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Abstract Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate this … Abstract Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate this parameter. Several recent publications’ aim was to improve the Hill estimator, using different methods, for example the bootstrap, or the Kolmogorov–Smirnov metric. These methods are asymptotically consistent, but for tail index $$\xi &gt;0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ξ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math> the estimations fail to approach the theoretical value for realistic sample sizes. In this paper, we introduce new empirical methods, which combine the advantages of the Kolmogorov–Smirnov approach and the bootstrap. We demonstrate that our estimators are able to estimate large tail index parameters well and might also be useful for relatively small sample sizes. As an application, we consider the classic Danish fire data set and the most destructive natural disasters in Europe.
Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail … Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was aimed by recent works with different methods, for example by using bootstrap, or Kolmogorov-Smirnov metric. These methods are asymptotically consistent, but for tail index $\xi >1$ and smaller sample sizes the estimation fails to approach the theoretical value for realistic sample sizes. In this paper, we introduce a new empirical method, which can estimate high tail index parameters well and might also be useful for relatively small sample sizes.
In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For … In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index in British Columbian forests might be modelled by GEV distribution, but the stationarity of the time series is questionable. This property can lead us to different approaches to test if there is a significant trend in past few years data or not. An approach is a likelihood ratio based procedure which has favourable asymptotic properties, but for realistic sample sizes it might have a large error. In this paper we analyse the properties of the likelihood ratio test for extremes by bootstrap simulations and aim to determine a minimal required sample size. With the theoretical results we re-asses the trends of fire weather index in British Columbian forests.
Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail … Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was aimed by recent works with different methods, for example by using bootstrap, or Kolmogorov-Smirnov metric. These methods are asymptotically consistent, but for tail index $ξ&gt;1$ and smaller sample sizes the estimation fails to approach the theoretical value for realistic sample sizes. In this paper, we introduce a new empirical method, which can estimate high tail index parameters well and might also be useful for relatively small sample sizes.
In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools. In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools.
Introduction and objectives Medical costs of patients with chronic obstructive pulmonary disease (COPD) are high, however data from Eastern European countries are scarce. We aimed to study healthcare payments for … Introduction and objectives Medical costs of patients with chronic obstructive pulmonary disease (COPD) are high, however data from Eastern European countries are scarce. We aimed to study healthcare payments for patients with COPD on maintenance inhaled therapy in Hungary and analyse the trends and influencing factors between 2011 and 2019 in a retrospective financial database analysis. Patients We collected data of patients from the Hungarian National Insurance Fund, who were &gt; 40 years old, received maintenance inhaled therapy &gt; 90 days within 12 months prescribed for J41-44 International Classification of Diseases-10 codes. All-cause and COPD-specific healthcare costs were compared between 2011 and 2019. We used a generalized mixed regression model to analyse the effects of calendar years, age, sex, Charlson comorbidity index, status of incidence, annual duration of inhaled therapy, the number of COPD-related hospitalization and geographical regions. Results We analysed the data of 227 254 patients. In 2019, cumulative all-cause and COPD-specific spendings reached 401.15 million and 118.14 million USD, respectively. Annual total and COPD-related costs per patient in 2011 vs. 2019 were 2707 ± 3598 vs. 3332 ± 4463 USD and 927 ± 1162 vs. 981 ± 1534 USD, respectively (mean ± standard deviation). The increase in all-cause costs was above, while the rise in COPD-related costs was below the Hungarian inflation rate. The costs of medication and inpatient care comprised of the highest payment segments. The number of COPD-related hospitalizations had the most significant effect on the expenditures, while comorbidity burden and spendings on inhaled maintenance therapy were related to all-cause and COPD-specific costs, respectively. Increasing age was associated to higher spendings, but women had lower costs. Conclusions The costs of inpatient care and medication are responsible for the largest segments of healthcare spendings for patients with COPD. Prevention of hospitalizations due to COPD and the close follow-up of comorbidities can help reduce medical costs.
