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