Browsing by Author "Kulatunga, D.D.S."

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Analysis of Fatalities in Road Accidents considering Peliyagoda Police Area in Gampaha District as a Case Study
(University of Kelaniya, 2012) Dissanayaka, D.M.P.V.; Kulatunga, D.D.S.
Road accidents have become a leading cause of death and injury as well as property damage worldwide. In Sri Lanka, a steady increase of road accidents has been reported resulting in a rising trend of fatalities too. In 2006, there were 2069 fatalities, while 2263 fatalities were reported in 2010. There are a number of factors that increase the risk of road accidents, including vehicle design, speed of operation, road design, road environment, driver’s skill and driver’s behaviour. The objective of this study is to find the factors that mostly contribute to fatal road accidents caused by motor vehicle drivers, using Logistic Regression Analysis. This study investigates the factors affecting fatalities in road accidents in the Peliyagoda Police Area in Gampaha district, using Logistic Regression Analysis. Accident data [519 accidents] recorded at the Peliyagoda Police Station in 2009 were considered. A total number of 506 road accidents where the motor vehicles were at fault were included in the analysis. Based on the data obtained from the police records, several predictor variables were employed in three independent Logistic Regression models in this study. A multinomial logistic model was used in one of them to deal with the multiple nature of dependent variables such as fatal, grievous, non grievous compared to damage only accidents. A binary logistic regression model was also developed to evaluate the odds of fatal accidents compared to non fatal accidents. The odds of an accident being fatal due to the collisions with pedestrians were high in both models with a positive effect. Since there were only 17 fatal accidents (3.4%), both these models were unsuccessful with huge coefficients. Re-categorizing fatal, grievous and non grievous accidents as human damage accidents, and damage only accidents as non human damage accidents, a binary logistic regression model was constructed. Head on crashes, approaching crashes, rear end crashes, crashes in conjunction with turning movements, crashes with pedestrians and passengers were positively related to human damage accidents rather than single crashes. Similarly, in the first two models, crashes with pedestrians and passengers had high impact on increasing the odds of human damage accidents. The odds of an accident being human damage were increased by a factor of 6.888 by having no traffic control rather than having police traffic control. The odds of an accident being human damage by a driver/rider with a valid or probationary driving license were about 25% and 13% respectively, lower than for accidents caused by the drivers/riders without valid license. The odds of an accident being human damage rather than being non-human damage are increased by a factor of 6.742 for motor cycles and bicycles rather than heavy vehicles. For every one-unit increase in the age of the vehicle, we can expect a 1.074 increase in the odds of human damage accidents, holding all other independent variables constant. In the Peliyagoda Police area, analyzing human damage accidents is more effective than analysing fatal accidents. However, a further study is recommended for an area where fatal accidents are more significant.
Approximate for the null distribution of a statistic caused by random combinations
(Applied Statistics Association of Sri Lanka, 2000) Kulatunga, D.D.S.; Kudo, A.; Azuma, S.
Convergence of multivariate isotonic regression
(University of Kelaniya, 2006) Fernando, W.T.P.S.; Kulatunga, D.D.S.
Statistical inference in the presence of order restrictions is an important area of statistical analysis. Isotonic regression theory plays a key role in this field. Let K= {1,…,k} be a finite set on which a partial order « is defined. A real vector (θ1, …,θk) is said to be isotonic if μ, υ ∈ K, μ « υ imply θμ ≤ θυ. Given real numbers x , , xk 1 K and positive numbers k w , ,w 1 K , a vector ( ) k θ θ ) K ) , , 1 is said to be the univariate isotonic regression of k x , , x 1 K with weights k w , ,w 1 K if it is isotonic and minimizes ( ) ν ν ν ν x θ w kΣ= − 1 2 under the restriction that (θ1,…,θk) is isotonic. Isotonic regression is closely related to the maximum likelihood estimate of ordered parameters of univariate normal distribution and some other univariate distributions. Various algorithms are given in the literature for computing univariate isotonic regression. Multivariate generalization of the isotonic regression and multivariate extensions of related theorems are given and proved by Sasabuchi, Inutsuka and Kulatunga (1983, 1992). A p × k real matrix ( ) k θ θ ,...,θ 1 = is said to be isotonic with respect to the partial order « , if μ, υ ∈ K, μ « υ imply μ ν θ ≤θ , where μ ν θ ≤θ means all the elements of ν μ θ −θ are nonnegative . Given p-dimensional real vectors k x , , x 1 K and p × p positive-definite matrices k Λ , ,Λ 1 K , a p × k matrix ( ) k θ θ ) K ) , , 1 is said to be the multivariate, in fact p-variate, isotonic regression of k x , , x 1 K with weights 1 1 1 , , Λ − Λ − K k if it is isotonic and satisfies min ( ) ( ) ( ) 1 ( ), 1 1 ' 1 * ' θ ν ν ν ν ν ν ν ν ν ν ν ν θ θ θ θ ) ) − Λ − = − Λ − − = − = Σ x x Σ x x k k Where min * (.) θ to denotes the minimum for all θ isotonic with respect to the partial order. An algorithm for the computation of multivariate isotonic regression is given in Sasabuchi et al. (1983, 1992). This algorithm involves iterative computation of univariate isotonic regression. The convergence of this algorithm is also studied there and it has been observed that the convergence follows only under certain conditions. (Corollary 4.1 of Sasabuchi et al (1992).) However, the simulation study conducted in Sasabuchi, Miura and Oda (2003) under special cases, has shown that the condition given in Corollary 4.1 of Sasabuchi et al. (1992) is not necessary for the convergence of this algorithm. We have written a Fortran subroutine for the computation of multivariate isotonic regression and also noted that the algorithm converges in general. This motivates us to consider a proof for the convergence of this algorithm. In this study we give a proof for the convergence of this algorithm in the bivariate case.
