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I'm trying to calculate the cumulative binomial probability of 'n' trials, with 'p' probability and 'r' as the successful outcome of each trial. I have written the following code that works sometimes, but not always:

Console.WriteLine (); Console.WriteLine ("B~(n, p)"); incorrectN: Console.WriteLine ("Enter value of 'n': "); int n = Convert.ToInt32 (Console.ReadLine ()); if (n < 0) { Console.WriteLine ("ERROR: 'n' must be greater than 0"); goto incorrectN; } incorrectP: Console.WriteLine (); Console.WriteLine ("Enter value of 'p': "); double p = Convert.ToDouble (Console.ReadLine ()); if (p > 1) { Console.WriteLine (); Console.WriteLine ("ERROR: 'p' must be between 0 and 1"); goto incorrectP; } Console.WriteLine (); incorrectS: int r = GetR(); int k = r; double binomTotal = 0; for (int j = r + 1; j > 0; j--) { int nCr = Factorial(n) / (Factorial(n - (r - k)) * Factorial(r - k)); binomTotal = binomTotal + nCr * Math.Pow(p, (r - k)) * Math.Pow(1 - p, (n - (r - k))); k--; } Console.WriteLine(); Console.WriteLine(binomTotal);

P.S. I have written the GetR() and Factorial() functions elsewhere within the class, where GetR() asks the user for the value of 'r' and Factorial() is defined as follows:

public static int Factorial(int x) { return x <= 1 ? 1 : x * Factorial(x - 1); }

I tested the code with values n = 10, p = 0.5 and r = 5 and the output is 0.623046875, which is correct. However, when I use n = 13, p = 0.35 and r = 7, I get 0.297403640622647 instead of 0.9538.

Any help would be much appreciated.

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    Where does n come from? Please post actual, tested and compiling code. Commented Feb 16, 2015 at 13:08
  • 4
    No related but ... don't use goto or the .Net evil will eat your soul on an infinite agony ... :) Commented Feb 16, 2015 at 13:16
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    Factorial(13) = 6227020800 > Int32.MaxValue = 2147483647 :) Change the return type of the factorial method to long. Commented Feb 16, 2015 at 13:17
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    It'd make sense to use double for factorials here, since the answer needn't be exact. Commented Feb 16, 2015 at 13:19
  • Would help if you gave links to some definitions as well, and maybe a brief explanation of what is possible to explain in plain English as well Commented Feb 16, 2015 at 13:22

2 Answers 2

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In addition to your own answer:

public static double Factorial(double x) { return x <= 1 ? 1 : x * Factorial(x - 1); }

accepts a double parameter, which means that x is not restricted to be an integer. So you could call your Factorial method like this.

var fac1 = Factorial(1.4); var fac2 = Factorial(2.7);

However, this does not make sense since the factorial n! is defined only* for n, meaning that 1.7! is undefined.

So, instead of using double and allowing for invalid inputs, you should be using long instead, which has a greater range than int.

public static long Factorial(long x) { return x <= 1 ? 1 : x * Factorial(x - 1); }

* there are some cases where factorials can be used with real values as well - e.g. by using the gamma function - but I don't think they're relevant to your use case and therefore you should not allow invalid parameters.

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Change:

public static int Factorial(int x) { return x <= 1 ? 1 : x * Factorial(x - 1); }

To:

public static double Factorial(double x) { return x <= 1 ? 1 : x * Factorial(x - 1); }

Because Factorial(13) is too large for Int32.

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