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Estimation of Skewness and Kurtosis for Muscat Stock Market Data
Muhammad Idrees Ahmad
Department of Mathematics and Statistics,

Sultan Qaboos University,

Muscat, Oman.

It is well documented in the finance literature that the empirical distribution of daily stock market returns has very specific shape which is far from normal. It may have very long left tail and specifically high peak. The fund managers require information about the shape of distribution for their portfolio diversification. Skewness is a measure of length of tail while the kurtosis measures are highly correlated, they together are usually used to measure the shape of distribution. Conventionally the skewness and kurtosis are estimated by first four central moments. But these estimates are usually biased and have large variances which increases further if the underlying distribution is not normal. In the present study several alternative and robust methods of measuring skewness and kurtosis for the empirical distribution of Muscat Stock Market daily returns are investigated. These consist of the methods based on Central Moments, Standardized moments, Linear Combination of Order Statistics and percentiles. Estimates of skewness and kurtosis by each of these methods are compared in terms of their non parametric bootstrap standard errors and length of percentile confidence intervals.


On The Asymptotic Variance of Sample Vector Variance
Erna T. Herdiani and Maman A. Djauhari
Faculty of Mathematics and Natural Sciences,

Institut Teknologi Bandung, Indonesia

The most popular and widely used measure of multivariate dispersion is the generalized variance. However, its computation is quite cumbersome when the number of variables p is large and it does not work anymore when the covariance matrix is singular. The singularity of sample covariance matrix occurs, for example, when p is greater than the sample size n. This paper discusses an alternative measure called vector variance which can eliminate these obstacles and has been successfully used as the stopping rule in Fast MCD algorithm. It is known that the sample vector variance converges in distribution to a p2-variate normal distribution. The mean is quite sample, i.e. equal to the trace of the square of population covariance matrix. However, the asymptotic variance has a complicated formulation and is tedious to compute because it involves a matrix multiplication of size (p2 x p2). Using the properties of vec operator, we show that the asymptotic variance can be represented in a simple form.


Generalized Addictive Mixed Models for Small Area Estimation
Anang Kunia & Khairi l A. Notodiputro
Department of Statistics

Bogor Agriculture University,

Jl. Meranti, Wing 22 Level 4

Kampus IPB Darmaga,

16680 Bogor,


Small Area Estimation (SAE) is a statistical technique to estimate parameters of sub-population containing small size of samples with adequate precision. This technique is very important to be developed due to the increasing needs of statistic for small domains, such as districts or villages. Some SAE techniques have been developed in Canada, USA, and UE based on real data. We adapted this technique to produce small area statistic in Indonesia based on national data collected by the Central Bureau of Statistic. We found that the linear model applied to auxiliary data produced estimates with low precision. In this paper we propose a class of generalized additive mixed model to improve the model of auxiliary data in small area estimation.


The Impacts of Age-Related Hearing Loss
Azmin Azliza Aziz
Department of Finance and Banking,

Faculty of Business and Accountancy,

Universiti Malaya,

50603 Kuala Lumpur.

Hearing impairment has become a very common chronic health problem among the older generation Presbycusis or age-related hearing loss is defined as the loss of auditory sensitivity that is the result of aging. It may affect the quality of an individual’s life particularly in the social activities. In this paper, the impacts of hearing loss are determined by investigating the association between the level of hearing loss and their effects on the quality of life. This study considered two possible approaches in analyzing the data, i.e. a single model and a correlated model. In both approaches, the concept of logistic regression analysis was applied with the assumption that the responses have a binomial distribution. Analyses using individual logistic regression and correlated data provide almost consistent results for the greatest and least impacts of hearing loss. Finally, the comparisons between the results for individual logistic regression models and correlated model are discussed.


