package jhplot.fit;

import hep.aida.ref.function.AbstractIFunction;
import jhplot.math.num.pdf.*;
import java.lang.Math;


/**
 * Negative binomial distribution.
 * Returns the sum of the terms 0 through k of the Negative Binomial Distribution.
 * 
 *   k
 *   --  ( n+j-1 )   n      j
 *   >   (       )  p  (1-p)
 *   --  (   j   )
 *  j=0
 * 
 * In a sequence of Bernoulli trials, this is the probability
 * that k or fewer failures precede the n-th success.
 * 

 * The terms are not computed individually; instead the incomplete
 * beta integral is employed, according to the formula
 * 

 * y = negativeBinomial( k, n, p ) = Gamma.incompleteBeta( n, k+1, p ).
 *
 * All arguments must be positive, 
 * p[0] - scale  factor 

 * p[1] - the number of trials. 
 
 * p[2] - the probability of success (must be in (0.0,1.0)).
*/
 
public class NegativeBinomial extends AbstractIFunction {

	public NegativeBinomial() {
		this("NegativeBinomial");
	}

	public NegativeBinomial(String title) {
		super(title, 1, 3);
	}

	public NegativeBinomial(String[] variableNames, String[] parameterNames) {
		super(variableNames, parameterNames);
	}

	
	/**
	 * Get value of this function
	 */
	public double value(double[] v) {

		 int numberOfSuccesses=(int)p[1];
		 double probabilityOfSuccess=p[2];
		 int x=(int)v[0];
			 
			 
		 double ret;
	        if (x < 0) {
	            ret = 0.0;
	        } else {
	            ret = Math.exp(jhplot.math.num.pdf.SaddlePoint.logBinomialProbability(
	                numberOfSuccesses, x + numberOfSuccesses, probabilityOfSuccess,
	                1.0 - probabilityOfSuccess));
	            ret = (numberOfSuccesses * ret) / (x + numberOfSuccesses);
	        }
	        return p[0] * ret;	
		
	}

	
	
	
	
	// Here change the parameter names
	protected void init(String title) {
            parameterNames[0] = "norm";
            parameterNames[1] = "numbertrials";
            parameterNames[2] = "probsuccess";

		super.init(title);
	}
}