Coxmodel is popular in survival analysis. In the case of time-varying covariate;
several subject-specific attributes possibly to change more frequently than others. This
paper deals with that issue. This study aims to analyze survival data with time-varying
covariate using a time-dependent covariate Cox model. The two case studies employed in
this work are (1) delisting time of companies from IDX and (2) delisting time of company
from LQ45 (liquidity index). The survival time is the time until a company is delisted
from IDX or LQ45. The determinants are eighteen quarterly financial ratios and two
macroeconomics indicators, i.e., the Jakarta Composite Index (JCI) and BI interest rate
that changes more frequent. The empirical results show that JCI is significant for both
delisting and liquidity whereas BI rate is significant only for liquidity. The significant
firm-specific financial ratios vary for delisting and liquidity.
Johor Bahru with its rapid development where pollution is an issue that needs to be considered because it has contributed to the number of asthma cases in this area. Therefore, the goal of this study is to investigate the behaviour of asthma disease in Johor Bahru by count analysis approach namely; Poisson Integer Generalized Autoregressive Conditional Heteroscedasticity (Poisson-INGARCH) and Negative Binomial INGARCH (NB-INGARCH) with identity and log link function. Intervention analysis was conducted since the outbreak in the asthma data for the period of July 2012 to July 2013. This occurs perhaps due to the extremely bad haze in Johor Bahru from Indonesian fires. The estimation of the parameter will be done by quasi-maximum likelihood estimation. Model assessment was evaluated from the Pearson residuals, cumulative periodogram, the probability integral transform (PIT) histogram, log-likelihood value, Akaike’s Information Criterion (AIC) and Bayesian information criterion (BIC). Our result shows that NB-INGARCH with identity and log link function is adequate in representing the asthma data with uncorrelated Pearson residuals, higher in log likelihood, the PIT exhibits normality yet the lowest AIC and BIC. However, in terms of forecasting accuracy, NB-INGARCH with identity link function performed better with the smaller RMSE (8.54) for the sample data. Therefore, NB-INGARCH with identity link function can be applied as the prediction model for asthma disease in Johor Bahru. Ideally, this outcome can assist the Department of Health in executing counteractive action and early planning to curb asthma diseases in Johor Bahru.
Riverbank filtration (RBF) system is a surface water technology that is based
on the natural treatment of filtration instead of the use of chemicals, to pre-treat sur-
face water and provides public water supplies. Hydraulic conductivity value is one of the
significant factors affecting the water quality in RBF systems. In this article, an analyti-
cal modelling is developed to investigate the effect of this parameter on one dimensional
contaminant transport in RBF system. The model is solved by using Green’s function
approach. The model is applied for the first RBF system conducted in Malaysia. Gener-
ally, the results show that increasing the hydraulic conductivity value lead to an increase
in contaminant concentration in pumping well area.
The proposed modified methods of Cramer's rule consider the column vector as well as the coefficient matrix concurrently in the linear system. The modified methods can be applied since Cramer's rule is typically known for solving the linear systems in $WZ$ factorization to yield Z-matrix. Then, we presented our results to show that there is no tangible difference in performance time between Cramer's rule and the modified methods in the factorization from improved versions of MATLAB. Additionally, the Frobenius norm of the modified methods in the factorization is better than using Cramer's rule irrespective of the version of MATLAB used.
Regression is one of the basic relationship models in statistics. This paper focuses on the formation of regression models for the rice production in Malaysia by analysing the effects of paddy population, planted area, human population and domestic consumption. In this study, the data were collected from the year 1980 until 2014 from the website of the Department of Statistics Malaysia and Index Mundi. It is well known that the regression model can be solved using the least square method. Since least square problem is an unconstrained optimisation, the Conjugate Gradient (CG) was chosen to generate a solution for regression model and hence to obtain the coefficient value of independent variables. Results show that the CG methods could produce a good regression equation with acceptable Root Mean-Square Error (RMSE) value.
In numerical methods, boundary element method has been widely used to solve
acoustic problems. However, it suffers from certain drawbacks in terms of computational
efficiency. This prevents the boundary element method from being applied to large-scale
problems. This paper presents proposal of a new multiscale technique, coupled with
boundary element method to speed up numerical calculations. Numerical example is
given to illustrate the efficiency of the proposed method. The solution of the proposed
method has been validated with conventional boundary element method and the proposed
method is indeed faster in computation.
Conjugate Gradient (CG) methods have an important role in solving large
scale unconstrained optimization problems. Nowadays, the Three-Term CG method has
become a research trend of the CG methods. However, the existing Three-Term CG
methods could only be used with the inexact line search. When the exact line search
is applied, this Three-Term CG method will be reduced to the standard CG method.
