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A weighted version of Gamma distribution

100%
Jain K., Singla N., Gupta R.
Discussiones Mathematicae Probability and Statistics
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2014
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tom 34
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nr 1-2
89-111
EN
Weighted Gamma (WG), a weighted version of Gamma distribution, is introduced. The hazard function is increasing or upside-down bathtub depending upon the values of the parameters. This distribution can be obtained as a hidden upper truncation model. The expressions for the moment generating function and the moments are given. The non-linear equations for finding maximum likelihood estimators (MLEs) of parameters are provided and MLEs have been computed through simulations and also for a real data set. It is observed that WG fits better than its submodels (WE), Generalized Exponential (GE), Weibull and Exponential distributions.
2
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Robust m-estimator of parameters in variance components model

100%
Zmyślony R., Zontek S.
Discussiones Mathematicae Probability and Statistics
|
2002
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tom 22
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nr 1-2
61-71
EN
It is shown that a method of robust estimation in a two way crossed classification mixed model, recently proposed by Bednarski and Zontek (1996), can be extended to a more general case of variance components model with commutative a covariance matrices.
3
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Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data

100%
Karbauskaitė R., Dzemyda G.
International Journal of Applied Mathematics and Computer Science
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2015
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tom 25
|
nr 4
895-913
EN
One of the problems in the analysis of the set of images of a moving object is to evaluate the degree of freedom of motion and the angle of rotation. Here the intrinsic dimensionality of multidimensional data, characterizing the set of images, can be used. Usually, the image may be represented by a high-dimensional point whose dimensionality depends on the number of pixels in the image. The knowledge of the intrinsic dimensionality of a data set is very useful information in exploratory data analysis, because it is possible to reduce the dimensionality of the data without losing much information. In this paper, the maximum likelihood estimator (MLE) of the intrinsic dimensionality is explored experimentally. In contrast to the previous works, the radius of a hypersphere, which covers neighbours of the analysed points, is fixed instead of the number of the nearest neighbours in the MLE. A way of choosing the radius in this method is proposed. We explore which metric-Euclidean or geodesic-must be evaluated in the MLE algorithm in order to get the true estimate of the intrinsic dimensionality. The MLE method is examined using a number of artificial and real (images) data sets.
4
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On optimality of the orthogonal block design

86%
Synówka-Bejenka E., Zontek S.
Discussiones Mathematicae Probability and Statistics
|
2012
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tom 32
|
nr 1-2
59-68
EN
In the paper a usual block design with treatment effects fixed and block effects random is considered. To compare experimental design the asymptotic covariance matrix of a robust estimator proposed by Bednarski and Zontek (1996) for simultaneous estimation of shift and scale parameters is used. Asymptotically A- and D- optimal block designs in the class of designs with bounded block sizes are characterized.
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