Normal distribution (Multi variables)
Where do you meet this distribution?
- Finance, Economics : Value at Risk
Shape of Distribution
- For n-variables, means for each variable (n-dimensional vector), standard deviations for each variable (n-dimensional 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
- NTBINROMDIST is singular, when correlation coefficient and x1=x2.
- Probability density function
- Function reference : NTBINORMDIST
li>How to compute these on Excel.
- How to generate random numbers on Excel.
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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
- Generating random numbers based on Mersenne Twister algorithm: NTRANDMULTINORM
- Computing probability for 2-variables : NTBINORMDIST