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Asked by sadoune sadoune
on 9 May 2013

Hi,

I would like to know if it is possible to use Matlab for very small numbers (smaller than 10^-308 ). It's very important for my application "statistical genetics". in this field, somes probabilities are smaller than 10^-500.

Thank you

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Answer by Sean de Wolski
on 9 May 2013

Edited by Sean de Wolski
on 9 May 2013

You can do this using `vpa()` in the Symbolic Math Toolbox:

v = vpa('3.14159^-5000')

And for more info:

You could also use exact symbolic arithmetic:

sym('3.1415^-34334')

sadoune sadoune
on 10 May 2013

Thank you for your answer,

I tried vpa function with the following example:

for i=1:400 tab(i)=0.1; end

v = vpa(prod(tab))

and the result was v =0.0 :(

Sean de Wolski
on 10 May 2013

That's because you're doing the computation as a double and then converting it to `vpa()`. Convert it to vpa before doing the computation:

for i=400:-1:1 tab(i)=vpa(0.1); end v = (prod(tab))

Answer by Peter Perkins
on 11 May 2013

Quite often in statistics when one has very small probabilities, one works on the log scale. That's why one typically maximizes the LOG-likelihood, and not the likelihood.

## 4 Comments

## John Doe

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/75223#comment_148146

I'm sorry, but I just have to ask: How can a probability of 10^-500 be of any relevance, ever? (I'm actually curious)

## Sean de Wolski

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/75223#comment_148147

+1 @Robert's comment

## sadoune sadoune

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/75223#comment_148148

Hi Robert,

You can imagine a vector length 500, each case represent a probability, and the probability i would like to compute is the product of all this probabilities (independance).

## John Doe

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/75223#comment_148150

Ok, then I see where you get the number from, but if you are ending up with a probability that low, it is literally impossible for it to happen. Isn't OK to just let it be equal to 0?

I don't mean to be rude or condescending, I just don't get how it would make sense to keep working with numbers that low.

Anyhow, I hope someone can provide an answer for you, and good luck =)