The main purpose of this paper is to develop a locally asymptotically optimal statistical new test for detecting the presence of random parameters in a Generalized Autoregessive Moving Average (GARMA) process. The purpose of the procedure study is to derive the powerful test for the hypothesis that the GARMA coefficients are constant overtime against the alternative that vary according to random effects. The asymptotic distribution and its tests properties are established under the Local Asymptotic Normality. It is shown that the proposed test statistic is; consistent, locally asymptotically optimal, performs better than the competing tests available in the literature, and constitutes a powerful technical tool for detecting the random effects in GARMA models. A simulation study was carried out to investigate the performance of this procedure. In fact, Monte Carlo method shows that the test has very good power for all cases considered. Additionally, a real data analysis is conducted to examine the performance of this procedure.
A quality control technique called statistical process control (SPC) makes it possible to use statistical approaches for process monitoring. Since the true distribution of the quality characteristic in question is unknown, nonparametric control charts-such as the Tukey's control chart (TCC) are a reliable and efficient tool for evaluating a method. Because it can quickly identify changes, the new extended exponentially weighted moving average (NEEWMA) control chart was used to track the mean process. In order to optimize the advantages of both control charts, we created a technique called NEEWMA-TCC, which blends NEEWMA and TCC. Using a variety of individual and aggregate performance metrics based on average run length (ARL), the effectiveness of the suggested chart was assessed under both symmetrical and asymmetrical distributions. According to our results, the recommended chart performs better in rapidly identifying shifts than control charts such as the traditional Shewhart, EWMA, and Extended EWMA control charts, however, the new extended EWMA (NEEWMA) chart outperformed to detect the small and moderate magnitudes of shift when the process observations are from normal, Laplace and Gamma distribution. Otherwise, the mixed NEEWMA-TCC perform better than other control chart for the case of exponential distribution, moderate shifts and short production run process. This research presents a case study from real data on urinary tract infection (UTI) in hospital. According to the study's findings, the NEEWMA chart is more successful than other similar control charts at identifying changes, while the NEWMA-TCC control chart performs the second-best in terms of detection.
This study proposes a binary logistic regression (BLR) framework with outlier and cutoff adjustments for predicting the Dermatology Life Quality Index (DLQI) in stress-affected psoriasis patients. Data from 149 patients, with DLQI as a binary response and eight predictive features, were analyzed. Cooks distance and M-estimators were applied to address outliers, and alternative cutoff thresholds, including the proportional method and Youdens index, were employed to improve classification accuracy. Adopting Cook's distance and Youden's index, the modified BLR model outperformed others. Subsequently, age, comorbidity and stress were identified as significant features and their odd ratios (OR) are 0.9228, 3.8425 and 1.1448, respectively. Cooks distance demonstrated superior performance, yielding the lowest Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values, the highest Cox and Snell R-squared (R-CS(2)) and Nagelkerke's R-squared (R-N(2)), and improved classification metrics. Youdens index further optimized sensitivity and specificity. Models incorporating these adjustments exhibited robust predictive capabilities, enhancing DLQI classification. These findings highlight the importance of addressing outliers and selecting appropriate cutoff thresholds in BLR modeling, offering valuable insights for improving clinical assessments and treatment strategies for psoriasis patients affected by stress.
Effective handling of missing data is essential in Big Data analytics, as missing values, particularly those occurring randomly across input variables, can significantly affect the reliability and accuracy of results. This research compares and evaluates the effectiveness of eleven imputation techniques: Mean Imputation (MI), Median Imputation (MEI), Deterministic Linear Regression (DLR), Stochastic Linear Regression (SLR), Bayesian Linear Regression (BLR), Bootstrap Linear Regression (BTLR), Predictive Mean Matching (PMM), Expectation-Maximization (EM), K-Nearest Neighbors with Median (KNNM), K-Nearest Neighbors with Weighted Average (KNNW), and Random Forest (RF). The study utilized nine numeric datasets of varying sizes: three small, three medium, and three large, to assess these techniques. Multivariate missing data were simulated using the Missing Completely at Random (MCAR) mechanism, with missing rates ranging from 10% to 50%. The effectiveness of imputation techniques is evaluated using NRMSE, while their performance consistency is tested with Kendalls W test. The results indicated that MI outperformed MEI. Among the linear regression techniques, DLR excelled compared to the other methods, including SLR, BLR, and BTLR. Additionally, KNNW demonstrated better performance than KNNM. In terms of overall dataset performance, RF, KNNW, and EM were the top performers. For recommending imputation techniques, EM is most suitable for small datasets, KNNW or EM are effective for medium datasets, and RF shows the best performance for large datasets. However, both RF and KNNW demand considerably longer processing times, particularly with large datasets. These insights provide practical guidance for selecting the most appropriate imputation method based on the characteristics of the dataset.
In this study, we present a new and generalized family of distributions referred to as the Gamma Odd Lindley Generalized-G (GOLG-G) distribution. Some structural properties of the new family of distributions including hazard rate function, quantile function, moments, incomplete moments, distribution of the order statistics and Renyi entropy are derived. The parameters of the new family of distributions are estimated via the method of maximum likelihood. A simulation study to examine the bias and mean square error of the maximum likelihood estimates and applications to real data sets to illustrate the usefulness and applicability of the generalized family of distributions are given.
