In probability theory and statistics, a shape parameter is a kind of numerical parameter of a parametric family of probability distributions.

A shape parameter is any parameter of a probability distribution that is neither a location parameter nor a scale parameter (nor a function of either or both of these only, such as a rate parameter). Such a parameter must affect the shape of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does).

The following continuous probability distributions have a shape parameter:

Beta distribution

Burr distribution

Erlang distribution

Exponential power distribution

Gamma distribution

Generalized extreme value distribution

Log-logistic distribution

Inverse-gamma distribution

Pareto distribution

Pearson distribution

Tukey lambda distribution

Weibull distribution

Student's t-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

 

概率论，数理统计，形状参数

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