density function of the bivariate normal random vector,

X =  X1, X2)T

which is

bravais distribution PDF

Haight published a simple formula for the bivariate normal:

and refers the reader to a version published in an article in the 1958 Volume 19 of Skandinavisk Aktuarietidskrift.  The unnamed author (I was unable to locate a copy of the journal to find the authors name) probably named this distribution after Bravais [3], who developed and published his study of normal frequency distributions in two and more variables.


[1] Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.

[2] Teugels & Sundt. (2004) Encyclopedia of Actuarial Science. Wiley.

[3] Bravais, August, 1846: “Analyse MathCmatique sur les probabilities des erreurs de situation d’un point,” Memoirs Presentes par Divers Savants, 2nd Series, Vol. 9, Institut de France, Acadamie des Sciences, Paris, France, pp. 255-332