code: /**
   * Copyright (C) 2015-2016, BMW Car IT GmbH and BMW AG
   * Author: Stefan Holder (stefan.holder@bmw.de)
   *
   * Licensed under the Apache License, Version 2.0 (the "License");
   * you may not use this file except in compliance with the License.
   * You may obtain a copy of the License at
   *
   *    http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package com.graphhopper.matching;
  
  import static java.lang.Math.PI;
  import static java.lang.Math.exp;
  import static java.lang.Math.log;
  import static java.lang.Math.pow;
  import static java.lang.Math.sqrt;
  
  /**
   * Implements various probability distributions.
   */
  public class Distributions {
  
      static double normalDistribution(double sigma, double x) {
          return 1.0 / (sqrt(2.0 * PI) * sigma) * exp(-0.5 * pow(x / sigma, 2));
      }
  
      /**
       * Use this function instead of Math.log(normalDistribution(sigma, x)) to avoid an
       * arithmetic underflow for very small probabilities.
       */
      public static double logNormalDistribution(double sigma, double x) {
          return Math.log(1.0 / (sqrt(2.0 * PI) * sigma)) + (-0.5 * pow(x / sigma, 2));
      }
  
      /**
       * @param beta =1/lambda with lambda being the standard exponential distribution rate parameter
       */
      static double exponentialDistribution(double beta, double x) {
          return 1.0 / beta * exp(-x / beta);
      }
  
      /**
       * Use this function instead of Math.log(exponentialDistribution(beta, x)) to avoid an
       * arithmetic underflow for very small probabilities.
       *
       * @param beta =1/lambda with lambda being the standard exponential distribution rate parameter
       */
      static double logExponentialDistribution(double beta, double x) {
          return log(1.0 / beta) - (x / beta);
      }
  }
  