content: /*******************************************************************************
   * Copyright (c) 2010 Haifeng Li
   *   
   * 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 smile.stat.distribution;
  
  import java.io.Serializable;
  
  /**
   * Probability distribution of univariate random variable. A probability
   * distribution identifies either the probability of each value
   * of a random variable (when the variable is discrete), or
   * the probability of the value falling within a particular interval (when
   * the variable is continuous). When the random variable takes values in the
   * set of real numbers, the probability distribution is completely described
   * by the cumulative distribution function, whose value at each real x is the
   * probability that the random variable is smaller than or equal to x.
   *
   * @see MultivariateDistribution
   *
   * @author Haifeng Li
   */
  public interface Distribution extends Serializable {
  
      /**
       * The number of parameters of the distribution.
       */
      int npara();
  
      /**
       * The mean of distribution.
       */
      double mean();
      
      /**
       * The variance of distribution.
       */
      double var();
      
      /**
       * The standard deviation of distribution.
       */
      double sd();
  
      /**
       * Shannon entropy of the distribution.
       */
      double entropy();
  
      /**
       * Generates a random number following this distribution.
       */
      double rand();
      
      /**
       * The probability density function for continuous distribution
       * or probability mass function for discrete distribution at x.
       */
      double p(double x);
  
      /**
       * The density at x in log scale, which may prevents the underflow problem.
       */
      double logp(double x);
  
      /**
       * Cumulative distribution function. That is the probability to the left of x.
       */
      double cdf(double x);
  
      /**
       * The quantile, the probability to the left of quantile is p. It is
       * actually the inverse of cdf.
       */
      double quantile(double p);
  
      /**
       * The likelihood of the sample set following this distribution.
       */
      double likelihood(double[] x);
      
      /**
       * The log likelihood of the sample set following this distribution.
       */
      double logLikelihood(double[] x);
  }
  