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    Tytuł:
    Two component modified Lilliefors test for normality
    Autorzy:
    Sulewski, Piotr
    Powiązania:
    https://bibliotekanauki.pl/articles/22444332.pdf
    Data publikacji:
    2021
    Wydawca:
    Instytut Badań Gospodarczych
    Tematy:
    Kolmogorov-Smirnov test
    Opis:
    Research background: Commonly known and used parametric tests e.g. Student, Behrens? Fisher, Snedecor, Bartlett, Cochran, Hartley tests are applicable when there is an evidence that samples come from the Normal general population. What makes things worse is that testers are not fully aware in what degree of abnormality distorts results of parametric tests listed above and suchlike. So, it is no exaggeration to say that testing for normality (goodness-of-fit testing, GoFT) is a gate to proper parametric statistical reasoning. It seems that the gate opens too easily. In other words, most popular goodness-of-fit tests are weaker than statisticians want them to be. Purpose of the article: The main purpose of this paper is to put forward the GoFT that is, in particular circumstances, more powerful than GoFTs used until now. The other goals are to define a similarity measure between an alternative distribution and the normal one and to calculate the power of normality tests for a big set of alternatives. And, of course, to interest statisticians in using the GoFTs in their practice. Method: There are two ways to make GoFT more powerful: extensive and intensive one. The extensive method consists in drawing large samples. The intensive method consists in extracting more information from mall samples. In order to make the test method intensive, the test statistics, as distinct from all existing GoFTs, has two components. The first component (denoted by ?) is a classic Kolmogorov / Lilliefors test statistics i.e. the greatest absolute difference between theoretical and empirical cumulative distribution functions. The second component is the order statistics (r) at which the ?_max^((r) ) locate itself. Of course ?_max^((r) ) is the conditional random variable with (r) being the condition. Large scale Monte Carlo simulations provided data sufficient to in-depth study of properties of distributions of ?_max^((r) ) random variable. Findings & value-added: Simulation study shows that the Two Component Modified Lilliefors test for normality is the most powerful for some type of alternatives, especially for the symmetrical, unimodal and bimodal distributions with positive excess kurtosis, for symmetrical and unimodal distributions with negative excess kurtosis and small sample sizes. Due to the values of skewness and excess kurtosis, and the defined similarity measure between the ND and an alternative, alternative distributions are close to the normal distribution. Numerous examples of real data show the usefulness of the proposed GoFT.
    Źródło:
    Equilibrium. Quarterly Journal of Economics and Economic Policy; 2021, 16, 2; 429-455
    1689-765X
    2353-3293
    Pojawia się w:
    Equilibrium. Quarterly Journal of Economics and Economic Policy
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Simulation study of two-sample Kolmogorov-Smirnov test in randomly censored data
    Test zgodności Kotmogorowa-Smirnowa dla danych losowo cenzurowanych - analiza symulacyjna
    Autorzy:
    Rossa, Agnieszka
    Powiązania:
    https://bibliotekanauki.pl/articles/905373.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
    Tematy:
    censored data
    Kolmogorov-Smirnov test
    Monte Carlo simulations
    Opis:
    W artykule przedstawione są trzy wersje testu zgodności Kołmogorowa-Smimowa dla danych prawostronnie cenzurowanych. Poszczególne testy różnią się sposobem podejścia do obserwacji cenzurowanych. Moc testów została zbadana i porównana za pomocą symulacji Monte Carlo.
    The paper deals with a problem of testing the non-parametric hypothesis that two populations are equally distributed in the situation when the observations are subject to random censoring. A general metric for measuring the distance between two distributions is the Kolmogorov metric and the corresponding test is the Two-Sample Kolmogorov-Smirnov test. In the report below we present results of a simulation study performed for three versions of the Two-Sample Kolmogorov-Smirnov test for censored data. These three versions are generated by three methods of treating censored observations. Basic statistical properties of these tests are inspected by means of Monte Carlo simulations.
