Examples of com.opengamma.analytics.math.statistics.distribution.GeneralizedParetoDistribution

com.opengamma.analytics.math.statistics.distribution.GeneralizedParetoDistribution

The generalized Pareto distribution is a family of power law probability distributions with location parameter $\mu$, shape parameter $\xi$ and scale parameter $\sigma$, where $$ \begin{eqnarray*} \mu&\in&\Re,\\ \xi&\in&\Re,\\ \sigma&>&0 \end{eqnarray*} $$ and with support $$ \begin{eqnarray*} x\geq\mu\quad\quad\quad(\xi\geq 0)\\ \mu\leq x\leq\mu-\frac{\sigma}{\xi}\quad(\xi<0) \end{eqnarray*} $$ The cdf is given by: $$ \begin{align*} F(z)&=1-\left(1 + \xi z\right)^{-\frac{1}{\xi}}\\ z&=\frac{x-\mu}{\sigma} \end{align*} $$ and the pdf is given by: $$ \begin{align*} f(z)&=\frac{\left(1+\xi z\right)^{-\left(\frac{1}{\xi} + 1\right)}}{\sigma}\\ z&=\frac{x-\mu}{\sigma} \end{align*} $$ Given a uniform random number variable $U$ drawn from the interval $(0,1]$, a Pareto-distributed random variable with parameters $\mu$, $\sigma$ and $\xi$ is given by $$ \begin{align*} X=\mu + \frac{\sigma\left(U^{-\xi}-1\right)}{\xi}\sim GPD(\mu,\sigma,\xi) \end{align*} $$

    double[] bracket = BRACKETER.getBracketedPoints(ksiFunction, 0, 0.33333);
    final double ksi = ROOT_FINDER.getRoot(ksiFunction, bracket[0], bracket[1]);
    final double ksiP1 = 1 - ksi;
    final double sigma = Math.sqrt(variance * (1 - 2 * ksi) * ksiP1 * ksiP1);
    final double mu = mean - sigma / ksiP1;
    return new GeneralizedParetoDistribution(mu, sigma, ksi);
  }

  }


  @Test
  public void test() {
    final double eps = 0.05;
    final GeneralizedParetoDistribution result = (GeneralizedParetoDistribution) ESTIMATOR.evaluate(X);
    assertEquals(MU, result.getMu(), MU * eps);
    assertEquals(SIGMA, result.getSigma(), SIGMA * eps);
    assertEquals(KSI, result.getKsi(), KSI * eps);
  }

Examples of com.opengamma.analytics.math.statistics.distribution.GeneralizedParetoDistribution

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