MATLAB: How can i calculate a equation including exceeding value of realmax

calculatefactorialrealmax

Hi I want to calculate some kind of Poisson random variable. However, when i calculate 1000^x/factorial(x) with large x, the result comes NAN. I know the value of each 1000^x or factorial(x) exceeds the realmax. But, the calculated value of 1000^x/factorial(x) doesn't exceed the realmax. Is any other method to calculate that equation?

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It is essential that you include the exp(-lambda), which is part of the Poisson distribution, in your calculations.

p(x,lambda) = exp(-lambda+x*log(lambda)-sum(log(1:x)));

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MATLAB: Realmax + 1 infinity

Because the value 1 is nowhere near the smallest value that can be added to realmax to create a new value. You would need to add a value that is more than half the difference between representable values around the magnitude of realmax. To get that value try using eps:

>> val = eps(realmax) % much bigger than 1.
val = 1.9958e+292
>> realmax + val/2
ans = Inf
>> realmax + val/3
ans = 1.7977e+308

This is exactly the same as if you add 1e-300 to 10: the answer is 10, because 1e-300 is nowhere near the difference in representable values around the magnitude 10, so adding 1e-300 makes absolutely no difference to the 10.

MATLAB: Modulo of realmax in matlab

MATLAB double datatype is based on IEEE-754 format: https://en.wikipedia.org/wiki/Double-precision_floating-point_format. This is a finite precision datatype, and you cannot represent all possible integer values accurately in this format.

flintmax

gives the maximum consecutive integer values, which can be accurately represented in this format. Above that, only a few integer values are precisely represented. In your case, realmax-10000 will just round off to realmax since double() data type does not have the precision to represent it.

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MATLAB: Realmax + 1 infinity

MATLAB: Modulo of realmax in matlab

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