• Communications for Statistical Applications and Methods
• /
• v.23 no.2
• /
• pp.119-129
• /
• 2016

A new sampling method is introduced based on the idea of a ranked set sampling scheme in which taken samples in each set are dependent on previous ones. Some theoretical results are presented and distribution-free confidence intervals are derived for the quantiles of any continuous population. It is shown numerically that the proposed sampling scheme may lead to 95% confidence intervals (especially for extreme quantiles) that cannot be found based on the ordinary ranked set sampling scheme presented by Chen (2000) and Balakrishnan and Li (2006). Optimality aspects of this scheme are investigated for both coverage probability and minimum expected length criteria. A real data set is also used to illustrate the proposed procedure. Conclusions are eventually stated.

• Communications for Statistical Applications and Methods
• /
• v.30 no.6
• /
• pp.531-550
• /
• 2023

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.

• The Korean Journal of Applied Statistics
• /
• v.25 no.1
• /
• pp.101-114
• /
• 2012

In car insurance, the loss ratio is the ratio of total losses paid out in claims divided by the total earned premiums. In order to minimize the loss to the insurance company, estimating extreme quantiles of loss ratio distribution is necessary because the loss ratio has essential prot and loss information. Like other types of insurance related datasets, the distribution of the loss ratio has heavy-tailed distribution. The Peaks over Threshold(POT) and the Hill estimator are commonly used to estimate extreme quantiles for heavy-tailed distribution. This article compares and analyzes the performances of various kinds of parameter estimating methods by using a simulation and the real loss ratio of car insurance data. In addition, we estimate extreme quantiles using the Hill estimator. As a result, the simulation and the loss ratio data applications demonstrate that the POT method estimates quantiles more accurately than the Hill estimation method in most cases. Moreover, MLE, Zhang, NLS-2 methods show the best performances among the methods of the GPD parameters estimation.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2017.05a
• /
• pp.228-232
• /
• 2017

Extreme hydrological events can cause serious threats to the society. Hence, the selection of probability distributions for extreme rainfall is a fundamental issue. For this reason, this study was focused on understanding possible distributional changes in annual daily maximum rainfalls (AMRs) over time in Sri Lanka using quantile regression. A simplified nine-category distributional-change scheme based on comparing empirical probability density function of two years (i.e. the first year and the last year), was used to determine the distributional changes in AMRs. Daily rainfall series of 13 station over Sri Lanka were analyzed for the period of 1960-2015. 4 distributional change categories were identified for the AMRs. 5 stations showed an upward trend in all the quantiles (i.e. 9 quantiles: from 0.05 to 0.95 with an increment of 0.01 for the AMR) which could give high probability of extreme rainfall. On the other hand, 8 stations showed a downward trend in all the quantiles which could lead to high probability of the low rainfall. Further, we identified a considerable spatial diversity in distributional changes of AMRs over Sri Lanka.

• Wind and Structures
• /
• v.34 no.6
• /
• pp.469-482
• /
• 2022

The generalized extreme value distribution (GEVD) is frequently used to fit the block maximum of environmental parameters such as the annual maximum wind speed. There are several methods for estimating the parameters of the GEV distribution, including the least-squares method (LSM). However, the application of the LSM with the expected order statistics has not been reported. This study fills this gap by proposing a fitting method based on the expected order statistics. The study also proposes a plotting position to approximate the expected order statistics; the proposed plotting position depends on the distribution shape parameter. The use of this approximation for distribution fitting is carried out. Simulation analysis results indicate that the developed fitting procedure based on the expected order statistics or its approximation for GEVD is effective for estimating the distribution parameters and quantiles. The values of the probability plotting correlation coefficient that may be used to test the distributional hypothesis are calculated and presented. The developed fitting method is applied to extreme thunderstorm and non-thunderstorm winds for several major cities in Canada. Also, the implication of using the GEVD and Gumbel distribution to model the extreme wind speed on the structural reliability is presented and elaborated.

