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: The main objective of this study is to find a suitable approach to monitor the land infrastructure growth over a period of time using multispectral satellite images. Bi-temporal change detection method is unable to indicate the continuous change occurring over a long period of time. To achieve this objective, the approach used here estimates a statistical model from series of multispectral image data over a long period of time, assuming there is no considerable change during that time period and then compare it with the multispectral image data obtained at a later time. The change is estimated pixel-wise. Statistical composite hypothesis technique is used for estimating pixel based change detection in a defined region. The generalized likelihood ratio test (GLRT) is used to detect the changed pixel from probabilistic estimated model of the corresponding pixel. The changed pixel is detected assuming that the images have been co-registered prior to estimation. To minimize error due to co-registration, 8-neighborhood pixels around the pixel under test are also considered. The multispectral images from Sentinel-2 and Landsat-8 from 2015 to 2018 are used for this purpose. There are different challenges in this method. First and foremost challenge is to get quite a large number of datasets for multivariate distribution modelling. A large number of images are always discarded due to cloud coverage. Due to imperfect modelling there will be high probability of false alarm. Overall conclusion that can be drawn from this work is that the probabilistic method described in this paper has given some promising results, which need to be pursued further.
Abstract: Extreme temperature of several stations in Malaysia is
modelled by fitting the monthly maximum to the Generalized
Extreme Value (GEV) distribution. The Mann-Kendall (MK) test
suggests a non-stationary model. Two models are considered for
stations with trend and the Likelihood Ratio test is used to determine
the best-fitting model. Results show that half of the stations favour a
model which is linear for the location parameters. The return level is
the level of events (maximum temperature) which is expected to be
exceeded once, on average, in a given number of years, is obtained.
Abstract: In recent years, the use of vector variance as a
measure of multivariate variability has received much attention in
wide range of statistics. This paper deals with a more economic
measure of multivariate variability, defined as vector variance minus
all duplication elements. For high dimensional data, this will increase
the computational efficiency almost 50 % compared to the original
vector variance. Its sampling distribution will be investigated to make
its applications possible.