Practical Forecasting Approach for Malaysia Electricity Load Forecasting
Zuhaimy Ismail and Mohd Fuad Jamaludin
Department of Mathematics, Faculty of Science,UTM

Interest in the appliedresearch on short and medium-term electricity load forecasting has been remarkable during the past few years. Forecasting electricity loads with linear methods has always been a challenging task, since the load series exhibit several superimposed levels of seasonality, together with the nonlinear effects of many important exogenous variables, such as temperature, holiday and special events. Furthermore, forecasting load profiles (the series of 24 hourly loads in the target day) as a vector forecasting problem is an order of magnitude more difficult. Yet, it is precisely the forecasting of these profiles that has been the typical operational, and the market requirement for electric utilities. This paper examines the issues of forecasting using conventional regression-based methods and other methods such as neural networks and expert system. Some discussion on the practicality of using expert system and neural network for forecasting the 24 hours of daily electricity load and very much conducive to this approach. We employ the data on the daily electricity load demand from Tenaga Nasional Berhad (TNB). The forecast accuracy is measured based on the error statistics of forecast between the models for half an hour ahead for the short term forecast and a month ahead for the medium term are presented and behavior of data is also observed.


Analysis Effect of Terrorism toward Tourism by Intervention Model
Riswan Effendi1 & Suhartono2
1Mathematics Department, UIN Suska Riau-Indonesia.

2Statistics Department, ITS Surabaya-Indonesia.

Intervention model is a time series model that can be used for describing and explaining the effect of an intervention caused by external or internal factor, which happens on a time series data. In general, this model can also apply for modeling time series with change in regime. The aim of this paper is to discuss the results of theoretical and empirical studies about intervention model, particularly pulse function intervention. Theoretical study is focused on the derivation of statistics terms that be used as basic for determining the order of intervention model. Then, the results of this theoretical study are applied to construct a model building procedure of intervention model. Finally, the effect of the first Bali bomb to the occupancy level of five star hotels in Bali is used as a case study. The data are observed starting from January 1997 to September 2005. In this case, the first Bali bomb that happens on October 12th, 2002 is an intervention of external factor whose effect will be evaluated. The result of this empirical study shows that interventional model can describe and explained exactly the quantity and the length of the first Bali bomb effect toward the decreasing of the occupancy level of five star hotels in Bali.


Generalization of a Stochastic Model for Analysis of Multivariate Longitudinal Measurements
Khalid Ali Salah
Institute for Mathematical Research (INSPEM), Universiti Putra Malaysia,

43400 Serdang, Selangor

For a given random process over a time interval, and a function, we define a random variable, and wish to generalize its probability distribution in long-time limit. We consider the case of the Ornstein-Uhlenbck (OU) process, in which depending upon whether is non-vanished or vanished for the parameters and. The process will be extended over the infinite time interval. Our emphasis will be on generalization of the stochastic process with particular regard to the concept of Integrated Ornstein-Uhlenbck (IUO) process. To incorporate this process in multivariate longitudinal measurements, we specify a structure for the within subject covariance based on a stochastic process. In general, for the analysis of longitudinal repeated measurements data we consider the model

where is the observed measurements of subject , are fixed and random effects respectively, is the IOU stochastic process and is the measurement error.


Stochastic Logistic Model for Fermentation Process
Arifah Bahar & Madihah Salleh
Department of Mathematics, Faculty of Science, Universiti Teknologi Malaysia

In our study we consider stochastic logistic model for modeling the microbial growth in fermentation process. The model concerns on environmental stochasticity that affects the growth. Thus, we introduce stochastic perturbation to logistic model via its growth coefficient. We show that the resulting Itô’s stochastic differential, has a positive and global solution which does not contradict its deterministic counterpart. We also show that the solution is stochastically bounded.


ARPS Hyperbolic Decline Model
1,4Sri Wahyuningsih, 1Sutawanir Darwis, 2Agus Yodi Gunawan, 3Asep Kurnia Permadi
1Statistics Research Group, Faculty of Mathematics & natural Sciences, Institut Teknologi Bandung, Indonesia.
2Financial & Industrial Mathematics Research Group, Faculty of Mathematics & Natural Sciences, Institut Teknologi Bandung, Indonesia.
3Reservoir Engineering Group, Faculty of Earth Sciences & Mineral Technology, Institut Teknologi Bandung, Indonesia.
4Statistics Study Program, Faculty of Mathematics & Natural Sciences, Universitas Mulawarman, Samarinda, East Kalimantan Indonesia.