Hence in this paper, a new Three-Term CG method that could be used with the exact
line search is proposed. This new Three-Term CG method satisfies the descent condition
using the exact line search. Performance profile based on numerical results show that
this proposed method outperforms the well-known classical CG method and some related
hybrid methods. In addition, the proposed method is also robust in term of number of
iterations and CPU time.
The fast-growing urbanization has contributed to the construction sector be- coming one of the major sectors traded in the world stock market. In general, non- stationarity is highly related to most of the stock market price pattern. Even though stationarity transformation is a common approach, yet this may prompt to originality loss of the data. Hence, the non-transformation technique using a generalized dynamic principal component (GDPC) were considered for this study. Comparison of GDPC was performed with two transformed principal component techniques. This is pertinent as to observe a larger perspective of both techniques. Thus, the latest weekly two-years observations of nine constructions stock market price from seven different countries were applied. The data was tested for stationarity before performing the analysis. As a re- sult, the mean squared error in the non-transformed technique shows eight lowest values. Similarly, eight construction stock market prices had the highest percentage of explained variance. In conclusion, a non-transformed technique can also present a better result outcome without the stationarity transformation.
This study presents a mathematical model examining wastewater pollutant removal through
an oxidation pond treatment system. This model was developed to describe the reaction
between microbe-based product mPHO (comprising Phototrophic bacteria (PSB)), dissolved
oxygen (DO) and pollutant namely chemical oxygen demand (COD). It consists
of coupled advection-diffusion-reaction equations for the microorganism (PSB), DO and
pollutant (COD) concentrations, respectively. The coupling of these equations occurred
due to the reactions between PSB, DO and COD to produce harmless compounds. Since
the model is nonlinear partial differential equations (PDEs), coupled, and dynamic, computational
algorithm with a specific numerical method, which is implicit Crank-Nicolson
method, was employed to simulate the dynamical behaviour of the system. Furthermore,
numerical results revealed that the proposed model demonstrated high accuracy when
compared to the experimental data.
Subsea cable laying is a risky and challenging operation faced by engineers, due to many uncertainties arise during the operation. In order to ensure that subsea cables are laid out diligently, the analysis of subsea cable tension during the laying operation is crucial. This study focuses on the fatigue failure of cables that will cause large hang-off loads based on catenary configuration after laying operation. The presented problem was addressed using mathematical modelling with consideration for a number of defining parameters, which include external forces such as current velocity and design parameters such as cable diameter. There were two types of subsea cable tension analyses studied: tensional analysis of catenary configurations and tensional analysis of lazy wave configurations. The latter involved a buoyancy module that was incorporated in the current catenary configuration that reduced subsea cable tension and enhanced subsea cable lifespan. Both analyses were solved using minimization through the gradient- based approach concerning on the tensional analysis of the subsea cable in different configurations. Lazy wave configurations were shown to successfully reduce cable tension, especially at the hang-off section.
Invadopodia are finger-like protrusions located at subcellular membrane which can lead to cancer cell invasion. The formation of invadopodia involves several steps such as actin polymerizations, degradation of extracellular matrix which produce ligand and signal stimulation that is occurred from the binding of ligand with epidermal growth factor receptor. In this paper, a mathematical model of signal transduction is investigated. Both signal and ligand are represented by Laplace equation with Dirichlet boundary condition for each region. The cell membrane is treated as free boundary surface to separate any activity that occurred in intracellular and extracellular regions. The motion of the interface is taken as gradient of interior signal and the cell membrane is set as zero level set function. The problem is solved numerically using finite difference scheme of upwind, interpolation and extrapolation methods. The results showed that the formation of invadopodia is formed when protrusions exist on the cell membrane.
In this paper, we look at the propagation of internal solitary waves over three
different types of slowly varying region, i.e. a slowly increasing slope, a smooth bump and
a parabolic mound in a two-layer fluid flow. The appropriate mathematical model for this
problem is the variable-coefficient extended Korteweg-de Vries equation. The governing
equation is then solved numerically using the method of lines. Our numerical simulations
show that the internal solitary waves deforms adiabatically on the slowly increasing slope.
At the same time, a trailing shelf is generated as the internal solitary wave propagates
over the slope, which would then decompose into secondary solitary waves or a wavetrain.
On the other hand, when internal solitary waves propagate over a smooth bump or a
parabolic mound, a trailing shelf of negative polarity would be generated as the results of
the interaction of the internal solitary wave with the decreasing slope of the bump or the
parabolic mound. The secondary solitary waves is observed to be climbing the negative
trailing shelf.
Life table is a table that shows mortality experience of a nation. However, in Malaysia, the information in this table is provided in the five-years age groups (abridged) instead of every one-year age. Hence, this study aims to estimate the one-year age mor- tality rates from the abridged mortality rates using several interpolation methods. We applied Kostaki method and the Akima spline method to five sets of Malaysian group mortality rates ranging from period of 2012 to 2016. The result were then compared with the one-year mortality rates. We found that the method by Akima is the best method for Malaysian mortality experience as it gives the least minimum of sum of square errors. The method does not only provide a good fit but also, shows a smooth mortality curve.
