Multivariate Laplace distribution - Quiz
  • 1. What are multivariate Laplace distributions extensions of?
A) The Laplace distribution and the asymmetric Laplace distribution to multiple variables
B) Only the standard Laplace distribution
C) Univariate uniform distributions
D) The normal distribution to multiple variables
  • 2. What are the marginal distributions of symmetric multivariate Laplace distribution variables?
A) Uniform distributions
B) Laplace distributions
C) Normal distributions
D) Asymmetric Laplace distributions
  • 3. What are the marginal distributions of asymmetric multivariate Laplace distribution variables?
A) Symmetric Laplace distributions
B) Asymmetric Laplace distributions
C) Standard normal distributions
D) Exponential distributions
  • 4. In the characteristic function of the symmetric multivariate Laplace distribution, what does the symbol represent?
A) The covariance matrix
B) The standard deviation vector
C) The correlation coefficient
D) The vector of means for each variable
  • 5. In the characteristic function of the symmetric multivariate Laplace distribution, what does represent?
A) The dimension parameter
B) The modified Bessel function
C) The vector of means
D) The covariance matrix
  • 6. How do symmetric multivariate Laplace variables behave when the covariance matrix has zero covariance and correlation, compared to the multivariate normal distribution?
A) They are not independent
B) They become uniformly distributed
C) They are independent
D) They have zero variance
  • 7. What geometric property does the symmetric multivariate Laplace distribution possess?
A) It is linear
B) It is spherical only
C) It is rectangular
D) It is elliptical
  • 8. In the probability density function when equals zero, what does represent?
A) The correlation coefficient
B) The mean vector
C) The dimension of the distribution
D) The standard deviation
  • 9. In the probability density function formula, what function is represented by?
A) The gamma function
B) The modified Bessel function of the second kind
C) The standard normal cumulative distribution function
D) The characteristic function
  • 10. What is the mean of the asymmetric multivariate Laplace distribution?
A) mu
B) Sigma
C) One
D) Zero
  • 11. What does the covariance of the asymmetric multivariate Laplace distribution become?
A) Sigma squared
B) Sigma
C) mu' mu
D) Sigma + mu' mu
  • 12. Under what condition is the asymmetric multivariate Laplace distribution elliptical?
A) Sigma = 0
B) mu = 1
C) Sigma = mu
D) mu = 0
  • 13. In the probability density function, what parameter is defined as v = (2 - k) / 2?
A) Sigma
B) v
C) k
D) mu
  • 14. What is the formula for X in the simulation method of bivariate asymmetric Laplace variables?
A) sqrt(W) * Y + W * mu
B) W * Y + mu
C) W * sqrt(Y) + W * mu
D) sqrt(W * Y) + mu
  • 15. What is the dimension of the asymmetric multivariate Laplace distribution denoted by in the pdf formula?
A) Y
B) k
C) v
D) W
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