Reliability Evaluation on Estimated Parameters of 2-Parameter Lognormal Distribution

Abstract

The reliability of the estimated parameters is evaluated by using the entropy to posterior distribution in the 2-parameter lognormal distribution. When λ and ζ are parameters representing the expectation and the variance of the hydrological value transformed into logarithm respectively, the following cases are discussed.(1)λ: unknown, ζ: known, (2)λ: known, ζ: unknown, (3)λ, ζ: unknown. In each case, the posterior distribution of the unknown parameter (s) is derived from Bayes Theorem, and its entropy is developed. This model is applied to monthly rainfall, and the increase of the reliability, accompanied by the increase of the number of data, is investigated.