Cumulative Binomial Probability C#

Question

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.

Answer 1

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 is defined only* for , meaning that 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.}