Wyniki wyszukiwania - BazEkon

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Liniowe kombinacje statystyk pozycyjnych - estymatory parametrów położenia i skali w uogólnionych rozkładach Pareto

100%

Śpiewak D.

Prace Naukowe Akademii Ekonomicznej we Wrocławiu. Ekonometria

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2003

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12

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nr 1002 Zastosowania metod ilościowych

65-83

W niniejszej pracy przedstawiono specyficzne techniki estymacji parametrycznej dla parametrów μ (parametr położenia) i σ (parametr skali) w uogólnionym rozkładzie Pareto. Zaprezentowane estymatory są prostymi kombinacjami liniowymi statystyk pozycyjnych. Zapewniają one "dobre" oszacowania interesujących nas parametrów zarówno w przypadku, kiedy parametr kształtu rozkładu ζ jest znany, jak i wtedy, gdy jest nieznany (fakt o dużym znaczeniu w zastosowaniach). Wielką zaletą tych estymatorów jest to, że wykazują dobre statystyczne własności przy niewielkiej liczbie obserwacji. W modelowaniu zdarzeń o małym prawdopodobieństwie wystąpienia (zdarzenia ekstremalne) dużą rolę odgrywają uogólnione rozkłady Pareto (GP), zapewniają niezbędne teoretyczne i praktyczne narzędzie do ich analizy. (fragment tekstu)

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Limit Property of a Compound of the Generalized Negative Binomial and Beta Distributions

100%

Gerstenkorn T.

Acta Universitatis Lodziensis. Folia Oeconomica

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2009

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225 Methodological Aspects and Applications of Multivariate Statistical Analysis

111-115

W czasopiśmie „Central European Journal of Mathematics (CEJM)", 2(4) 2004, 527-537 T. Gerstenkorn podał rozkład prawdopodobieństwa, który jest wynikiem złożenia uogólnionego ujemnego rozkładu dwumianowego z uogólnionym beta. Zakładając, że jeden z parametrów rozkładu (w) dąży do nieskończoności, otrzymuje się nowy rozkład graniczny, ciekawy także w przypadkach szczególnych. (abstrakt oryginalny)

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A New Generalization of the Pareto Distribution and its Applications

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Almetwally E. M., Haj Ahmad H. A.

Statistics in Transition

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2020

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21

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nr 5

61-84

This paper introduces a new generalization of the Pareto distribution using the Marshall-Olkin generator and the method of alpha power transformation. This new model has several desirable properties appropriate for modelling right skewed data. The Authors demonstrate how the hazard rate function and moments are obtained. Moreover, an estimation for the new model parameters is provided, through the application of the maximum likelihood and maximum product spacings methods, as well as the Bayesian estimation. Approximate confidence intervals are obtained by means of an asymptotic property of the maximum likelihood and maximum product spacings methods, while the Bayes credible intervals are found by using the Monte Carlo Markov Chain method under different loss functions. A simulation analysis is conducted to compare the estimation methods. Finally, the application of the proposed new distribution to three real-data examples is presented and its goodness-of-fit is demonstrated. In addition, comparisons to other models are made in order to prove the efficiency of the distribution in question. (original abstract)

4

Probabilistic Predictive Analysis of Business Cycle Fluctuations in Polish Economy

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Mazur B.

Equilibrium

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2017

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12

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nr 3

435-452

Research background: The probabilistic setup and focus on evaluation of uncertainties and risks has become more widespread in modern empirical macroeconomics, including the analysis of business cycle fluctuations. Therefore, forecast-based indicators of future economic conditions should be constructed using density forecasts rather than point forecasts, as the former provide description of forecast uncertainty.Purpose of the article: We discuss model-based probabilistic inference on business cycle fluctuations in Poland. In particular, we consider model comparison for probabilistic prediction of growth rates of the Polish industrial production. We also develop a class of indicators of future economic conditions constructed using probabilistic information on the rates (that make use of joint predictive distribution over several forecast horizons).Methods: We use Bayesian methods (in order to capture the estimation uncertainty) and consider two groups of models. The first group consists of Dynamic Conditional Score models with the generalized t conditional distribution (with conditional heteroscedasticity and heavy tails, being important for modelling of extreme observations). Another group of models relies on deterministic cycle modelling using Flexible Fourier Form. Ex-post density forecasting performance of the models is compared using the criteria for probabilistic prediction: Log-Predictive Score (LPS) and Continuous Ranked Probability Score (CRPS).Findings & Value added: The pre-2013 data support the deterministic cycle models whereas more recent observations can be explained by a simple mean-reverting Gaussian AR(4) process. The results indicate a structural change affecting Polish business cycle fluctuations after 2013. Hence, forecast pooling strategies are recommended as a tool for further research. We find rather limited support in favor of the first group of models. The probabilistic indicator of future economic conditions considered here leads actual phases of the growth cycle quite well, though the effect is less obvious after 2013. (original abstract)

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Comparison of the Tails of Market Return Distributions

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Koronkiewicz G., Jamróz P.

Optimum : studia ekonomiczne

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2014

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nr 5 (71)

103-113

The aim of this study is to analyze the tails of the distributions of stock market returns and to compare the differences between them. It is a well-established fact that the vast majority of stock market return distributions exhibit fat tails (a bigger probability of extreme outcomes then in the case of the normal probability). Apart from that, there seems to be a popular opinion that most market returns are negatively skewed with a fatter left tail. The study utilizes two methods for comparing the tails of a distribution. A simple approached based on the sample kurtosis, with a modification that allows for the calculation of kurtosis separately for the right and the left tail of a single distribution and a more complex approach based on the maximum likelihood fitting of the Generalized Pareto Distribution to both tales of standardized return distributions. The second approach is based on the assumptions of the Extreme Value Theory (EVT) and the Pickands-Balkema-de Haan theorem. Both approaches provide similar conclusions. Results suggest that whether the left or the right tail of the return distribution is bigger varies from market to market. All four major equity indices of the Polish Warsaw Stock Exchange exhibited a fatter left tale. However, in the whole sample it was actually more common for the right tail to be heavier, with 12 indices out of 20 exhibiting a fatter right tail then the left. The sample kurtosis indicated that all stock market return's distributions were heavy tailed, whereas the estimates of Generalized Pareto Distribution parameters did indicate standard or thin tails in two cases. Statistical tests indicate that the differences between the tails of stock market distributions are not statistically significant. (original abstract)

6

Count Copula Regression Model using Generalized Beta Distribution of the Second Kind

84%

Safari-Katesari H., Zaroudi S.

Statistics in Transition

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2020

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21

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nr 2

1-12

Modelling claims severity for obtaining insurance premium is one of the major concerns of the insurance industry. There is a considerable amount of literature on the actuarial application of the copula model to calculate the pure premium. In this paper, we model claims severity for computing the pure premium in the collision market by means of the count copula model. Moreover, we apply a regression model using a generalized beta distribution of the second kind (GB2) to compute the premium for an average claim and the conditional computation for all coverage levels. Like many other researchers, we assume that the number of accidents is independent from the size of claims. For real data application, we use a portfolio of a major automobile insurer in Iran in 2007-2008, with a subsample of 59,547 policies available in their portfolio. We then proceed to compare the estimated premiums with the real premiums. The results demonstrate that there is strong positive dependency between the real premium and the estimated one. (original abstract)