Tables for Testing Simultaneous Homogeneity against Ordered Alternatives in 3-Way Layout and Latin Square Design
(University of Kelaniya, 2008) Premarathna, L.P.N.D.; Kulatunga, D.D.S.
The likelihood ratio test for testing simultaneous homogeneity of main effects of several factors against ordered alternatives in multifactor designs has been developed in the literature. But the level probabilities needed to implement these tests have been computed only for the 2-way layout. We use these results to calculate critical points for testing simultaneous homogeneity of main effects against simple order alternatives in 3-way layout and Latin square design. Tabulation of critical values requires finding values of c that satisfy _2 m+n+t Pr(E (m,n,t);:::: c)= I Q(l;m,n,t)Pr(B1 1 ;:::: c), for 3-way layout and l=4 -(/-3) -(mnt-1+2) 2 ' 2 _2 3 m Pr(E (m,m,m);:::: c)= I Q(l;m,m,m)Pr(B1 1 2 ;:::: c), for Latin Square -(l-3) -(m -/+2) l=4 2 ' 2 -2 Design, where E is the corresponding likelihood ratio test statistic, Q(l;m, n,t) are convolution of probabilities used in order restricted inference and Ba,b is the Beta distribution with parameters a, b. The tables presented here provide critical values for testing at significance level a for the combinations of m,n,t and a, where m,n,t = 2(1)10, a= 0.1, 0.05, 0.025, 0.01, 0.005. An application in the case of Latin Square Design and FORTRAN programs for the computation of critical values in several layouts are also presented.
Tests against tree order restriction in Poisson intensities
(University of Kelaniya, 2006) Fernando, W.T.P.S.; Kulatunga, D.D.S.
We consider a situation in which one wishes to compare several Poisson intensities with a control or standard when it is believed that the intensities are higher than the control. For instance, if λ1 is the average accident rate per k.m. of a truck driver who has undergone an extensive training in driving and if λj, for j=2,3,...,k, are the average accident rates of the jth truck drivers without any prior training; and if the intensities are believed to produce at least as large an intensity as the control, then one would expect that λ1 ≤ λj for j=2,3,…,k. If xi is the number of accidents incurred by the ith of the k truck drivers and ti be the number of k.m. he drove and λi be the average accident rate per k.m., we can mathematically formulate this situation as follows: Suppose X1,…,Xk are independent Poisson variables with means μi = λiti and let Ho: λ1= λ2=…= λk and H1: λ1 ≤ λj , for j=2,3,…,k, where λ1 is the control intensity and λj, for j =2,3,...,k, are the other intensities. The ordering specified by H1 is called a tree ordering. We are interested in testing Ho versus H1-Ho . The likelihood ratio test for Ho versus H1- Ho is computed and we derive the asymptotic distribution of it. Robertson and Wegman (1978) considered order restricted tests for members of the exponential family. Their results can be applied in the testing situation considered here only if the ti are all equal. Some results are also obtained in the literature for other order restrictions (Magel & Wright (1984) and Barmi et al.(1996)). In this study we obtain explicit formulae for the null distribution of the test statistic under tree ordering.
An Urban Water Consumption Model for Gampaha District, Sri Lanka
(University of Kelaniya, 2012) Gunawardana, K.D.A.M.; Kulatunga, D.D.S.
Water is a limited and an essential resource for living and its importance is understood by all. Climate change along with increase in population and economic growth exert stress on existing water resources. Sri Lanka experiences drought very frequently. Therefore, careful consumption of water is of high importance and there is a need to develop new methods to use water wisely. This study discusses an approach to understand and estimate the socio-demographic and climatic relationship with water consumption using Multivariate Analysis Techniques and comprises the formulation of an urban water consumption model using Multiple Regression Analysis. Water consumption data of the Gampaha district during the period 2000-2009 were examined to develop a model of urban water consumption. The analysis was done with water consumption as a dependent variable, and selected socio-demographic and meteorological data such as number of water connections, average annual temperature, total annual rainfall, GDP at current market price, population and ratio of population to university students as independent variables. The factor analysis revealed the variables of high influence on water consumption. The various factors and factor scores gave an understanding of the influence of each of the socio-demographic variables and the meteorological observations and helped to classify them into groups based on their interrelationships. The results indicated that urban water consumption is quite strongly affected by the number of water connections, average annual temperature and GDP at current market price. Regression models in seven different functional forms were investigated using independent variables. It was noted that six of these models showed higher adjusted R2 value approximately equal to 0.99. Among all the functional forms used, three of the models were the best with high R2 values and low standard errors. Various plots of residuals, the assumption of normality and the constant variance and independence of the error terms were also valid for the three models. The selected three models were used to simulate the behaviour of the forecast water consumption in relation to the actual water consumption. Data during the year 2010 was used for verification of the model’s validity. The obtained results were then used to recommend an appropriate model for water consumption in the Gampaha district.