Choosing Normalization to Create Bell Curve with Mean 1

[vaibhavtewari]

I have a 40*40 matrix which has elements very close to 1 on diagonal and very small off-diagonal elements.
I find determinant of many of these randomly generated matrix, determinant is roughly multiplication of diagonal matrix squared. As (.95)^40 is a small number and (1.05)^40 is a bignumber, I get a histogram that increases from zero reaches a maxima and then fall to zero when I plot all these determinant values. It has a mean of 1 but peak at around .1

What kind of nomalization should I use such that when I make histogram it looks like a bell curve with a mean of 1.

 

[Stephen Tashi]

Are you using the term "normalization" to refer to a change of variable meets very specific technical requirements or would you be happy with "any old change of variable"?

You could histogram the logarithms of the determinant values. That might be bell shaped. You would probably have to add some constant to the logs to get the mean to be 1.

 

[bpet]

If you mean D~Prod(1+eps.Bjj) or D~Prod(1+eps.Bjj)^2 where B is a random matrix, that would be approximately lognormal (use CLT on log(D)).