Estimating reserves and predicting production in geothermal reservoirs has been challenge for a long time. Many methods have been developed in the last several decades. One frequently-used technique is decline curve analysis approach. Most of the existing decline curve analysis techniques are based on the empirical Arps equation. The equation was proposed more that sixty years ago. However a great number of studies on production decline analysis are still based on this empirical method. The equation represents the relationship between production and time for oil wells during pseudo steady-state period. The three types of decline are exponential, hyperbolic and harmonic. It is difficult to foresee which equation the geothermal reservoir will follow because geothermal product is steam, no fluid and no gas. A wide variety of approaches to the problem of decline curve fitting have been presented in the petroleum literature. The hyperbolic type of decline, which occurs most frequently in applications, can be recognized by the fact that the lost ratios are constant or nearly constant. Stochastic approaches have increasingly been used to study the uncertainty in remaining reserves estimates. In this talk, we shall derive the hyperbolic decline model as AR(1) process, the Autoregressive model with order 1, by means of the discretization of the flow rate equation. We found that the hyperbolic decline model leads to an AR(1) process with time varying parameter. This is a new approach in petroleum literature. This study will extend Kalman filter vector in reservoir multiwall system. We then apply the present model to simulate the geothermal performance data. The results can be used to forecast remaining reserves and optimum maintainance.


Primary Hip Stem Stability: The Effect of Bone Pathology on Micromotion
A. K. Mohammed Rafiq & K. Nazri
Biomechanics and Tissue Engineering Research Group (Bio-TEG),

Faculty of Mechanical Engineering,

Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

The effect of bone quality on the success of hip arthroplasty remains a topic of debate. Skeletal disease such as osteoporosis cause a significant loss of cancellous bone stock and structural deterioration of bone tissue. The reduced bone quality affects the decision made by surgeons in terms of selection of suitable hip stem as osteoporosis increases the likelihood of fracture and instability. It has been suggested that patients with poor bone stock would be better served having cemented hip stems to ensure strong primary fixation. However, there are reports that also cementless stems are reliable for patients suffering osteoporosis. A finite element model in conjunction with a novel methodology for predicting hip stem stability was experimentally validated in a previous study. In this study the methodology was applied to two CT datasets from osteoarthritic patients about to undergo hip replacement. Based on DEXA scans of the two patients, the Young Adult T-score showed in one case marked osteoporosis in all regions of the femur. 3D models were constructed from these two CT datasets and the material properties were assigned based on the grey-scale values on an element-by-element basis. A third femur model was created as ‘non-pathological’ control using the Visible Human Project (VHP) CT dataset. During the analyses, all interfacial contacts on surfaces with micromotion larger than a threshold limit for bone ingrowth of  were removed, and the iteration continues until either a stable-state condition is achieved or instability occurred. The results showed that the stems fixed in the control and osteoarthritic bones were stable. For the osteoporotic bone, the stem was found to be unstable due to a progressive reduction in surface area feasible for bone ingrowth. The results showed that bone quality affects the stability and therefore the potential success of hip stems.


Matrix Transfer and Coupled Mode Equation for Nonlinear Photonic Bandgap as Optical Signal Processing
Ayi Bahtiar & Irwan Ary Dharmawan
Department of Physics, Universitas Padjadjaran,

Jl. Raya Bandung-Sumedang KM.21,

45363 Sumedang, Indonesia.

An all-optical switching device is a crucial component for developing high speed data transmission and signal processing in telecommunication network. The device is based on nonlinear optical material, whose refractive index depends on light intensity. Various concepts for all-optical switching devices have been studied; however as the best of our knowledge, until now there is no purely optical switching devices have been realized. Recently, photonic crystals have been considerable interest both theoretically and experimentally for switching devices. Due to the practical reason, we studied one-dimensional nonlinear photonic crystal for all-optical switching devices. We use transfer matrix method and nonlinear coupled mode equation to determine photonic bandgap and optical switching process. We applied both methods to three different structures: nonlinear Distributed Bragg Reflector (DBR), photonic crystal with defect layer and nonlinear photonic crystal which has similar linear refractive index but has different sign of nonlinear refractive index. By using an appropriate combination of refractive indices, it was found that the first two structures can be used as all-optical switching in telecommunication wavelength (1.55µm). The third structure can be used both for switching and optical limiter at the wavelength of 1.0 µm.


