Class TDistribution

  • All Implemented Interfaces:
    ProbabilityDistribution

    public class TDistribution
    extends Object
    implements ProbabilityDistribution
    The Student t distribution is the probability distribution of t, where \[ t = \frac{\bar{x} - \mu}{s / \sqrt N} \]
    • \(\bar{x}\) is the sample mean;
    • μ is the population mean;
    • s is the square root of the sample variance;
    • N is the sample size;
    The importance of the Student's distribution is when (as in nearly all practical statistical work) the population standard deviation is unknown and has to be estimated from the data. This is especially true when the sample size is small. When the sample size is large, the Student's distribution converges to the Normal distribution.

    The R equivalent functions are dt, pt, qt, rt.

    See Also:
    Wikipedia: Student's t-distribution
    • Constructor Summary

      Constructors 
      Constructor Description
      TDistribution​(double v)
      Construct a Student's t distribution.
    • Method Summary

      All Methods Instance Methods Concrete Methods 
      Modifier and Type Method Description
      double cdf​(double x)
      Gets the cumulative probability F(x) = Pr(X ≤ x).
      double density​(double x)
      The density function, which, if exists, is the derivative of F.
      double entropy()
      Gets the entropy of this distribution.
      double kurtosis()
      Gets the excess kurtosis of this distribution.
      double mean()
      Gets the mean of this distribution.
      double median()
      Gets the median of this distribution.
      double moment​(double x)
      The moment generating function is the expected value of etX.
      double quantile​(double u)
      Gets the quantile, the inverse of the cumulative distribution function.
      double skew()
      Gets the skewness of this distribution.
      double variance()
      Gets the variance of this distribution.