Abstract: Higher ground-level ozone (GLO) concentration adversely affects human health, vegetations as well as activities in the ecosystem. In Malaysia, most of the analysis on GLO concentration are carried out using the average value of GLO concentration, which refers to the centre of distribution to make a prediction or estimation. However, analysis which focuses on the higher value or extreme value in GLO concentration is rarely explored. Hence, the objective of this study is to classify the tail behaviour of GLO using generalized extreme value (GEV) distribution estimation the return level using the corresponding modelling (Gumbel, Weibull, and Frechet) of GEV distribution. The results show that Weibull distribution which is also known as short tail distribution and considered as having less extreme behaviour is the best-fitted distribution for four selected air monitoring stations in Peninsular Malaysia, namely Larkin, Pelabuhan Kelang, Shah Alam, and Tanjung Malim; while Gumbel distribution which is considered as a medium tail distribution is the best-fitted distribution for Nilai station. The return level of GLO concentration in Shah Alam station is comparatively higher than other stations. Overall, return levels increase with increasing return periods but the increment depends on the type of the tail of GEV distribution’s tail. We conduct this study by using maximum likelihood estimation (MLE) method to estimate the parameters at four selected stations in Peninsular Malaysia. Next, the validation for the fitted block maxima series to GEV distribution is performed using probability plot, quantile plot and likelihood ratio test. Profile likelihood confidence interval is tested to verify the type of GEV distribution. These results are important as a guide for early notification on future extreme ozone events.
Abstract: In this paper, we consider the application of Extreme
Value Theory as a risk measurement tool. The Value at Risk, for a set
of indices, from six Stock Exchanges of Frontier markets is
calculated using the Peaks over Threshold method and the
performance of the model index-wise is evaluated using coverage
tests and loss functions. Our results show that “fattailedness” alone of
the data is not enough to justify the use of EVT as a VaR approach.
The structure of the returns dynamics is also a determining factor.
This approach works fine in markets which have had extremes
occurring in the past thus making the model capable of coping with
extremes coming up (Colombo, Tunisia and Zagreb Stock
Exchanges). On the other hand, we find that indices with lower past
than present volatility fail to adequately deal with future extremes
(Mauritius and Kazakhstan). We also conclude that using EVT alone
produces quite static VaR figures not reflecting the actual dynamics
of the data.
Abstract: This paper focuses on operational risk measurement
techniques and on economic capital estimation methods. A data
sample of operational losses provided by an anonymous Central
European bank is analyzed using several approaches. Loss
Distribution Approach and scenario analysis method are considered.
Custom plausible loss events defined in a particular scenario are
merged with the original data sample and their impact on capital
estimates and on the financial institution is evaluated. Two main
questions are assessed – What is the most appropriate statistical
method to measure and model operational loss data distribution? and
What is the impact of hypothetical plausible events on the financial
institution? The g&h distribution was evaluated to be the most
suitable one for operational risk modeling. The method based on the
combination of historical loss events modeling and scenario analysis
provides reasonable capital estimates and allows for the measurement
of the impact of extreme events on banking operations.
Abstract: This paper tries to represent a new method for
computing the reliability of a system which is arranged in series or
parallel model. In this method we estimate life distribution function
of whole structure using the asymptotic Extreme Value (EV)
distribution of Type I, or Gumbel theory. We use EV distribution in
minimal mode, for estimate the life distribution function of series
structure and maximal mode for parallel system. All parameters also
are estimated by Moments method. Reliability function and failure
(hazard) rate and p-th percentile point of each function are
determined. Other important indexes such as Mean Time to Failure
(MTTF), Mean Time to repair (MTTR), for non-repairable and
renewal systems in both of series and parallel structure will be
computed.