Precipitation Statistics Fit Analysis

Two parameters Kappa distribution is always used to simulate rainfall precipitation in the climatologically statistics. Firstly this paper obtain the moment estimate, maximum likelihood estimate and inverse moment estimate of Kappa distribution under full sample size case and study the existence of the estimators. After doing that this paper show the accuracy of the moment estimators by Monte-Carlo simulation and find out that the accuracy will be better if the sample size is larger. For maximum likelihood estimators and inverse moment estimators, Monte-Carlo examples are shown.As kappa distribution is the distribution with two parameters, this paper also considers the moment estimate, maximum likelihood estimate and inverse moment estimate of Kappa distribution when one parameter is known. And also give the Monte-Carlo examples.Finally this paper illustrates the feasibility of this method by the detailed climatic statistical date of Tianjin's monthly total precipitation.