Kamarulzaman Ibrahim

Analysis of drought condition and risk in Peninsular Malaysia using Standardised Precipitation Index

Contrary to the belief that Peninsular Malaysia experiences wet condition throughout the year, prolonged dry condition has lately become a recurrent phenomenon in this region. As a result, countrys agricultural sector and water resources have been under severe constraints from this situation. To get a clearer picture of the dry condition in Peninsular Malaysia, the Standardised Precipitation Index, based on the data of monthly rainfall from 50 stations, is derived. Spatial analysis is used to illustrate the percentage of occurrences of dry and very dry events. To evaluate the potential risk due to the dry conditions, we modelled the joint distribution of severity and duration of dry condition by means of bivariate copula. Several copula models were tested, and the model, which best represents the relationship between severity and duration, is determined using Akaike information criterion. Based on the results, the return period for the drought severity, based on the longest duration of drought at each station, can be estimated. This enables the drought risk to be calculated, thus planning on the measures to minimise the impact of a prolonged drought to the societies, which can be done by the relevant authorities.

On the application of structural equation modeling for the construction of a health index.

ObjectiveThe health of an individual is influenced by many factors. These could include factors that are related to the economy and the environment, as well as social and biological factors. Many studies have been carried out to study the effect of these factors on health, in terms of the individual factors or combined factors. The main purpose of this study was to demonstrate the value of structural equation modeling for the construction of an index to describe the health status of an individual.MethodsStructural equation modeling was applied to data obtained from 5035 respondents in a survey conducted in the district of Hulu Langat, Malaysia, in the year 2001 by the Department of Community Health, Medical Faculty, Universiti Kebangsaan Malaysia, Malaysia. The survey involved the gathering of information on the respondents’ demography, lifestyles, mental health condition, and biomarkers.ResultsSocio-demography and mental health condition were found to have a direct effect on the health index. However, lifestyle had an indirect effect on the health index, as mediated by the mental health. Based on the indicator of model fit, the proposed model fits the data well.ConclusionsStructural equation modeling was found to be pertinent to be used for analyzing the health index of a particular individual.

Bayesian structural equation modeling for the health index

There are many factors which could influence the level of health of an individual. These factors are interactive and their overall effects on health are usually measured by an index which is called as health index. The health index could also be used as an indicator to describe the health level of a community. Since the health index is important, many research have been done to study its determinant. The main purpose of this study is to model the health index of an individual based on classical structural equation modeling (SEM) and Bayesian SEM. For estimation of the parameters in the measurement and structural equation models, the classical SEM applies the robust-weighted least-square approach, while the Bayesian SEM implements the Gibbs sampler algorithm. The Bayesian SEM approach allows the user to use the prior information for updating the current information on the parameter. Both methods are applied to the data gathered from a survey conducted in Hulu Langat, a district in Malaysia. Based on the classical and the Bayesian SEM, it is found that demographic status and lifestyle are significantly related to the health index. However, mental health has no significant relation to the health index.

Modeling air quality in main cities of Peninsular Malaysia by using a generalized Pareto model

The air pollution index (API) is an important figure used for measuring the quality of air in the environment. The API is determined based on the highest average value of individual indices for all the variables which include sulfur dioxide (SO2), nitrogen dioxide (NO2), carbon monoxide (CO), ozone (O3), and suspended particulate matter (PM10) at a particular hour. API values that exceed the limit of 100 units indicate an unhealthy status for the exposed environment. This study investigates the risk of occurrences of API values greater than 100 units for eight urban areas in Peninsular Malaysia for the period of January 2004 to December 2014. An extreme value model, known as the generalized Pareto distribution (GPD), has been fitted to the API values found. Based on the fitted model, return period for describing the occurrences of API exceeding 100 in the different cities has been computed as the indicator of risk. The results obtained indicated that most of the urban areas considered have a very small risk of occurrence of the unhealthy events, except for Kuala Lumpur, Malacca, and Klang. However, among these three cities, it is found that Klang has the highest risk. Based on all the results obtained, the air quality standard in urban areas of Peninsular Malaysia falls within healthy limits to human beings.

Stochastic modeling of rainfall in peninsular Malaysia using Bartlett Lewis rectangular pulses models

Three versions of Bartlett Lewis rectangular pulse rainfall models, namely, the Original Bartlett Lewis (OBL), Modified Bartlett Lewis (MBL), and 2N-cell-type Bartlett Lewis model (BL2n), are considered. These models are fitted to the hourly rainfall data from 1970 to 2008 obtained from Petaling Jaya rain gauge station, located in Peninsular Malaysia. The generalized method of moments is used to estimate the model parameters. Under this method, minimization of two different objective functions which involve different weight functions, one weight is inversely proportional to the variance and another one is inversely proportional to the mean squared, is carried out using Nelder-Mead optimization technique. For the purpose of comparison of the performance of the three different models, the results found for the months of July and November are used for illustration. This performance is assessed based on the goodness of fit of themodels. In addition, the sensitivity of the parameter estimates to the choice of the objective function is also investigated. It is found that BL2n slightly outperforms OBL. However, the best model is theModified Bartlett Lewis MBL, particularly when the objective function considered involves weight which is inversely proportional to the variance.