    Źródło:
    Acta Universitatis Lodziensis. Folia Oeconomica; 2002, 156
    0208-6018
    2353-7663
    Pojawia się w:
    Acta Universitatis Lodziensis. Folia Oeconomica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Podobieństwo województw w Polsce pod względem rozkładu wydatków ich mieszkańców
    Similarity of voivodeships in Poland in terms of their residents’ distribution of expenditures
    Autorzy:
    Turczak, Anna
    Zwiech, Patrycja
    Powiązania:
    https://bibliotekanauki.pl/articles/570136.pdf
    Data publikacji:
    2015
    Wydawca:
    Wydawnictwo Uniwersytetu Ekonomicznego we Wrocławiu
    Tematy:
    distribution of expenditures
    total expenditures per capita
    Kolmogorov-Smirnov test
    households
    taxonomy
    Opis:
    The purpose of the paper was to determine the degree of similarity between the distribution of total monthly expenditures per capita in the individual voivodeships and to single out voivodeships most similar in that respect. All calculations were carried out based on non-identifiable individual data from the household budget survey by the Central Statistical Office. What is really important is the fact that surveying budgets by the CSO is conducted using the representative method, which allows for the generalization of the obtained results over all households in Poland. The paper included 37,427 analyzed households which were grouped into sixteen statistical populations with respect to the voivodeships. Two research tasks were implemented. The first concerned verification whether the distribution of spending per capita in individual voivodeships was the same. In order to complete this task relevant statistical hypotheses were set and verified using the Kolmogorov-Smirnov test. The verification procedure was performed for each pair of voivodeships, i.e. one hundred and twenty times.The significance level of 0.01 was adopted, and therefore the risk of rejection of a true hypothesis was only 1 in 100 cases. The finalization of the first task has allowed the conclusion that the observed differences between the distributions of total monthly spending per capita in individual voivodeships of Poland are statistically significant, and thus the variable which is the subject of research has a different distribution in each of the voivodeships. The second research task was to divide the voivodeships into groups of most similar distributions. In order to accomplish this task the Wrocław taxonomy was employed. As a measure of the degree of similarity of distributions λ (lambda) statistic was used, which is based on the maximum absolute value of the difference between two empirical cumulative distribution functions. On the basis of the value of the λ statistic calculated for each of the pairs of distributions the sixteen voivodeships were divided into three uniform classes. This division resulted in the creation of a single-element group, one eight-element group and one seven-element group. The single-element group comprised the Mazovian voivodeship, the eight-element group included the Lower Silesian, Silesian, Pomeranian, Opole, Łódź, West Pomeranian, Lesser Poland and Lubuskie voivodeships, and the seven-element group comprised the Kujawsko-Pomorskie, Podlaskie, Lublin, Greater Poland, Świętokrzyskie, Warmia-Mazury and Podkarpackie voivodeships. In 2012, the average monthly spending in the individual voivodeships amounted to: in the Mazovian voiv. PLN 1,330 per person, in the Lower Silesian PLN 1,139 per person, in the Silesian voiv. PLN 1,123 per person, in the Pomeranian voiv. PLN 1,081 per person, in the Opole voiv. PLN 1,079 per person, in the Łódź voiv. PLN 1,075 per person, in the West Pomeranian voiv. PLN 1,057 per person, in the Lesser Poland voiv. PLN 998 per person, in the Lubuskie voiv. PLN 996 per person, in the Kujawsko-Pomorskie voiv. PLN 947 per person, in the Podlaskie voiv. PLN 939 per person, in the Lublin voiv. PLN 938 per person, in the Greater Poland voiv. PLN 931 per person, in the Świętokrzyskie voiv. PLN 884 per person, in the Warmia-Mazury voiv. PLN 865 per person and in the Podkarpackie voiv. PLN 848 per person. In turn, the average difference in monthly spending of residents of the Mazovian voivodeship in 2012 amounted to PLN 1,171 per person, the Lower Silesian voiv. PLN 854 per person, the Silesian voiv. PLN 783 per person, the Pomeranian voiv. PLN 843 per person, the Opole voiv. PLN 606 per person, the Łódź voiv. PLN 755 per person, the West Pomeranian voiv. PLN 731 per person, the Lesser Poland voiv. PLN 649 per person, the Lubuskie voiv. PLN 581 per person, the Kujawsko-Pomorskie voiv. PLN 635 per person, the Podlaskie voiv. PLN 712 per person, the Lublin voiv. PLN 793 per person, the Greater Poland voiv. PLN 675 per person, the Świętokrzyskie voiv. PLN 578 per person, the Warmia-Mazury voiv. PLN 700 per person, the Podkarpackie voiv. PLN 478 per person.
    Źródło:
    Ekonomia XXI Wieku; 2015, 3 (7); 100-112
    2353-8929
    Pojawia się w:
    Ekonomia XXI Wieku
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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