Computing the Kullback-Leibler Divergence between two Generalized Gamma Distributions

We derive a closed form solution for the Kullback-Leibler divergence between two generalized gamma distributions. These notes are meant as a reference and provide a guided tour towards a result of practical interest that is rarely explicated in the literature.

[1]  Christian Bauckhage,et al.  Mathematical Models of Fads Explain the Temporal Dynamics of Internet Memes , 2013, ICWSM.

[2]  Esther de Ves,et al.  Wavelet-Based Texture Retrieval Modeling the Magnitudes of Wavelet Detail Coefficients with a Generalized Gamma Distribution , 2010, 2010 20th International Conference on Pattern Recognition.

[3]  D. F. Hays,et al.  Table of Integrals, Series, and Products , 1966 .

[4]  J. Crank.  Tables of Integrals , 1962 .

[5]  E. Stacy.  A Generalization of the Gamma Distribution , 1962 .

[6]  L. Amoroso,et al.  Ricerche intorno alla curva dei redditi , 1925 .

[7]  Christian Bauckhage,et al.  The Weibull as a Model of Shortest Path Distributions in Random Networks , 2013 .

[8]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[9]  John H. Lienhard,et al.  A physical basis for the generalized gamma distribution , 1967 .

[10]  Kenneth Ward Church,et al.  Improving Random Projections Using Marginal Information , 2006, COLT.

[11]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[12]  Gavin E. Crooks,et al.  The Amoroso Distribution , 2010, 1005.3274.

[13]  Mohamed Najim,et al.  Centroid-based texture classification using the generalized Gamma distribution , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[14]  Christian Bauckhage,et al.  Computing the Kullback-Leibler Divergence between two Weibull Distributions , 2013, ArXiv.

[15]  Chong-Sze Tong,et al.  Statistical Wavelet Subband Characterization Based on Generalized Gamma Density and Its Application in Texture Retrieval , 2010, IEEE Transactions on Image Processing.