Package smile.stat.distribution

Class ShiftedGeometricDistribution

java.lang.Object
smile.stat.distribution.DiscreteDistribution
smile.stat.distribution.ShiftedGeometricDistribution
All Implemented Interfaces:
Serializable, DiscreteExponentialFamily, Distribution
public class ShiftedGeometricDistribution extends DiscreteDistribution implements DiscreteExponentialFamily
The "shifted" geometric distribution is a discrete probability distribution of the number of failures before the first success, supported on the set {0, 1, 2, 3, …}. If the probability of success on each trial is p, then the probability that the k-th trial (out of k trials) is the first success is Pr(X = k) = (1 - p)k p
See Also:

  • Field Details

    • p

      public final double p
      The probability of success.

  • Constructor Details

    • ShiftedGeometricDistribution

      public ShiftedGeometricDistribution(double p)
      Constructor.
      Parameters:
      p - the probability of success.

  • Method Details

    • fit

      public static ShiftedGeometricDistribution fit(int[] data)
      Estimates the distribution parameters by MLE.
      Parameters:
      data - the training data.
      Returns:
      the distribution.

    • length

      public int length()
      Description copied from interface: Distribution
      Returns the number of parameters of the distribution. The "length" is in the sense of the minimum description length principle.
      Specified by:
      length in interface Distribution
      Returns:
      The number of parameters.

    • mean

      public double mean()
      Description copied from interface: Distribution
      Returns the mean of distribution.
      Specified by:
      mean in interface Distribution
      Returns:
      The mean.

    • variance

      public double variance()
      Description copied from interface: Distribution
      Returns the variance of distribution.
      Specified by:
      variance in interface Distribution
      Returns:
      The variance.

    • sd

      public double sd()
      Description copied from interface: Distribution
      Returns the standard deviation of distribution.
      Specified by:
      sd in interface Distribution
      Returns:
      The standard deviation.

    • entropy

      public double entropy()
      Description copied from interface: Distribution
      Returns Shannon entropy of the distribution.
      Specified by:
      entropy in interface Distribution
      Returns:
      Shannon entropy.

    • toString

      public String toString()
      Overrides:
      toString in class Object

    • rand

      public double rand()
      Description copied from interface: Distribution
      Generates a random number following this distribution.
      Specified by:
      rand in interface Distribution
      Returns:
      a random number.

    • p

      public double p(int k)
      Description copied from class: DiscreteDistribution
      The probability mass function.
      Specified by:
      p in class DiscreteDistribution
      Parameters:
      k - a real value.
      Returns:
      the probability.

    • logp

      public double logp(int k)
      Description copied from class: DiscreteDistribution
      The probability mass function in log scale.
      Specified by:
      logp in class DiscreteDistribution
      Parameters:
      k - a real value.
      Returns:
      the log probability.

    • cdf

      public double cdf(double k)
      Description copied from interface: Distribution
      Cumulative distribution function. That is the probability to the left of x.
      Specified by:
      cdf in interface Distribution
      Parameters:
      k - a real number.
      Returns:
      the probability.

    • quantile

      public double quantile(double p)
      Description copied from interface: Distribution
      The quantile, the probability to the left of quantile is p. It is actually the inverse of cdf.
      Specified by:
      quantile in interface Distribution
      Parameters:
      p - the probability.
      Returns:
      the quantile.

    • M

      public DiscreteMixture.Component M(int[] x, double[] posteriori)
      Description copied from interface: DiscreteExponentialFamily
      The M step in the EM algorithm, which depends on the specific distribution.
      Specified by:
      M in interface DiscreteExponentialFamily
      Parameters:
      x - the input data for estimation
      posteriori - the posteriori probability.
      Returns:
      the (unnormalized) weight of this distribution in the mixture.