Multifractal Characterization of Weibull and Gamma Probability Distribution Functions

The intrinsic properties of probability distribution functions is important for its several applications especially atmospheric and climate studies. In this study, the multifractal strength of two probability distribution function - Weibull and Gamma distribution functions, in wide range of parameter space was investigated. Results obtained that the multifractal spectra of the two distribution functions are independent of the scale but dependent on the shape parameter. A mathematical model of the form \(y=ce^{-kx}\) was developed to characterize the relationship between multifractality and shape parameter of the distribution functions. The developed model was found to be a good fit with \(r^2\ge 0.98\) in the two probability distribution function.