## Accord.Net binomial probability mass function result differs from Excel result

By : Staeff
Source: Stackoverflow.com
Question!

I'm trying to implement some functionality that was formerly provided via an Excel sheet into a C# application, but the probability mass function of Accord.NET differs for some reason from the excel function.

In excel the probabilty mass function, is used this way

=BINOM.DIST(250; 3779; 0.0638; FALSE)

Result: 0.021944019794458

When I try it with Accord.NET

var binom = new BinomialDistribution(3779, 0.0638);
binom.ProbabilityMassFunction(250);

// Result: Infinity

But the cumulative distribution seems to work properly (except for the last few digits, but I assumed this is just some kind of precision error)

Excel:

=BINOM.DIST(250; 3779; 0.0638; TRUE)

Result: 0.736156366002849

Accord.NET:

var binom = new BinomialDistribution(3779, 0.0638);
binom.DistributionFunction(250);

// Result: 0.736156366002318

Why are the results so different? And is there a way to get the Excel result with Accord?

EDIT: Extreme.Numerics calculates the same result as Excel, but I don't want to use this library, as the license system of this library always led to trouble in the past.

EDIT 2: Seems like some kind of overflow error.

When I use this I get the right result:

Math.Exp(binom.LogProbabilityMassFunction(250));

Any ideas why this could be happening?

By : Staeff

Inspecting the source code of Accord.NET implementation it can be seen that ProbabilityMassFunction works like this:

//...
return Special.Binomial(numberOfTrials, k) * Math.Pow(probability, k)
* Math.Pow(1 - probability, numberOfTrials - k);

In your case numberOfTrials is 3779 and k is 250. Binomial function of 3779 over 250 is more than 10398, which seems too much for the double data type (approximate range is up to a bit more than 10308). So you get Infinity in the first multiplication term, which determines the final result here.

I'm not sure how Extreme.Numerics implements that, but your results suggest that they do it in a more clever way. Also, sadly it doesn't seem that Accord.NET provides decimal version of their interface.

This issue seems to have been fixed in the latest Accord.NET implementation. The implementation looks now as follows:

double log = Special.LogBinomial(numberOfTrials, k) + k * Math.Log(probability)
+ (numberOfTrials - k) * Math.Log(1 - probability);

return Math.Exp(log);
By : BartoszKP