Shape parameter

In probability theory and statistics, a shape parameter (also known as form parameter)[1] is a kind of numerical parameter of a parametric family of probability distributions[2] that is neither a location parameter nor a scale parameter (nor a function of these, 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). For example, "peakedness" refers to how round the main peak is.[3]

Probability density functions for selected distributions with mean 0 and variance 1.
  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. ^ Everitt B.S. (2002) Cambridge Dictionary of Statistics. 2nd Edition. CUP. ISBN 0-521-81099-X
  3. ^ Birnbaum, Z. W. (1948). "On Random Variables with Comparable Peakedness". The Annals of Mathematical Statistics. 19 (1). Institute of Mathematical Statistics: 76–81. doi:10.1214/aoms/1177730293. ISSN 0003-4851.