• Journal of the Korean Statistical Society
• /
• v.30 no.4
• /
• pp.667-678
• /
• 2001

The asymptotic behavior and distribution for quantiles estimators using ranked samples are introduced. Applications of quantiles estimation on finding the normal ranges (2.5% and 97.5% percentiles) and the median of some medical characteristics and on finding the Hodges-Lehmann estimate are discussed. The conclusion of this study is, whenever perfect ranking is possible, the relative efficiency of quantiles estimation using ranked samples relative to SRS is high. This may translates to large savings in cost and time. Also, this conclusion holds even if the ranking is not perfect. Computer simulation results are given and real data from lows 65+ study is used to illustrate the method.

• Journal of Korea Water Resources Association
• /
• v.45 no.3
• /
• pp.263-274
• /
• 2012

Recently, due to various climate variabilities, extreme rainfall events have been occurring all over the world. Extreme rainfall events in Korea mainly result from the summer typhoon storms and the localized convective storms. In order to estimate appropriate quantiles for extreme rainfall, this study considered the probability behavior of daily rainfall from the typhoons and the convective storms which compose the annual maximum rainfalls (AMRs). The conventional rainfall frequency analysis estimates rainfall quantiles based on the assumption that the AMRs are extracted from an identified single population, whereas this study employed a mixed distribution function to incorporate the different statistical characteristics of two types of rainfalls into the hydrologic frequency analysis. Selecting 15 rainfall gauge stations where contain comparatively large number of measurements of daily rainfall, for various return periods, quantiles of daily rainfalls were estimated and analyzed in this study. The results indicate that the mixed Gumbel distribution locally results in significant gains and losses in quantiles. This would provide useful information in designing flood protection systems.

• Proceedings of the Korea Water Resources Association Conference
• /
• 1997.05a
• /
• pp.340-345
• /
• 1997

• Wind and Structures
• /
• v.15 no.2
• /
• pp.87-109
• /
• 2012

A substantial part of South Africa is subject to more than one strong wind source. The effect of that on extreme winds is that higher quantiles are usually estimated with a mixed strong wind climate estimation method, compared to the traditional Gumbel approach based on a single population. The differences in the estimated quantiles between the two methods depend on the values of the Gumbel distribution parameters for the different strong wind mechanisms involved. Cluster analysis of the distribution parameters provides a characterization of the effect of the relative differences in their values, and therefore the dominance of the different strong wind mechanisms. For gusts, cold fronts tend to dominate over the coastal and high-lying areas, while other mechanisms, especially thunderstorms, are dominant over the lower-lying areas in the interior. For the hourly mean wind speeds cold fronts are dominant in the south-west, south and east of the country. On the West Coast the ridging of the Atlantic Ocean high-pressure system dominate in the south, while the presence of a deep trough or coastal low pressure system is the main strong wind mechanism in the north. In the central interior cold fronts tend to share their influence almost equally with other synoptic-scale mechanisms.

• The Korean Journal of Applied Statistics
• /
• v.20 no.1
• /
• pp.1-9
• /
• 2007

This investigation on the change of the daily maxima temperature in Seoul, Daegu, Chunchen, Youngchen was triggered by news items such as the earth is getting warmer and a recent news item that said that Korea is getting warmer due to this climatic change. A statistical analysis on the daily maxima for June over this period in Seoul revealed a positive trend of 1.1190 centigrade over the 45 years, a change of 0.0249 degrees annually. Due to the large variation on these maximum temperatures, one can raise the question on the significance of this increase. To check the goodness of fit of the proposed extreme value model, we shown a Q-Q plot of the observed quantiles against the simulated quantiles and a probability plot. And we calculated statistics each month and a tolerance limit. This is tested through simulating a large number of similar datasets from an Extreme Value distribution which described the observed data very well. Only 0.02% of the simulated datasets showed an increase of this degrees or larger, meaning that the probability is very low for such an event to occur.