This paper proposes, with justification, two exponential ratio estimators of population mean in simple random sampling without replacement. Their biases and mean squared error are derived and compared with existing related ratio estimators. Analytical and numerical results show that at optimal conditions, the proposed ratio estimators are always more efficient than the regression estimator and some existing estimators under review.
This study assessed five approaches for imputing missing values. The evaluated methods include Singular Value Decomposition Imputation (svdPCA), Bayesian imputation (bPCA), Probabilistic imputation (pPCA), Non-Linear Iterative Partial Least squares imputation (nipalsPCA) and Local Least Squares imputation (llsPCA). A 5%, 10%, 15% and 20% missing data were created under a missing completely at random (MCAR) assumption using five (5) variables (Net Foreign Assets (NFA), Credit to Core Private Sector (CCP), Reserve Money (RM), Narrow Money (M1), Private Sector Demand Deposits (PSDD) from Nigeria quarterly monetary aggregate dataset from 1981 to 2019 using R-software. The data were collected from the Central Bank of Nigeria statistical bulletin. The five imputation methods were used to estimate the artificially generated missing values. The performances of the PCA imputation approaches were evaluated based on the Mean Forecast Error (MFE), Root Mean Squared Error (RMSE) and Normalized Root Mean Squared Error (NRMSE) criteria. The result suggests that the bPCA, llsPCA and pPCA methods performed better than other imputation methods with the bPCA being the more appropriate method and llsPCA, the best method as it appears to be more stable than others in terms of the proportion of missingness.
An alternative ratio estimator is proposed for a finite population mean of a study variable Y in simple random sampling using information on the mean of an auxiliary variable X, which is highly correlated with Y. Expressions for the bias and the mean square error of the proposed estimator are obtained. Both analytical and numerical comparisons have shown the proposed alternative estimator to be more efficient than some existing ones. The bias of the proposed estimator is also found to be negligible for all populations considered, indicating that the estimator is as good as the regression estimator and better than the other estimators under consideration.
Several researches have been done to provide better alternative to the existing replacement models, but the research works did not adequately address the replacement problem for items that fail suddenly. Hence, a modified replacement model for items that fail suddenly has been proposed using the knowledge of probability distribution of failure times as well as that of variable replacement cost. The modified cost functions for implementing both individual and group replacements were derived. The modified cost functions were minimized using the principle of classical optimization in order to find the age at which replacement of items would be appropriate. Conditions under which the individual and group replacement policies should be adopted were derived. Two real data sets on failure time of LED bulbs and their replacement costs were used to validate the theoretical claims of this work. In essence, goodness-of-fit test was used to select appropriate probability distribution of failure times as well as that of replacement costs for data sets I and II respectively. The goodness-of-fit results showed that failure times of LED bulbs follow the Smallest Extreme Value and Laplace distributions for data sets I and II respectively. Similarly, it was observed that individual replacement cost followed the two-parameter Gamma and Largest Extreme Value distributions for data sets I and II respectively. Further, the group replacement cost was found to follow the log-normal and two-parameter Weibull distributions for data sets I and II respectively. Based on the empirical study, we observed that individual replacement policy is better than group replacement policy in terms of cost minimization for both existing model and the proposed model. In view of the results, the proposed replacement policy was recommended over the existing one because it yielded lower replacement costs than the existing replacement model.
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