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This paper aims to find efficient methods for estimating the parameters (shape =α , scale = β ) of Weibull distribution in different situations. The maximum likelihood estimation method (MLE), the median rank regression method (MRR), the least square method (LSM) and the weighted least square method (WLSM) are considered for the estimation of the parameters. The root mean square error (RMSE) criterion is used to measure the relative efficiency of the estimators experimentally (Monte Carlo simulation). From the simulation study, it is observed that the MLE produces the lowest RMSE, irrespective of all sample sizes, for decreasing hazard function(α << β ) (α is considerably smaller than β ) and roughly linear hazard function with a positive slope (α >1) . When (α >> β ) the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) but for large sample sizes it is the MLE, irrespective of all types of hazard functions. When (α ,β →1), the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) and the MLE for large sample sizes irrespective of all types of hazard functions. This pattern becomes reversed whenα and β have the larger value. Only the MLE gets stuck when the hazard function is parallel to Y − axis (α >> β ) and the WLSM is suitable in such a situation (lowest RMSE) irrespective of all sample sizes. Finally, the utility of simulation results have been illustrated by analyzing two real-life data sets. Dhaka Univ. J. Sci. 71(1): 17-25, 2023 (Jan)

The Gaussian distribution is often considered to be the underlying distribution of many observed samples for modelling purposes, and hence simulation from the Gaussian density is required to verify the fitted model. Several methods, most importantly, Box-Muller method, inverse transformation method and acceptance-rejection method devised by Box and Muller1, Rao et al.7 and Sigman8 respectively, are available in the literature to generate samples from the Gaussian distribution. Among these methods, Box-Muller method is the most popular and widely used because of its easy implementation and high efficiency,which produces exact samples2. However, generalizing this method for generating non-standard multivariate Gaussian variates is not discovered yet. On the other hand, inverse transformation method uses numerical approximation to the CDF of Gaussian density which may not be desirable in some situations while performance of acceptance-rejection method depends on choosing efficient proposal density. In this paper, we introduce a more general technique by exploiting the idea invented by Wakefield9 under acceptance rejection framework to generate one dimensional Gaussian variates, in which we don’t require to choose any proposal density and it can be extended easily for non-standard multivariate Gaussian density. The proposed method is compared to the existing acceptance-rejection method (Sigman8 method), and we have shown both mathematically and empirically that the proposed method performs better than Sigman8 method as it has a higher acceptance rate (79.53 %) compared to Sigman (76.04 %) method. Dhaka Univ. J. Sci. 67(2): 123-130, 2019 (July)

In a classification problem with binary outcome attribute, if the input attributes are both continuous and categorical, the Nearest Neighbor (KNN) technique cannot be used. On the other hand, the Decision Tree (DT) technique handles the continuous attributes by discretization which leads to loss of information.To overcome the limitations of the KNN and DT techniques, we propose a new technique in this study which is called Nearest Neighbor Decision Tree (KNNDT). The proposed technique uses a combination of KNN and DT to classify the test instances. KNNDT first uses the KNN technique to select homogeneous groups of training instances by using the continuous attributes and then builds local decision trees on these homogeneous groups by using the categorical attributes.An extensive simulation study was conducted to compare the performances of KNNDT and DT. In general, the proposed KNNDT gives better results compared to DT.