Let p be the density 2(2) 1 2 exp( x2 ) (x 0) of the modulus x lzl of a standard normal variate z and let q be the density 1 exp( x ) (x 0) of an E() distribution Find the value of such that q is as close an approximation top as possible in the sense that the Kullback Leibler divergence (q p) is a ...

To find the value of that minimizes the KullbackLeibler KL divergence between the two distributions we need to calculate the KL divergence and then ta ...

Let p be the density 2(2) - 1/2 exp(- x2 ) (x > 0) of the modulus

Question:

Let p be the density 2(2π)^-^1/2 exp(-½^x2) (x > 0) of the modulus x = lzl of a standard normal variate z and let q be the density β^-1exp(-x/β) (x > 0) of an E(β) distribution. Find the value of β such that q is as close an approximation top as possible in the sense that the Kullback-Leibler divergence (q : p) is a minimum.