Replicated linear functional relationship model is often used to describe
relationships between two circular variables where both variables have error terms and
replicate observations are available. We derive the estimate of the rotation parameter
of the model using the maximum likelihood method. The performance of the proposed
method is studied through simulation, and it is found that the biasness of the estimates
is small, thus implying the suitability of the method. Practical application of the
method is illustrated by using a real data set.
In this work, a non-abelian metabelian group is represented by G while represents conjugacy class graph. Conjugacy class graph of a group is that graph associated with the conjugacy classes of the group. Its vertices are the non-central conjugacy classes of the group, and two distinct vertices are joined by an edge if their cardinalities are not coprime. A group is referred to as metabelian if there exits an abelian normal subgroup in which the factor group is also abelian. It has been proven earlier that 25 non-abelian metabelian groups which have order less than 24, which are considered in this work, exist. In this article, the conjugacy class graphs of non-abelian metabelian groups of order less than 24 are determined as well as examples of some finite groups associated to other graphs are given.
A mechanistic model has been used to explain the effect of radiation. The
model consists of parameters which represent the biological process following ionizing
radiation. The parameters in the model are estimated using local and global optimiza-
tion algorithms. The aim of this study is to compare the efficiency between local and
global optimization method, which is Pattern Search and Genetic Algorithm respectively.
Experimental data from the cell survival of irradiated HeLa cell line is used to find the
minimum value of the sum of squared error (SSE) between experimental data and sim-
ulation data from the model. The performance of both methods are compared based on
the computational time and the value of the objective function, SSE. The optimization
process is carried out by using the built-in function in MATLAB software. The parameter
estimation results show that genetic algorithm is more superior than pattern search for
this problem.
Simulation is used to measure the robustness and the efficiency of the forecasting
techniques performance over complex systems. A method for simulating multivariate
time series was presented in this study using vector autoregressive base-process. By
applying the methodology to the multivariable meteorological time series, a simulation
study was carried out to check for the model performance. MAPE and MAE performance
measurements were used and the results show that the proposed method that consider
persistency in volatility gives better performance and the accuracy error is six time smaller
than the normal hybrid model.
This journal renders the random walk behaviour of the Malaysian daily share return, through tests of efficient market hypothesis (EMH) based on three different financial periods, namely growth, financial crisis, and recovery period. This review also covers the behaviour of extreme return for weekly and monthly series generated from Block maxima-minima method. Autocorrelation Function test (ACF) and Ljung-Box test had been employed to measure average correlation between observations, while Augmented Dickey-Fuller (ADF), Phillips-Perron (PP), Kwiatkowski Phillips Schmidt Shin (KPSS) test had been used to scan the unit root and the stationarity. Multiple variance ratio tests had also been conducted to examine the random walk behaviour. Serial correlation test indicated that the movement of daily return during the financial crisis period was weak-form efficiency. The unit root and stationary tests suggested that each daily series was stationary, but trend stationary for extreme cases. Variance ratio tests indicated that the return during the recovery period was weak-form inefficiency due to the short lag autocorrelation in series.
The box plot has been used for a very long time since 70s in checking the existence
of outliers and the asymmetrical shape of data. The existing box plot is constructed
using five values of statistics calculated from either the discrete or continous data. Many
improvement of box plots have deviated from the elegant and simplier approach of exploratory
data analysis by incorporating many other statistic values resulting the turning
back of the noble philosophy behind the creation of box plot. The modification using
range value with the minimum and maximum values are being incorporated to suit the
need of selected discrete distribution when outliers is not an important criteria anymore.
The new modification of box plot is not based on the asymmetrical shape of distribution
but more on the spreading and partitioning data into range measure. The new propose
name for the box plot with only three values of statistics is called range-box plot.
Recently, oil refining industry is facing with lower profit margin due to un-
certainty. This causes oil refinery to include stochastic optimization in making a decision
to maximize the profit. In the past, deterministic linear programming approach is widely
used in oil refinery optimization problems. However, due to volatility and unpredictability
of oil prices in the past ten years, deterministic model might not be able to predict the
reality of the situation as it does not take into account the uncertainties thus, leads to
non-optimal solution. Therefore, this study will develop two-stage stochastic linear pro-
gramming for the midterm production planning of oil refinery to handle oil price volatility.
Geometric Brownian motion (GBM) is used to describe uncertainties in crude oil price,
petroleum product prices, and demand for petroleum products. This model generates the
future realization of the price and demands with scenario tree based on the statistical
specification of GBM using method of moment as input to the stochastic programming.
The model developed in this paper was tested for Malaysia oil refinery data. The result
of stochastic approach indicates that the model gives better prediction of profit margin.