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- ItemThe McDonald generalized Beta-Binomial distribution(University of Peradeniya, 2013) Chandrabose, Manoj; Wijekoon, Pushpa; Yapa, Roshan D.The binomial outcome data are widely encountered in many real world applications. The Binomial distribution often fails to model the binomial outcomes since the variance of the observed binomial outcome data exceeds the nominal Binomial distribution variance, a phenomenon known as overdispersion. One way of handling overdis- persion is modeling the success probability of the Binomial distribution using a continuous distribution defined on the standard unit interval. The resultant general class of univariate discrete distributions is known as the class of Binomial mixture distributions. The Beta-Binomial (BB) distribution is a prominent member of this class of distributions. The Kumaraswamy-Binomial (KB) distribution is another recent member of this class. In this paper we focus the emphasis on the McDonald’s Generalized Beta distribution of the first kind as the mixing distribu- tion and introduce a new Binomial mixture distribution called the McDonald Generalized Beta-Binomial distribu- tion(McGBB). Some theoretical properties of McGBB are discussed. The parameters of the McGBB distribution are estimated via maximum likelihood estimation technique. A real world dataset is modeled by using the new McGBB mixture distribution, and it is shown that this model gives better fit than its nested models. Finally, an ex- tended simulation study is presented to compare the McGBB distribution with its nested distributions in handling overdispersed binomial outcome data.
- ItemImprovement of the preliminary test estimator when stochastic restrictions are available in linear regression model(University of Peradeniya,, 2013) Arumairajan, Sivarajah; Wijekoon, PushpakanthiRidge type estimators are used to estimate regression parameters in a multiple linear regression model when multi- colinearity exists among predictor variables. When different estimators are available, preliminary test estimation proce- dure is adopted to select a suitable estimator. In this paper, two ridge estimators, the Stochastic Restricted Liu Estimator and Liu Estimator are combined to define a new preliminary test estimator, namely the Preliminary Test Stochastic Re- stricted Liu Estimator (PTSRLE). The stochastic properties of the proposed estimator are derived, and the performance of PTSRLE is compared with SRLE in the sense of mean square error matrix (MSEM) and scalar mean square error (SMSE) for the two cases in which the stochastic restrictions are correct and not correct. Moreover the SMSE of PTSRLE based on Wald (WA), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are derived, and the per- formance of PTSRLE is compared using WA, LR and LM tests as a function of the shrinkage parameter d with respect to the SMSE. Finally a numerical example is given to illustrate some of the theoretical findings.
- ItemImprovement of ridge estimator when stochastic restrictions are available in the linear regression model(University of Peradeniya, 2014) Arumairajan, Sivarajah; Wijekoon, PushpakanthiIn this paper we propose another ridge type estimator, namely Stochastic Restricted Ordinary Ridge Estimator (SRORE) in the multiple linear regression model when the stochastic restrictions are available in addition to the sample information and when the explanatory variables are multicollinear. Necessary and sufficient conditions for the superiority of the Stochastic Restricted Ordinary Ridge Estimator over the Mixed Estimator (ME), Ridge Estimator (RE) and Stochastic Mixed Ridge Estimator (SMRE) are obtained by using the Mean Square Error Matrix (MSEM) criterion. Finally the theoretical findings of the proposed estimator are illustrated by using a numerical example and a Monte Carlo simulation.
- ItemOrientation of easy axis of ferromagnetic films as explained by third order perturbed Heisenberg Hamiltonian(University of Peradeniya, 2013) Samarasekara, P.; Rajakaruna, PrabhaniThe third order perturbed Heisenberg Hamiltonian has been applied to explain the magnetic easy axis orientation. Ferromagnetic CoPt/AlN multilayer thin films with number of layers N=11, 16 and 21synthesized on fused quartz substrates using dc magnetron sputtering technique have been employed as experimental data. According to experimental research performed by some other researchers, easy axis of these fcc structured ferromagnetic films is oriented in the plane of the film above one particular temperature. Average value of out of plane spin component was plotted against temperature in order to determine the spin reorientation temperature. The spin reorientation temperature was highly sensitive to 2nd order magnetic anisotropy constant.
- ItemThird order perturbed Heisenberg Hamiltonian of spinel ferrite ultra-thin films(2011) Samarasekara, P.; Mendoza, Wiliam, A.The classical Heisenberg Hamiltonian equation of spinel ferrite ultra-thin films will be solved for third order perturbation. When second order anisotropy constant do not vary within the film of N=2, the film behaves as an oriented film. But the film of N=3 does not behave as an oriented film even for invariant second order anisotropy. Also the second and third order perturbations become zero in perpendicular and in plane directions, indicating that films behave as oriented films. For N-2 film, nearest maximum and minimum can be observed at 45 0 and 135 0 , respectively. For N=3, the first nearest maximum and minimum are observed at 470 and 1370 , respectively. In both cases, the angle between easy and hard direction is 900 , and the energy at hard or easy directions does not vary with angle. The 3- D plot of total energy versus angle and stress induced anisotropy indicates some energy minimums. Fourth order anisotropy slightly destroys the smoothness of the energy curve with N=3.