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Logistic regression models can be applied for analysis of Bernoulli variables in studies of small areas. In the paper the logistic regression predictors for parameter of the Bernoulli distribution and an estimation of variance and MSE for these predictors arc considered for small areas. The results of simulation experiments conducted for analysis of properties of estimators of variance and mean square...
Rankings of income distributions are usually based on comparisons of social welfare. Assuming more or less general form of a social welfare function we can compare income distributions in time and in space. Income inequality can be compared by means of the well known Lorenz curve but the results will be ambiguous when the Lorenz functions of the considered populations intersect. Generalized Lorenz...
Artificial neural networks constitute one of the most developed conception of artificial intelligence. They are based on pragmatic mathematical theories adopted to tasks resolution. A wide range of their applications also includes financial investments issues. The reason for NN's popularity is mainly connected with their ability to solve complex or not well recognized computational tasks, efficiency...
Correct insurance premiums estimation constitutes the basis for the insurance activity. Premiums should be estimated in a way that does not let the insurance company incur financial losses and prevents the insured from paying too much or too little. A gross premium consists of a net premium enlarged by security loading and insurance activity costs. The paper compares two premium estimation methods:...
The assumption of multivariate normality is a basis of the classical multivariate statistical methodology. Consequences of departures from these assumptions have not been investigated well so far. There are many methods of constructing multivariate normality tests. Some of these tests ire broader versions of univariate normality tests. Most of the multivariate normality tests which can be found in...
In this paper we present some problems concerning artificial intelligence.
In the first two points there are presented algorithmic and heuristic procedures, which
are applied in solving problems and making optimal decision for the fixed states as
follows: beginning state, set of all states of a problem, subset of final states.
The fundamental part of the paper discusses three leaming-algorithms:...
The paper deals with the tests for paired variables called also tests for pairs of
variables. The observations are made of pairs of measurements. They can be correlated. It
causes the necessity of applying another significance test of differences for example between
means than in case of independent samples. We compare the power of nonparametric tests:
sign test, Munzel and Wilcoxon tests with...
In the paper some nonparametric estimators of regression function are studied:
Nadaraya-Watson estimator and k-nearest neighbour one. Properties of these estimators
and possibilities of using them in practice are taken into consideration. A comparative
study of the two estimators is presented. Different techniques of choosing method’s
parameters (kernel function, smoothing parameter h and parameter...
There are many methods of construction of multivariate normality
tests. The current review of the literature proves that there are at least 60 procedures of
verification of the hypothesis about multivariate normality of variable and random distributions.
We can indicate a few factors which prove an analysis of this class’s tests
ascd on skewness and kurtosis measures. It is easy to notice that...
The paper aims at reminding the classic risk measures and presenting
the RiskGrade measure (1994). This statistic allows comparisons between the investment
risk of different financial assets and also the risk of financial investments across different
regions of the World. Some advantages and disadvantages of this measure of volatility
and also technical problems of using will be described.
After...
We presented some properties of new procedures of multiple hypotheses testing for
discrete distributions. We choose the new procedure stepwise TWWk, based on Tarone, Westfall
and Welfinger ideas. We compare this procedure to multiple testing procedures like T*, TH* and
others and we show the power advantage of this procedure.
The comparing distributions of two discrete random variables appears often
in statistical research. In many cases we can apply the test for two means for it. If the
means are equal and we do not know the set of values of investigated variables, it is
possible to use the properties of sample proportions for testing the identity of two distributions.
In this paper testing the identity of distributions...
This paper presents some important earlier results of the research concerning the properties of the distribution of the quotient of random variables.
We present also our own ideas and results of the research concerning the mean and the variance of the distribution of the quotient of random quadratic forms.
Studies in the field of wage and income distribution concentrate on measuring income inequality.
We can investigate both the inequality within the population and the inequality
between the populations. The latter can be called the economic distance of one population with respect to another. In the paper we present economic distance ratios.
Do and D1 introduced by Dagum. They were calculated for...
The paper discusses the method of determining the sample division
indicator for the switching regression model in case of two states generating values of
the explained variable, which ensures the least risk of making a mistake, understood
as the expected value of relevant loss function. This paper is an attempt to take
advantage of the discrimination analysis elements in the switching regression...
The paper presents methods of small area statistics which can be applied
to investigate the phenomenon of unemployment in given subpopulations depending on
sampling and additional information about population. Some methods selected from this
group are shown on the example of analysis of unemployment among men, women and
all inhabitants in the Łódź Macroprovince. The analysis is conducted on the...
Sequential probability ratio tests can be used to verify hypotheses about truncated
distribution parameters when error probabilities of the first and the second type are set. For
parameters of normal and exponential distributions truncated on both sides and on the left
side, statistics of sequential probability ratio test were determined. Since the sample size in
these tests is the random variable,...
Kernel density estimation is one of the main methods available for univariate
density estimation. The problems of choosing the kernel function and choosing the smoothing
parametr are of crucial importance in density estimation. Various methods, used in practice,
for choosing smoothing parametr are discussed. Some of them are simple, some complicated
in calculations, but it must be emphasized that...
The Net Present Value (NPV) rule is a base of modern finance theory. The classical definition of NPV is based on unrealistic assumptions: it treats the discount rate as a deterministic and constant function. The above fact may lead to some situations when the classical NPV may mark the wrong direction of investing. Moreover, the deterministic formula makes the measurement of risk impossible - we can...
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