National Repository of Grey Literature 5 records found Search took 0.01 seconds.
 Parameter estimation of gamma distribution Zahrádková, Petra ; Kulich, Michal (advisor) ; Hlávka, Zdeněk (referee) It is well-known that maximum likelihood (ML) estimators of the two parame- ters in a Gamma distribution do not have closed forms. The Gamma distribution is a special case of a generalized Gamma distribution. Two of the three likeli- hood equations of the generalized Gamma distribution can be used as estimating equations for the Gamma distribution, based on which simple closed-form estima- tors for the two Gamma parameters are available. Intuitively, performance of the new estimators based on likelihood equations should be close to the ML estima- tors. The study consolidates this conjecture by establishing the asymptotic beha- viours of the new estimators. In addition, the closed-forms enable bias-corrections to these estimators. 1 Detailed record GOF tests for gamma distribution Klička, Petr ; Hlávka, Zdeněk (advisor) ; Kulich, Michal (referee) The Bachelor thesis deals with the goodness of fit test for the Gamma distribution. Initially, we show several ways how to estimate the parameters of the Gamma distribution - firstly, the maximum likelihood estimator is presented, followed by estimator gained by the method of moments and fi- nally, we introduce the new estimator based on the sample covariance. The last estimator is used for constructing the goodness of fit test for the Gamma distribution. We define the test statistics V ∗ n to this test and its asymptotic normality is derived under the assumption of the null hypothesis. At the end of the thesis the simulations are realized to obtain the empirical size of the test for various values of parameter a and parameter b which equals one. 1 Detailed record Sums of exponential random variables Michl, Marek ; Seidler, Jan (advisor) ; Maslowski, Bohdan (referee) Sums of exponential random variables are often found in applied mathematics. Their densities are known and are well documented in engineering articles. However, these articles usually lack detailed deductions. The purpose of this thesis is to give rigorous deductions of explicit formulas for densities of sums of independent exponential random variables, which are known. The thesis covers several cases depending on whether the variables have the same distribution or not. Furthermore, the thesis gives a summary of basic characteristics of exponential distribution and the relation between sums of identically distributed exponential random variables and a random variable with gamma distribution. Based on this relation the density of the sum of gamma random variables with the same intestity is given. Powered by TCPDF (www.tcpdf.org) Detailed record High-order stochastic dominance Mikulka, Jakub ; Kopa, Miloš (advisor) ; Branda, Martin (referee) The thesis deals with high-order stochastic dominance of random variables and portfolios. The summary of findings about high-order stochastic dominance and portfolio efficiency is presented. As a main part of the thesis it is proven that under assumption of both normal and gamma distribution the infinite-order stochastic dominance is equivalent to the second-order stochastic dominance. The necessary and sufficient condition for the infinite-order stochastic dominance portfolio efficiency is derived under the assumption of normality. The condition is used in the empirical part of the thesis where parametrical approach to the portfolio efficiency is compared to the nonparametric scenario approach. The derived necessary and sufficient condition is based on the assumption of normality; therefore we use two sets of data, one with fulfilled assumption of normality and the other for which the assumption of normality was unambigously rejected. Consequently, the influence of fulfillment of the normality assumption on the results of the necessary and sufficient condition for portfolio efficiency is estimated. Detailed record Statistical transformation of the precipitation data from regional climatic model to particular conditions of the Malse river basin Hnilica, Jan ; Šípek, Václav Paper describes procedure of statistical adaptation of the raw large-scale climate model data based on transformation between cumulative distribution functions of the model and real datasets. We developed two alternative ways and we validated those using data from Malse river basin. Detailed record

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