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Statistical analysis of ROC curves
Kutálek, David ; Bednář, Josef (referee) ; Michálek, Jaroslav (advisor)
The ROC (Receiver Operating Characteristic) curve is a projection of two different cumulative distribution functions F0 and F1. On axis are values 1-F0(c) and 1-F1(c). The c-parameter is a real number. This curve is useful to check quality of discriminant rule which classify an object to one of two classes. The criterion is a size of an area under the curve. To solve real problems we use point and interval estimation of ROC curves and statistical hypothesis tests about ROC curves.
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Bivariate Poisson distribution
Smolárová, Tereza ; Hudecová, Šárka (advisor) ; Hlubinka, Daniel (referee)
In the present thesis we deal with the bivariate Poisson distribution. A trivariate reduction method is used to define the bivariate Poisson dis- tribution. The theoretical characteristics of distribution, which this thesis deals with are the marginal distributions, covariance, a correlation coeffi- cient and the conditional distributions. A method of moments and a method of maximum likelihood are used to construct the point estimations of the parameters. Further, we focus on testing the goodness of fit by the index of dispersion test. A transforms of the sample correlation test is used to test the independence. Both methods for estimating the parameters and the statistic tests are applied to real data from the insurance field. 1
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Optimality of sample variance
Gleta, Filip ; Kulich, Michal (advisor) ; Anděl, Jiří (referee)
It is widely known that the most common estimators of the variance and the standard deviation based on i.i.d. data are not optimal with respect to the mean squared error. The aim of this thesis is to study and summarize the various approaches to seeking an improved estimator, which stem mainly from the innovative ideas presented by Stein (1964). Taken into consideration is the point estimator of the variance and the standard deviation. Each of the improved estimators include, in addition to their construction, a discussion regarding admissibility with respect to the MSE. Subsequently, using simple simulations for various distributions, it is examined whether obtained improvements lead to better results in practice. Powered by TCPDF (www.tcpdf.org)
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Bivariate Poisson distribution
Smolárová, Tereza ; Hudecová, Šárka (advisor) ; Hlubinka, Daniel (referee)
In the present thesis we deal with the bivariate Poisson distribution. A trivariate reduction method is used to define the bivariate Poisson dis- tribution. The theoretical characteristics of distribution, which this thesis deals with are the marginal distributions, covariance, a correlation coeffi- cient and the conditional distributions. A method of moments and a method of maximum likelihood are used to construct the point estimations of the parameters. Further, we focus on testing the goodness of fit by the index of dispersion test. A transforms of the sample correlation test is used to test the independence. Both methods for estimating the parameters and the statistic tests are applied to real data from the insurance field. 1
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Statistical analysis of ROC curves
Kutálek, David ; Bednář, Josef (referee) ; Michálek, Jaroslav (advisor)
The ROC (Receiver Operating Characteristic) curve is a projection of two different cumulative distribution functions F0 and F1. On axis are values 1-F0(c) and 1-F1(c). The c-parameter is a real number. This curve is useful to check quality of discriminant rule which classify an object to one of two classes. The criterion is a size of an area under the curve. To solve real problems we use point and interval estimation of ROC curves and statistical hypothesis tests about ROC curves.
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Estimated probability of unrepeatable events
Novák, Vít ; Hebák, Petr (advisor) ; Černý, Michal (referee)
Anywhere we see a prognostication system; we can run up against the need of evaluating it. For the evaluation is frequently used unsuitable methods. There are such cases where is need to correctly take effects of mistakes into consideration. And here we can use statistic based on information measure either entropy. The first part deals with this point of issue. In the second part I am trying to show possible areas of use, for example betting. I enclose practical remarks from this issue and the methods making these estimators, which are dependent on nature of issued events.
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