approximating a density by using a mixture density

[ltleung]

Is there any journal article discussing approximating a density by having a mixture density? Or even an exact conversion?

I plotted a mixture density with 2 normals ( N(0,1) and N(0,3), mean and SD in parentheses) with weights 0.5 and 0.5. It looks similar to a Cauchy(0, 1.15) although the Cauchy clearly shows longer tails.

[Dragan]

Is there any journal article discussing approximating a density by having a mixture density? Or even an exact conversion?

I plotted a mixture density with 2 normals ( N(0,1) and N(0,3), mean and SD in parentheses) with weights 0.5 and 0.5. It looks similar to a Cauchy(0, 1.15) although the Cauchy clearly shows longer tails.

It's simply a mixed normal distribution. Note that the distribution would indeed (theoretically) be a Cauchy distribution if you were taking the ratio of the two normals that you mention.