Shape Parameter - Examples


The following continuous probability distributions have a shape parameter:

  • Beta distribution
  • Burr distribution
  • Erlang distribution
  • ExGaussian distribution
  • Exponential power distribution
  • Gamma distribution
  • Generalized extreme value distribution
  • Log-logistic distribution
  • Inverse-gamma distribution
  • Pareto distribution
  • Pearson distribution
  • Skew normal distribution
  • Lognormal distribution
  • Student's t-distribution
  • Tukey lambda distribution
  • Weibull distribution

By contrast, the following continuous distributions do not have a shape parameter, so their shape is fixed and only their location or their scale or both can change. It follows that (where they exist) the skewness and kurtosis of these distribution are constants, as skewness and kurtosis are independent of location and scale parameters.

  • Exponential distribution
  • Cauchy distribution
  • Logistic distribution
  • Normal distribution
  • Raised cosine distribution
  • Uniform distribution
  • Wigner semicircle distribution

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