Shape Parameter

A shape parameter changes the shape of a family of statistical distributions rather than merely shifting it through a location parameter or rescaling it through a scale parameter. For example, the Weibull distribution has distribution function

for , with for . Here is a shape parameter and is a scale parameter. Setting gives the exponential distribution.

A family can have more than one shape parameter. The stable distribution has both an index of stability and a skewness parameter .

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National Institute of Standards and Technology. "Families of Distributions." §1.3.6.3 in NIST/SEMATECH e-Handbook of Statistical Methods. https://www.itl.nist.gov/div898/handbook/eda/section3/eda363.htm.National Institute of Standards and Technology. "Weibull Distribution." §1.3.6.6.8 in NIST/SEMATECH e-Handbook of Statistical Methods. https://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm.Nolan, J. P. Univariate Stable Distributions: Models for Heavy Tailed Data. Cham, Switzerland: Springer, 2020. https://doi.org/10.1007/978-3-030-52915-4.