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;
  
  /**
   * The exponential family is a class of probability distributions sharing
   * a certain form. The normal, exponential, gamma, chi-square, beta, Weibull
   * (if the shape parameter is known), Dirichlet, Bernoulli, binomial,
   * multinomial, Poisson, negative binomial, and geometric distributions
   * are all exponential families. The family of Pareto distributions with
   * a fixed minimum bound form an exponential family.
   * <p>
   * The Cauchy, Laplace, and uniform families of distributions are not
   * exponential families. The Weibull distribution is not an exponential
   * family unless the shape parameter is known.
   * <p>
   * The purpose of this interface is mainly to define the method M that is
   * the Maximization step in the EM algorithm. Note that distributuions of exponential
   * family has the close-form solutions in the EM algorithm. With this interface,
   * we may allow the mixture contains distributions of different form as long as
   * it is from exponential family.
   *
   * @see ExponentialFamilyMixture
   * @see DiscreteExponentialFamily
   * @see DiscreteExponentialFamilyMixture
   *
   * @author Haifeng Li
   */
  public interface ExponentialFamily {
  
      /**
       * The M step in the EM algorithm, which depends the specific distribution.
       *
       * @param x the input data for estimation
       * @param posteriori the posteriori probability.
       * @return the (unnormalized) weight of this distribution in the mixture.
       */
      Mixture.Component M(double[] x, double[] posteriori);
  }
  