Examples of GAMMADIST

com.nr.sf.Gammadist
org.boris.expr.function.excel.GAMMADIST
umontreal.iro.lecuyer.probdist.GammaDist
Extends the class {@link ContinuousDistribution} forthe gamma distribution with shape parameter α > 0 and scale parameter λ > 0. The density is

f (x) = λ^αx^α-1e^-λx/Γ(α), for x > 0,
where Γ is the gamma function, defined by

Γ(α) = ∫₀^∞x^α-1e^-xdx.
In particular, Γ(n) = (n - 1)! when n is a positive integer.

Examples of com.nr.sf.Gammadist

    // Test Gammadist
    System.out.println("Testing Gammadist");


    // Test special cases
    alpha=1.0; beta=1.0; u=1.0;
    Gammadist norm1 = new Gammadist(alpha,beta);
    localflag = abs(norm1.p(u)-exp(-1.0)) > sbeps;
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Special case #1 failed");
      
    }


    alpha=1.0; beta=2.0; u=1.0;
    Gammadist norm2 = new Gammadist(alpha,beta);
//    System.out.printf(abs(norm2.p(u)-2.0*exp(-2.0));
    localflag = abs(norm2.p(u)-2.0*exp(-2.0)) > sbeps;
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Special case #2 failed");
      
    }


    alpha=2.0; beta=1.0; u=1.0;
    Gammadist norm3 = new Gammadist(alpha,beta);
//    System.out.printf(abs(norm3.p(u)-x*exp(-1.0));
    localflag = abs(norm3.p(u)-u*exp(-1.0)) > sbeps;
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Special case #3 failed");
      
    }


    alpha=3.0; beta=1.0; u=1.0;
    Gammadist norm4 = new Gammadist(alpha,beta);
    localflag = abs(norm4.p(u)-u*u*exp(-1.0)/2.0) > sbeps;
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Special case #4 failed");
      
    }


    alpha=2.0; beta=2.0; u=2.0;
    Gammadist norm5 = new Gammadist(alpha,beta);
    localflag = abs(norm5.p(u)-4.0*u*exp(-4.0)) > sbeps;
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Special case #5 failed");
      
    }


    // integral of distribution is one
    sbeps=2.e-7;
    alpha=2.5; beta=1.5;
    func_Gammadist dist = new func_Gammadist(alpha,beta);
    Midpnt q2 = new Midpnt(dist,0.0,2.0);
    Midinf q3 = new Midinf(dist,2.0,1.0e99);
    integral=qromo(q2)+qromo(q3);
    localflag = abs(1.0-integral) > sbeps;
//    System.out.printf(setprecision(15) << 1.0-integral);
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Distribution is not normalized to 1.0");
      
    }


    // cdf agrees with incomplete integral
    sbeps=5.e-7;
    alpha=2.5; beta=1.5;
    func_Gammadist dist2 = new func_Gammadist(alpha,beta);
    Gammadist normcdf = new Gammadist(alpha,beta);
    localflag=false;
    for (i=0;i<N;i++) {
      q2 =new Midpnt(dist2,0.0,x[i]);
      integral=qromo(q2);
      c[i]=integral;
      d[i]=normcdf.cdf(x[i]);
//      System.out.printf(c[i]-d[i]);
      localflag = localflag || abs(c[i]-d[i]) > sbeps;
    }
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: cdf does not agree with result of quadrature");
      
    }


    // inverse cdf agrees with cdf
    alpha=2.5; beta=1.5;
    Gammadist normc = new Gammadist(alpha,beta);
    Ran myran = new Ran(17);
    sbeps=5.0e-14;
    localflag=false;
    for (i=0;i<1000;i++) {
      u=3.0*myran.doub();
      a=normc.cdf(u);
      b=normc.invcdf(a);
//      if (abs(u-b) > sbeps) {
//        System.out.printf(setprecision(15) << u << " %f\n", b << " %f\n", abs(u-b));
//      }
      localflag = localflag || abs(u-b) > sbeps;
    }
    globalflag = globalflag || localflag;
    if (localflag) {
      fail("*** Gammadist: Inverse cdf does not accurately invert the cdf");
      
    }
      
    // Fingerprint test
    alpha=2.5; beta=1.5;
    Gammadist normf = new Gammadist(alpha,beta);
    for (i=0;i<N;i++) {
      p[i]=normf.p(x[i]);
//      System.out.printf(setprecision(17) << p[i] << " %f\n", pexp[i]);
    }
//    System.out.println("Gammadist: Maximum discrepancy = %f\n", maxel(vecsub(p,pexp)));
    localflag = maxel(vecsub(p,pexp)) > sbeps;
    globalflag = globalflag || localflag;

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Examples of com.nr.sf.Gammadist

    double alpha,beta;
    Gammadist normi;
    func_Gammadist(double aalpha, double bbeta) {
      alpha=aalpha;
      beta=bbeta;
      normi = new Gammadist(alpha,beta);
    }

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Examples of com.nr.sf.Gammadist

      fail("*** Gammadev: dev() does not match fingerprint");
      
    }


    // Check statistics
    Gammadist expect=new Gammadist(alpha,beta);
    binsize=range/M;
    for (i=0;i<M;i++) {
      x[i]=binsize*i;
      ebins[i]=N*binsize*expect.p(x[i]+0.5*binsize);
      bins[i]=0;
    }
    for (i=0;i<N;i++) {
      nbin=(int)(floor(myran.dev()/binsize));
      if ((nbin >= 0) && (nbin < M)) bins[nbin] += 1;

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Examples of org.boris.expr.function.excel.GAMMADIST

        FTEST f = new FTEST();
        fail("FTEST not implemented");
    }


    public void testGAMMADIST() throws Exception {
        GAMMADIST g = new GAMMADIST();
        fail("GAMMADIST not implemented");
    }

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Examples of umontreal.iro.lecuyer.probdist.GammaDist

      this.stream = stream;
      dimension = alphas.length;
      ggens = new GammaAcceptanceRejectionGen[alphas.length];
      for (int k = 0; k < alphas.length; k++)
         ggens[k] = new GammaAcceptanceRejectionGen
            (stream, new GammaDist (alphas[k], 1.0/2.0));
   }

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