Entropy based derivation of probability distributions: A case study to daily rainfall

Advances in Water Resources

Volumn 45, Issue , 2012, Pages 51-57

  Papalexiou, Simon Michael ^a   Koutsoyiannis, Demetris ^a  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

Author keywords

Burr distribution; Daily rainfall; Generalized Beta distribution; Generalized Gamma distribution; Maximum entropy

Indexed keywords

BURR DISTRIBUTIONS; DAILY RAINFALL; GENERALIZED BETA DISTRIBUTION; GENERALIZED GAMMA DISTRIBUTION; MAXIMUM ENTROPY;

RAIN;

PROBABILITY DISTRIBUTIONS;

EMPIRICAL ANALYSIS; NUMERICAL MODEL; OPTIMIZATION; PRECIPITATION ASSESSMENT; PRECIPITATION INTENSITY; PROBABILITY; TESTING METHOD;

EID: 84864356737     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2011.11.007     Document Type: Article

References (21)

1. Burr I.W. Cumulative frequency functions. Ann Math Stat 1942, 13(2):215-232.
2. Esteban M.D., Morales D. A summary on entropy statistics. Kybernetika 1995, 31(4):337-346.
3. Goldie CM., Klüppelberg C. Subexponential distributions. A practical guide to heavy tails: statistical techniques and applications. Birkhäser Boston 1998, 435-459.
4. Havrda J., Charvát F. Concept of structural a-entropy. Kybernetika 1967, 3:30-35.
5. Hosking J.R. L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B: Methodol 1990, 521:105-124.
6. Jaynes E.T. Information theory and statistical mechanics. Phys. Rev. 1957, 106(4):620.
7. Jaynes E.T. Information theory and statistical mechanics. II. Phys. Rev. 1957, 108(2):171.
8. Jaynes E.T. Probability: the logic of science 2003, Cambridge University Press.
9. Kapur J.N. Maximum-entropy models in science and engineering 1989, John Wiley & Sons.
10. Kleiber C., Kotz S. Statistical size distributions in economics and actuarial sciences 2003, Wiley-Interscience.
11. Koutsoyiannis D. Uncertainty, entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling. J Hydrol Sci 2005, 50(3):381-404.
12. McDonald J.B. Some generalized functions for the size distribution of income. Econometrica 1984, 52(3):647-663.
13. McDonald J.B., Xu Y.J. A generalization of the beta distribution with applications. J Econ 1995, 66(1-2):133-152.
14. Mielke P.W., Johnson E.S. Some generalized beta distributions of the second kind having desirable application features in hydrology and meteorology. Water Resour Res 1974, 10(2):223-226.
15. Papalexiou SM, Koutsoyiannis D. Probabilistic description of rainfall intensity at multiple time scales. In: IHP 2008 Capri symposium: "The role of hydrology in water resources management" 2008. [accessed 06.10.10]. http://www.itia.ntua.gr/en/docinfo/884/.
16. Papalexiou SM, Koutsoyiannis D. Ombrian curves in a maximum entropy framework. In: European geosciences union general assembly 2008; 2008:00702. [accessed 06.10.10]. http://www.itia.ntua.gr/en/docinfo/851/.
17. Shannon C.E. The mathematical theory of communication. Bell Syst Tech J 1948, 27:379-423.
18. Singh V.P. Entropy theory for derivation of infiltration equations. Water Resour Res 2010, 46:20.
19. Stacy E.W. A generalization of the gamma distribution. Ann Math Stat 1962, 33(3):1187-1192.
20. Tadikamalla P.R. A look at the Burr and related distributions. Int Stat Rev/Rev Int Stat 1980, 48(3):337-344.
21. Tsallis C. Possible generalization of Boltzmann-Gibbs statistics. J Stat Phys 1988, 52(1):479-487.