mixture of normal distributions

[ajsa]

Hi David,

Could you explain how to mix normal distributions to create a fat-tail? I am asking because summation of normal distributions will create another normal distribution.. so I wonder how to "mix"

Thanks.

 

[David Harper CFA FRM]

Hi asja,

You are right about adding normals: it's an important property (that we use a lot) that a linear combination of normals is itself normal.
But a mixture distribution is a different thing. See: re mixture vs. convolution: http://forum.bionicturtle.com/viewreply/3226/

The normal mixture is a fabulous creature: easy, flexible and automatically fat-tailed
(could you ask for more in a distribution?)

Per my tutorial, see http://www.bionicturtle.com/premium/spreadsheet/2.c.4._rachev_normal_mixture/
see column E: you literally just simply weight the two normal functions

David

 

[JFZ2014]

This link is not working:
http://forum.bionicturtle.com/viewreply/3226/
why?

I don't understand why a mixture distribution is a different thing. I need to see the explaination.
Thanks.
Jennifer