Chi.java

public class Chi {

	// Quickly ported from javascript to java by Robert Gens 4/8/2012

	/*  The following JavaScript functions for calculating normal and
    chi-square probabilities and critical values were adapted by
    John Walker from C implementations
    written by Gary Perlman of Wang Institute, Tyngsboro, MA
    01879.  Both the original C code and this JavaScript edition
    are in the public domain.  */

	/*  POZ  --  probability of normal z value

    Adapted from a polynomial approximation in:
            Ibbetson D, Algorithm 209
            Collected Algorithms of the CACM 1963 p. 616
    Note:
            This routine has six digit accuracy, so it is only useful for absolute
            z values < 6.  For z values >= to 6.0, poz() returns 0.0.
	 */

	static double BIGX = 20.0;                  /* max value to represent exp(x) */

	static double poz(double z) {
		double y, x, w;
		double Z_MAX = 6.0;              /* Maximum meaningful z value */

		if (z == 0.0) {
			x = 0.0;
		} else {
			y = 0.5 * Math.abs(z);
			if (y >= (Z_MAX * 0.5)) {
				x = 1.0;
			} else if (y < 1.0) {
				w = y * y;
				x = ((((((((0.000124818987 * w
						- 0.001075204047) * w + 0.005198775019) * w
						- 0.019198292004) * w + 0.059054035642) * w
						- 0.151968751364) * w + 0.319152932694) * w
						- 0.531923007300) * w + 0.797884560593) * y * 2.0;
			} else {
				y -= 2.0;
				x = (((((((((((((-0.000045255659 * y
						+ 0.000152529290) * y - 0.000019538132) * y
						- 0.000676904986) * y + 0.001390604284) * y
						- 0.000794620820) * y - 0.002034254874) * y
						+ 0.006549791214) * y - 0.010557625006) * y
						+ 0.011630447319) * y - 0.009279453341) * y
						+ 0.005353579108) * y - 0.002141268741) * y
						+ 0.000535310849) * y + 0.999936657524;
			}
		}
		return z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5);
	}

	static double ex(double x) {
		return (x < -BIGX) ? 0.0 : Math.exp(x);
	}

	static double pochisq(double x, int df) {
		double a, y=0, s;
		double e, c, z;
		boolean even;                     /* True if df is an even number */

		double LOG_SQRT_PI = 0.5723649429247000870717135; /* log(sqrt(pi)) */
		double I_SQRT_PI = 0.5641895835477562869480795;   /* 1 / sqrt(pi) */

		if (x <= 0.0 || df < 1) {
			return 1.0;
		}

		a = 0.5 * x;
		even = df % 2 == 0;
		if (df > 1) {
			y = ex(-a);
		}
		s = (even ? y : (2.0 * poz(-Math.sqrt(x))));
		if (df > 2) {
			x = 0.5 * (df - 1.0);
			z = (even ? 1.0 : 0.5);
			if (a > BIGX) {
				e = (even ? 0.0 : LOG_SQRT_PI);
				c = Math.log(a);
				while (z <= x) {
					e = Math.log(z) + e;
					s += ex(c * z - a - e);
					z += 1.0;
				}
				return s;
			} else {
				e = (even ? 1.0 : (I_SQRT_PI / Math.sqrt(a)));
				c = 0.0;
				while (z <= x) {
					e = e * (a / z);
					c = c + e;
					z += 1.0;
				}
				return c * y + s;
			}
		} else {
			return s;
		}
	}

	/*  CRITCHI  --  Compute critical chi-square value to
                     produce given p.  We just do a bisection
                     search for a value within CHI_EPSILON,
                     relying on the monotonicity of pochisq().  */

	static double critchi(double p, int df) {
		double CHI_EPSILON = 0.000001;   /* Accuracy of critchi approximation */
		double CHI_MAX = 99999.0;        /* Maximum chi-square value */
		double minchisq = 0.0;
		double maxchisq = CHI_MAX;
		double chisqval;

		if (p <= 0.0) {
			return maxchisq;
		} else {
			if (p >= 1.0) {
				return 0.0;
			}
		}

		chisqval = df / Math.sqrt(p);    /* fair first value */
		while ((maxchisq - minchisq) > CHI_EPSILON) {
			if (pochisq(chisqval, df) < p) {
				maxchisq = chisqval;
			} else {
				minchisq = chisqval;
			}
			chisqval = (maxchisq + minchisq) * 0.5;
		}
		return chisqval;
	}

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		System.out.println("DF\tp=0.05\tp=0.01");
		for(int df=1; df<=100; df++)
			System.out.println(df + "\t" + String.format("%.2f",critchi(0.05,df)) + "\t" + String.format("%.2f",critchi(0.01,df)));
	}

}