Abstract
The principle of maximum entropy (POME) was employed to derive a new method of parameter estimation for the 3-parameter log-logistic distribution (LLD3). Monte Carlo simulated data were used to evaluate this method and compare it with the methods of moments (MOM), probability weighted moments (PWM), and maximum likelihood estimation (MLE). Simulation results showed that POME's performance was superior in predicting quantiles of large recurrence intervals when population skew was greater than or equal to 2.0. In all other cases, POME's performance was comparable to other methods.
Similar content being viewed by others
References
Ahmad, M. I.; Sinclair, C. D.; Werritti, A. 1988: Log-logistic flood frequency analysis. Journal of Hydrology 98, 205–224
Bennett, S. 1983: Log-logistic regression models for survival data. Applied Statistics 32, 165–171
Burr, I. W. 1942: Cumulative frequency functions. Ann. Math. Statist. 13, 215–232
Guo, H.; Singh, V. P. 1993: A comparative evaluation of estimators of log-logistic distributions by Monte Carlo simulation. Technical Report WRR26, Water Resources Program, Department of Civil Engineering, Louisiana State University, Baton Rouge, Louisiana, U.S.A.
Haktanir, T. 1991: Statistical modeling of annual maximum flows in Turkish rivers. Hydrological Sciences Journal 36, No. 4, 367–389
Jaynes, E. T. 1968: Prior probabilities. IEEE Transactions on Syst. Man. Cybern. 3 (SSC-4), 227–241
Lawless, J. F. 1986: A note on lifetime regression models. Biometrika 73, 2, 509–512
Levine, R. D.; Tribus, M. 1979: The maximum Entropy Formalism. Massachusetts: MIT Press
Mielke, P. W.; Johnson, E. S. 1973: Three-parameter kappa distribution maximum likelihood estimates and likelihood ratio tests. Monthly Weather Review 101, 701–709
Shoukri, M. M.; Mian, I. U. H.; Tracy, D. S. 1988: Sampling properties of estimators of the log-logistic distribution with application to Canadian precipitation data. The Canadian Journal of Statistics 16, No. 3, 223–236
Singh, V. P.; Rajagopal, A. K. 1986: Anewmethod of parameter estimation for hydrologic frequency analysis. Hydrological Science and Technology 2, No. 3, 33–40
Tribus, M. 1969: Rational Descriptors, Decisions and Designs. New York: Pergamon Press
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Singh, V.P., Guo, H. & Yu, F.X. Parameter estimation for 3-parameter log-logistic distribution (LLD3) by Pome. Stochastic Hydrol Hydraul 7, 163–177 (1993). https://doi.org/10.1007/BF01585596
Issue Date:
DOI: https://doi.org/10.1007/BF01585596