Fitting a circular distribution based on nonnegative trigonometric sums for wind direction in Malaysia

Wind direction has a substantial effect on the environment and human lives. As examples, the wind direction influences the dispersion of particulate matter in the air and affects the construction of engineering structures, such as towers, bridges, and tall buildings. Therefore, a statistical analysis of the wind direction provides important information about the wind regime at a particular location. In addition, knowledge of the wind direction and wind speed can be used to derive information about the energy potential. This study investigated the characteristics of the wind regime of Mersing, Malaysia. A circular distribution based on Nonnegative Trigonometric Sums (NNTS) was fitted to a histogram of the average hourly wind direction data. The Newton-like manifold algorithm was used to estimate the parameter of each component of the NNTS model. Next, the suitability of each NNTS model was judged based on a graphical representation and Akaike’s Information Criteria. The study found that the NNTS model with...

Outliers detection for Pareto distributed data

This study aims to examine the presence of outliers in the upper tail of Malaysian income distribution under the assumption that the data follow Pareto model. For this purpose, three types of boxplot: standard boxplot, adjusted boxplot and generalized boxplot are considered. The performance of these boxplots is determined by a simulation study. In this study, the data were simulated from Pareto distribution, P(1, α = 2, 3, 4), then the simulated data were contaminated by replacing a proportion e (3%, 5%, 10%) of randomly selected data. It is found that the generalized boxplot gives higher power value compared to the standard and adjusted boxplots. Therefore, the generalized boxplot was used for determining the presence of outliers in the upper tail of income distribution, while the threshold for Pareto tail modelling was determined by using Van Kerm’s formula. The results showed that 0.4%, 0.4%, 0.9% and 1.2% outliers were detected by the generalized boxplot in the household income data that exceeded the threshold for the years of 2007, 2009, 2012 and 2014.This study aims to examine the presence of outliers in the upper tail of Malaysian income distribution under the assumption that the data follow Pareto model. For this purpose, three types of boxplot: standard boxplot, adjusted boxplot and generalized boxplot are considered. The performance of these boxplots is determined by a simulation study. In this study, the data were simulated from Pareto distribution, P(1, α = 2, 3, 4), then the simulated data were contaminated by replacing a proportion e (3%, 5%, 10%) of randomly selected data. It is found that the generalized boxplot gives higher power value compared to the standard and adjusted boxplots. Therefore, the generalized boxplot was used for determining the presence of outliers in the upper tail of income distribution, while the threshold for Pareto tail modelling was determined by using Van Kerm’s formula. The results showed that 0.4%, 0.4%, 0.9% and 1.2% outliers were detected by the generalized boxplot in the household income data that exceeded the ...

On the Mean Estimation using Stratified Double Median Ranked Set Sampling

Stratified Double Median Ranked Set Sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the Simple Random Sampling (SRS), Stratified Simple Random Sampling (SSRS) and Stratified Ranked Set Sampling (SRSS) methods. It is shown that SDMRSS estimator is an unbiased of the population mean and is more efficient than the SRS, SSRS and SRSS counterparts. Also, SDMRSS increase the efficiency of mean estimation for specific value of the sample size. The SDMRSS is applied on real data set.

Annual maximum exchange rate in Southeast Asia based on methods of L-Moment and Maximum LikelihooD

The main objective of this study is to determine the best fitting distribution to describe the annual series of maximum daily exchange rate from 1993 to 2013 for 4 countries in Southeast Asia based on L-moment and Maximum Likelihood (ML). Four three-parameter extreme-value distributions which are considered are Generalized Extreme Value (GEV), Generalized Logistic Distribution (GLD), Generalized Pareto Distribution (GPD) and Pearson III (P3). The estimation of parameters of these distributions is determined using the L-moment and maximum likelihood. The adequacy of the distributions based on parameter estimates computed using the two methods are evaluated using goodness-of-fit tests. When the goodness-of-fit results for these distributions are compared, it is found that, on the average, the performance of L-moment is better than the performance of maximum likelihood. Although the best fitting distribution may very according to the method of estimation and country considered, in most cases, data for the majority of the several countries are found to follow the generalized logistic distribution.

On the comparison of the interval estimation of the Pareto parameter under simple random sampling and ranked set sampling techniques

Ranked set sampling (RSS) is recognized as a useful sampling scheme for improving the precision of the parameter estimates and increasing the efficiency of estimation. This type of scheme is appropriate when the variable of interest is expensive or time consuming to be quantified, but easy and cheap to be ranked. In this study, the estimation of the shape parameter of the Pareto distribution of the first type when the scale is known is studied for the data that are gathered under simple random sampling (SRS), RSS, and selective order statistics based on the maximum (SORSS(max)). The confidence intervals for the shape parameter of Pareto distribution under the sampling techniques considered are determined. A simulation study is carried out to compare the confidence intervals in terms of coverage probabilities (CPs) and expected lengths (ELs). When the coverage probabilities and expected lengths for the confidence intervals of the shape parameter of Pareto distribution determined based on the different samp...