Normal distribution (Multi variables)
Where do you meet this distribution?
 Finance, Economics : Value at Risk
Shape of Distribution
Basic Properties
 For nvariables, means for each variable (ndimensional vector), standard deviations for each variable (ndimensional vector ) and correlation coefficients for every pair of variables (n times n matrix. Called correlation matrix) are required (In practice, a covariance matrix calculated from standard deviation vector and correlation correlation matrix is required).
 Continuous distribution defined on
Probability
 NTBINROMDIST is singular, when correlation coefficient and x1=x2.
 Probability density function
 Function reference : NTBINORMDIST
li>How to compute these on Excel.


Random Numbers
 How to generate random numbers on Excel.
1 2 3 4 5 6 7 8
A B C D Data Data Data Description 1.44 0.48 0.36 cov. matrix 0.48 0.64 0 cov. matrix 0.36 0 0.25 cov. matrix Data Data Data Description 1 2 3 mean vector Formula Description (Result) =NTRANDMULTINORM(100,A2:C4,A6:C6) 100 normal deviates (x 3 variables) for the terms above
NtRand Functions
 Generating random numbers based on Mersenne Twister algorithm: NTRANDMULTINORM
 Computing probability for 2variables : NTBINORMDIST