I know that Laplacian distribution function is defined as follow
f(x)=(b/2)*exp(-b|x-\mu|)
Also, I know that the mean and variance for the ratio between two normal variables.
Anyone can guide how would be mean and variance for Laplacian distribution?
Please check this link:
http://math.stackexchange.com/questions/922521/deriving-mean-and-variance-of-laplace-distribution
Mohammad,
you can easily compute the exact probability density function of the ratio using
https://en.wikipedia.org/wiki/Ratio_distribution
and then you obtain the mean and variance (and all other higher order moments)
or you can get the mean and variance from those of the two original variable by using
http://www.stat.cmu.edu/~hseltman/files/ratio.pdf
Vincent
Hi Mohammad,
The formulas of the PNG file are wrong, since the following exemplary fact holds:
If the joint density f(x,y) is bounded as follows:
f(x,y) \ge c for |x|, |y| \le 1, where c > 0,
then the tails of the ratio are bounded by c \cdot t^{-1}, for t \ge 1
(please, make a drawing of the vicinity of the origin and put there a sector
| x/y | > t within the square [-1 , 1] \times [-1 , 1] ),
and consequently the expectation of the ratio is bounded from below suitably by
E{ |X/Y| } \ge c \cdot \int_1^\infty t^{-1} dt = \infty.
Best wishes
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