Acta Universitatis Lodziensis. Folia Oeconomica nr 141/1997SELECTED PROBLEMS OF MULTIVARIATE STATISTICAL ANALYSIShttp://hdl.handle.net/11089/62332021-06-17T17:44:59Z2021-06-17T17:44:59ZLimit laws for multivalued random variablesTrzpiot, Grażynahttp://hdl.handle.net/11089/62642018-02-01T11:17:58Z1997-01-01T00:00:00ZLimit 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.
1997-01-01T00:00:00ZA Monte Carlo investigation of two distance measures between statistical populations and their application to cluster analysisRossa, Agnieszkahttp://hdl.handle.net/11089/62632018-02-01T11:17:56Z1997-01-01T00:00:00ZA 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.
1997-01-01T00:00:00ZDecomposition of time series on the basis of modified grouping method of WardWywiał, Januszhttp://hdl.handle.net/11089/62622018-02-01T11:17:58Z1997-01-01T00:00:00ZDecomposition 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.
1997-01-01T00:00:00ZApplication of the sequential probability ratio test to verification of statistical hypothesesPekasiewicz, Dorotahttp://hdl.handle.net/11089/62612018-02-01T11:17:53Z1997-01-01T00:00:00ZApplication 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