Correlated gamma variables in the analysis of microbial densities in water

Advances in Water Resources

Volumn 28, Issue 4, 2005, Pages 329-335

  Loáiciga, Hugo A ^a   Leipnik, Roy B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Correlation; Gamma variables; Microbial densities; Ratio distribution

Indexed keywords

DENSITY MEASUREMENT (SPECIFIC GRAVITY); FOURIER TRANSFORMS; GAMMA RAYS; MICROBIOLOGY; POLYNOMIALS; PROBABILITY DENSITY FUNCTION; WATER RESOURCES;

BACTERIAL DENSITIES; MICROBIAL-DENSITY DATA; STREAM WATER; WATER RESOURCES DATA;

WATER;

BACTERIUM; MICROBIAL COMMUNITY; POPULATION DENSITY; PROBABILITY DENSITY FUNCTION; STREAMWATER;

BACTERIA (MICROORGANISMS);

EID: 14644403715     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2004.11.008     Document Type: Article

References (32)

1. D.J. Becker J.J.J. Roux A bivariate extension of the gamma distribution South African Statist J 15 1981 1-12
2. Charlier CVL. Researches in the theory of probability. K Fysiogr Sällsk Handbook 1906;16
3. Charlier CVL. Applications de la théorie des probabilities á la astronomie. In: Borel M (Ed.), Traité du calcul des probabilities, vol. 2, part 4. Paris: Gauthier-Villars; 1931
4. L.S. Clesceri A.E. Greenberg D.W. Eaton In: Standard methods for the examination of water and wastewater 20th ed. 1998 American Public Health Association Washington, DC
5. K.C. Cheriyan A bivariate correlated gamma-type distribution function J Indian Math Soc 5 1941 133-144
6. F.N. David E. Fix Proceedings of the fourth Berkeley symposium vol. I 1961 University of California Press Berkeley, CA p. 177-187
7. G.M. D'este A Morgenstern-type bivariate gamma distribution Biometrika 68 1981 339-340
8. G.K. Eagleson Polynomial expansions of bivariate distributions Ann Math Statist 35 1964 1208-1215
9. A. Erdelyi Tables of integral transforms vol. I 1954 McGraw-Hill New York
10. D.P. Gaver Multivariate gamma distributions generated by mixture Sankhyâ A 33 1970 123-126
11. I.S. Gradshteyn I.M. Ryzhik Tables of integrals, series, and products 5th ed. 1994 Academic Press San Diego, CA
12. R.F. Gunst T.T. Webster Density functions of the bivariate chi-square distribution J Statist Comput Simulat 2 1973 275-288
13. D.V. Hinkley On the ratio of two correlated normal random variables Biometrika 56 1969 635-651
14. M. Kendall The advanced theory of statistics vols. 1, 2, 4th ed 1977 Griffin London
15. W.F. Kibble A two-variate gamma type distribution Sankhyâ 5 1941 137-150
16. I. Kotlarski On bivariate random variables where the quotient of their coordinates follows some known distributions Ann Math Statist 1964 1673-1684
17. S. Kotz N. Balakrishnan N.L. Johnson Continuous multivariate distributions vol. 1, 2nd ed 2000 John Wiley New York
18. I.A. Koutrouvelis G.C. Canavos Estimation in the Pearson type III distribution Water Resour Res 35 1999 2693-2704
19. P.R. Krishnaiah M.M. Rao Remarks on a multivariate gamma distribution Amer Math Monthly 68 1961 392-396
20. A.S. Krishnamoorthy M. Parthasarathy A multivariate gamma-type distribution Ann Math Statist 22 1951 549-557
21. H.O. Lancaster The structure of bivariate distributions Ann Math Statist 29 1958 719-736
22. H.O. Lancaster Joint probability distributions in the Meixner classes J Roy Statist Soc B 1975 435-443
23. Loáiciga HA, Renehan S. Bacterial densities in Las Palmas Creek, Hope Ranch, California, 1999 - 2000. Report 2-2-2000, Department of Geography, University of California, Santa Barbara, CA, 2000.
24. H.A. Loáiciga Residence time, groundwater age, and solute output in steady-state groundwater systems Adv Water Resour 27 2004 681-688
25. J. Meixner Orthogonale polynomsysteme mit einer besonderen gestalt der erzeugenden function J London Math Soc 9 1934 6-13
26. P.A.P. Moran Statistical inference with bivariate gamma distributions Biometrika 56 1969 627-634
27. A. Prékopa T. Szántai A new multivariate gamma distribution and its fitting to empirical stream data Water Resour Res 14 1978 19-29
28. Y.R. Ramabhadran A multivariate gamma-type distribution Sankhyâ 11 1951 45-46
29. S. Sarmanov A generalized symmetric gamma distribution Doklady Akad Nauk SSSR 179 1968 1279-1285
30. D. Vere-Jones The infinite divisibility of a bivariate gamma distribution Sankhyâ A 27 1967 421-427
31. S.D. Wicksell On correlation surfaces of type 3.Biometrika 25 1933 121-133
32. E. Xekalaki J. Panaretos S. Psarakis A predictive model evaluation and selection approach - the correlated gamma ratio distribution In: J. Panaretos Stochastic musings: Perspectives from the pioneers of the late 20th century 2003 Laurence Erlbaum Publishing USA p.188-202