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Multivariate Laplace distribution - Quiz
Contributed by: McCabe
  • 1. What are multivariate Laplace distributions extensions of?
A) The normal distribution to multiple variables
B) Univariate uniform distributions
C) Only the standard Laplace distribution
D) The Laplace distribution and the asymmetric Laplace distribution to multiple variables
  • 2. What are the marginal distributions of symmetric multivariate Laplace distribution variables?
A) Asymmetric Laplace distributions
B) Uniform distributions
C) Normal distributions
D) Laplace distributions
  • 3. What are the marginal distributions of asymmetric multivariate Laplace distribution variables?
A) Symmetric Laplace distributions
B) Standard normal distributions
C) Exponential distributions
D) Asymmetric Laplace distributions
  • 4. In the characteristic function of the symmetric multivariate Laplace distribution, what does the symbol represent?
A) The vector of means for each variable
B) The covariance matrix
C) The correlation coefficient
D) The standard deviation vector
  • 5. In the characteristic function of the symmetric multivariate Laplace distribution, what does represent?
A) The vector of means
B) The covariance matrix
C) The modified Bessel function
D) The dimension parameter
  • 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 elliptical
C) It is rectangular
D) It is spherical only
  • 8. In the probability density function when equals zero, what does represent?
A) The mean vector
B) The correlation coefficient
C) The standard deviation
D) The dimension of the distribution
  • 9. In the probability density function formula, what function is represented by?
A) The standard normal cumulative distribution function
B) The modified Bessel function of the second kind
C) The gamma function
D) The characteristic function
  • 10. What is the mean of the asymmetric multivariate Laplace distribution?
A) One
B) Zero
C) mu
D) Sigma
  • 11. What does the covariance of the asymmetric multivariate Laplace distribution become?
A) mu' mu
B) Sigma
C) Sigma squared
D) Sigma + mu' mu
  • 12. Under what condition is the asymmetric multivariate Laplace distribution elliptical?
A) mu = 1
B) Sigma = mu
C) Sigma = 0
D) mu = 0
  • 13. In the probability density function, what parameter is defined as v = (2 - k) / 2?
A) k
B) Sigma
C) mu
D) v
  • 14. What is the formula for X in the simulation method of bivariate asymmetric Laplace variables?
A) W * Y + mu
B) W * sqrt(Y) + W * mu
C) sqrt(W) * 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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