Examples of LaplaceDistribution

com.opengamma.analytics.math.statistics.distribution.LaplaceDistribution

The Laplace distribution is a continuous probability distribution with probability density function $$ \begin{align*} f(x)=\frac{1}{2b}e^{-\frac{|x-\mu|}{b}} \end{align*} $$ where $\mu$ is the location parameter and $b$ is the scale parameter. The cumulative distribution function and its inverse are defined as: $$ \begin{align*} F(x)&= \begin{cases} \frac{1}{2}e^{\frac{x-\mu}{b}} & \text{if } x < \mu\\ 1-\frac{1}{2}e^{-\frac{x-\mu}{b}} & \text{if } x\geq \mu \end{cases}\\ F^{-1}(p)&=\mu-b\text{ sgn}(p-0.5)\ln(1-2|p-0.5|) \end{align*} $$ Given a uniform random variable $U$ drawn from the interval $(-\frac{1}{2}, \frac{1}{2}]$, a Laplace-distributed random variable with parameters $\mu$ and $b$ is given by: $$ \begin{align*} X=\mu-b\text{ sgn}(U)\ln(1-2|U|) \end{align*} $$

    final int n = x.length;
    double b = 0;
    for (int i = 0; i < n; i++) {
      b += Math.abs(x[i] - median);
    }
    return new LaplaceDistribution(median, b / n);
  }


  @Test
  public void test() {
    final double mu = 0.367;
    final double b = 1.4;
    final ProbabilityDistribution<Double> distribution = new LaplaceDistribution(mu, b, new MersenneTwister64(MersenneTwister.DEFAULT_SEED));
    final int n = 500000;
    final double[] x = new double[n];
    for (int i = 0; i < n; i++) {
      x[i] = distribution.nextRandom();
    }
    final LaplaceDistribution result = (LaplaceDistribution) ESTIMATOR.evaluate(x);
    final double eps = 1e-2;
    assertEquals(1, result.getB() / b, eps);
    assertEquals(1, result.getMu() / mu, eps);
  }

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Examples of LaplaceDistribution

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

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