http://hdl.handle.net/11089/6233 SELECTED PROBLEMS OF MULTIVARIATE STATISTICAL ANALYSIS 2026-04-06T21:33:28Z http://hdl.handle.net/11089/6264 Limit laws for multivalued random variables Trzpiot, Grażyna In the probability theory, the strong law of large numbers and the central limit theorem are the most important convergence theorems. 1997-01-01T00:00:00Z http://hdl.handle.net/11089/6263 A Monte Carlo investigation of two distance measures between statistical populations and their application to cluster analysis Rossa, Agnieszka The paper deals with a simulation study of one of the well-known hierarchical cluster analysis methods applied to classifying the statistical populations. In particular, the problem of clustering the univariate normal populations is studied. Two measures of the distance between statistical populations are considered: the Mahalanobis distance measure which is defined for normally distributed populations under assumption that the covariance matrices are equal and the Kullback-Leibler divergence (the so called Generalized Mahalanobis Distance) the use of which is extended on populations of any distribution. The simulation study is concerned with the set of 15 univariate normal populations, variances of which are chanched during successive steps. The aim is to study robustness of the nearest neighbour method to departure from the variance equality assumption when the Mahalanobis distance formula is applied. The differences between two cluster families, obtained for the same set of populations but with the different distance matrices applied, are studied. The distance between both final cluster sets is measured by means of the Marczewski-Steinhaus distance. 1997-01-01T00:00:00Z http://hdl.handle.net/11089/6262 Decomposition of time series on the basis of modified grouping method of Ward Wywiał, Janusz The trend of time series can change its direction. It is assumed that the time interval is divided into subintervals where the trend is given as particular linear function. The problem is how to divide the observation of time series into disjoint and coherent groups where they have linear trend. That is why the problem of the scatter of multivariable observation was first considered. The degree of data spread is measured by means of a coefficient called a discriminant of multivariable observation. It is equal to the sum of volumes of the parallelotops spanned on multidimensional observations. On the basis of it the modifications of the well known generalized variance were introduced. Geometrical properties of those parameters were investigated. The obtained results are used to generalize well-known clustering methods of Ward. One of the advantages of the method is that it finds clusters of high linear dependent multivariate observations. Finally, the results are used to partition a time series into homogeneous groups where observations are close to linear trend. There is considered an example. 1997-01-01T00:00:00Z http://hdl.handle.net/11089/6261 Application of the sequential probability ratio test to verification of statistical hypotheses Pekasiewicz, Dorota The paper deals with some problems concerning the sequential probability ratio tests (SPRT) and their application to verifying simple and composite statistical hypotheses. Besides properties and examples of SPRT, there are presented advantages o f this group of tests and reasons why we cannot always apply them in practice. 1997-01-01T00:00:00Z