Shape parameter

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In

numerical parameter of a parametric family of probability distributions[2]
that is neither a
shape
of a distribution rather than simply shifting it (as a location parameter does) or stretching/shrinking it (as a scale parameter does). For example, "peakedness" refers to how round the main peak is.
[3]

Probability density functions for selected distributions with mean 0 and variance 1.

Estimation

Many

Maximum likelihood
estimation can also be used.

Examples

The following continuous probability distributions have a shape parameter:

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.

See also

References

  1. ^ Ekawati, Dian; Warsono; Kurniasari, Dian (December 2014). "On the Moments, Cumulants, and Characteristic Function of the Log-Logistic Distribution" (PDF). The Journal for Technology and Science. 25.
  2. .