Introduction and objectives Medical costs of patients with chronic obstructive pulmonary disease (COPD) are high, however data from Eastern European countries are scarce. We aimed to study healthcare payments for … Introduction and objectives Medical costs of patients with chronic obstructive pulmonary disease (COPD) are high, however data from Eastern European countries are scarce. We aimed to study healthcare payments for patients with COPD on maintenance inhaled therapy in Hungary and analyse the trends and influencing factors between 2011 and 2019 in a retrospective financial database analysis. Patients We collected data of patients from the Hungarian National Insurance Fund, who were &gt; 40 years old, received maintenance inhaled therapy &gt; 90 days within 12 months prescribed for J41-44 International Classification of Diseases-10 codes. All-cause and COPD-specific healthcare costs were compared between 2011 and 2019. We used a generalized mixed regression model to analyse the effects of calendar years, age, sex, Charlson comorbidity index, status of incidence, annual duration of inhaled therapy, the number of COPD-related hospitalization and geographical regions. Results We analysed the data of 227 254 patients. In 2019, cumulative all-cause and COPD-specific spendings reached 401.15 million and 118.14 million USD, respectively. Annual total and COPD-related costs per patient in 2011 vs. 2019 were 2707 ± 3598 vs. 3332 ± 4463 USD and 927 ± 1162 vs. 981 ± 1534 USD, respectively (mean ± standard deviation). The increase in all-cause costs was above, while the rise in COPD-related costs was below the Hungarian inflation rate. The costs of medication and inpatient care comprised of the highest payment segments. The number of COPD-related hospitalizations had the most significant effect on the expenditures, while comorbidity burden and spendings on inhaled maintenance therapy were related to all-cause and COPD-specific costs, respectively. Increasing age was associated to higher spendings, but women had lower costs. Conclusions The costs of inpatient care and medication are responsible for the largest segments of healthcare spendings for patients with COPD. Prevention of hospitalizations due to COPD and the close follow-up of comorbidities can help reduce medical costs.
In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools. In this paper, we generalise an interesting geometry problem from the 1995 edition of the International Mathematical Olympiad (IMO) using analytic geometry tools.
Abstract Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate this … Abstract Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate this parameter. Several recent publications’ aim was to improve the Hill estimator, using different methods, for example the bootstrap, or the Kolmogorov–Smirnov metric. These methods are asymptotically consistent, but for tail index $$\xi &gt;0.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ξ</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>0.5</mml:mn></mml:mrow></mml:math> the estimations fail to approach the theoretical value for realistic sample sizes. In this paper, we introduce new empirical methods, which combine the advantages of the Kolmogorov–Smirnov approach and the bootstrap. We demonstrate that our estimators are able to estimate large tail index parameters well and might also be useful for relatively small sample sizes. As an application, we consider the classic Danish fire data set and the most destructive natural disasters in Europe.
In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For … In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index in British Columbian forests might be modelled by GEV distribution, but the stationarity of the time series is questionable. This property can lead us to different approaches to test if there is a significant trend in past few years data or not. An approach is a likelihood ratio based procedure which has favourable asymptotic properties, but for realistic sample sizes it might have a large error. In this paper we analyse the properties of the likelihood ratio test for extremes by bootstrap simulations and aim to determine a minimal required sample size. With the theoretical results we re-asses the trends of fire weather index in British Columbian forests.
Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail … Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was aimed by recent works with different methods, for example by using bootstrap, or Kolmogorov-Smirnov metric. These methods are asymptotically consistent, but for tail index $\xi >1$ and smaller sample sizes the estimation fails to approach the theoretical value for realistic sample sizes. In this paper, we introduce a new empirical method, which can estimate high tail index parameters well and might also be useful for relatively small sample sizes.
Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail … Estimating the tail index parameter is one of the primal objectives in extreme value theory. For heavy-tailed distributions the Hill estimator is the most popular way to estimate the tail index parameter. Improving the Hill estimator was aimed by recent works with different methods, for example by using bootstrap, or Kolmogorov-Smirnov metric. These methods are asymptotically consistent, but for tail index $ξ&gt;1$ and smaller sample sizes the estimation fails to approach the theoretical value for realistic sample sizes. In this paper, we introduce a new empirical method, which can estimate high tail index parameters well and might also be useful for relatively small sample sizes.