Influence of Occlusal Loads on Stress Distribution of Dental Implants
A. K. Mohammed Rafiq & M. I. Mohd Norshahid
Biomechanics and Tissue Engineering Research Group (Bio-TEG),

Faculty of Mechanical Engineering,

Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

The primary stability of abutment-implant and implant-bone system in prosthetic dentistry is crucial to its short-term and long-term success. The commercially available abutment designs can be categorized into one of three different types – interference fit, screw and a combination of both screw and interference fit. The interference fit design provide primary fixation through interface frictional resistance and a large contact pressure whilst design where a combination of both fixation exists may prove inefficient as the screw threads may not contribute to the fixation when the connection is primarily made by the interference fit. The implant-bone system is also crucial because instability at the interface would prevent surrounding bone from intimately attached to the implant. Though attachment through biological means is more favorable, reports have suggested that mechanical parameters could also achieve similar affects to biological active coating. Adequate stability and surface roughness have been found to provide conducive environment for bone attachment and growth. In this study, a new abutment mechanical interlocking design is proposed through an 8o double tape which locked mechanically once inserted into the dental implant body. In vitro finite element non-linear contact analyses were carried out on the proposed design, as well as the design based on screw and interference fit for comparison. The bone model simulating the mandible was separated into cortical and cancellous region with load simulating the occlusal forces was applied on the abutment. Results showed that stability for the two types of screw designs were 25% better than the interference fit design. However, larger stresses were exerted on the neck of the abutment for the screw design. Results also showed that implant with tapered design produced better load transfer than a pure cylindrical design. Micromotion was larger for the tapered design, but did not exceed the threshold limit for oseointegration. The double-tapered dental implant system has been found to achieve maximum load transfer at an acceptable interface micromotion for bone integration.


Doppler Frequency Model for Sea Surface Current Simulation from RADARSAT-1 SAR Images
Maged Marghany, Mohamed Miyas & Mazlan Hashim
Department of Remote Sensing,

Faculty of Geoinformation Science and Engineering,

Universiti Teknologi Malaysia

This paper presents results of Doppler frequency model has been applied over the RADARSAT-1 SAR data. Two dimensional Fourier transform was applied with kernel window size of pixels to convert the RADARSAT-1 SAR data into frequency domain. The centeroid Doppler shift frequency process applied on the subset images with kernel window sizes of . Non-linear transform spectra of Doppler frequency was applied in order to relate the Doppler frequency with real sea surface current. The mathematical derivation of this relation is explained in details in this paper.


Performance of Glenoid Prostheses in a Conventional Glenohumeral Joint Arthroplasty
A. K. Mohammed Rafiq & I. Alhamzee
Biomechanics and Tissue Engineering Research Group (Bio-TEG),

Faculty of Mechanical Engineering, Universiti Teknologi Malaysia,

81310 Skudai, Johor, Malaysia.

One of the primary concerns in glenohumeral joint arthroplasty is loosening of the glenoid component. Although there are many factors affecting glenoid component loosening, the design is arguably the most important factor as has been reported of the high loosening rates of fully-constrained prostheses. The off-center loading, normally termed the “rocking-horse” phenomenon is thought to be the main reason behind loosening of the prostheses. Two types of fixation design are normally used in glenoid component – the keeled and the pegged – with the pegged design varies in terms of its numbers and the degree of alignment. The pegged design has the advantage of minimizing bone resection but tend to be more difficult than the keeled due to problems getting adequate exposure of the glenoid. Four glenoid components representing each of the fixation design were modeled in three dimensions. The model of the scapula was created from CT datasets and truncated to a region around the glenoid to make the analyses more manageable. The glenoid was then virtually reamed to simulate the preparation of the bone bed for implant insertion. Each implant design therefore has its own reamed glenoid. The implants were then inserted into their respective prepared glenoid and off-center loading was then applied to simulate the “rocking-horse” phenomenon. The material properties of the bone were assigned based on the Hounsfield units from the CT datasets. Results showed that the maximum edge displacement of the pegged glenoids due to the off-center loading was clearly less than that of the keeled glenoids, with the slanted peg perform slightly better than the aligned one. The pegged design was superior than the keeled because the pegs are placed in the stronger peripheral bone.

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