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.
The Poisson distribution is a key model for describing rare events, from machinery failures in engineering to disease onset in medicine. While prior research has examined the determination of event size for testing equality between Poisson distributions, comprehensive approaches that integrate both statistical power and precision remain limited. To address this gap, our study aims to achieve two goals. First, we present methods for calculating event sizes based on incidence rate ratios, incorporating rejection, validity, and confidence interval width to ensure both power and precision. Second, we extend the discussion to prediction intervals, establishing the original event sizes needed to achieve a specified probability of coverage. Simulation studies confirm that the proposed methods yield valid results for coverage and target probabilities. To support practical use, we developed three interactive R Shiny applications, making the methodology accessible for researchers and practitioners. Together, the empirical validation and user-friendly tools demonstrate the practical value of our framework.
The Kenward-Roger (KR) test is an approximate F test, which is to say that it uses a test statistic that has approximately an F distribution under the null hypothesis. The test statistic is constructed so that in two special cases the test is an exact F test, with a test statistic that has exactly an F distribution under the null hypothesis. One of the special cases is testing for the significance of a fixed group effect in a one-factor ANOVA model. We show that this testing problem can be extended to a more general class of testing problems in which the KR test is an exact F test.
In this paper, a family of distributions named the power Lomax-generated family is presented. It is derived from the T-X family by using the power Lomax as its generator. Some distributions are derived from the proposed family, such as the power Lomax-normal, power Lomax-Weibull, and power Lomax-beta distributions. Various properties of the proposed family, including the quantile function, skewness, kurtosis, order statistics, and moments, are provided. The maximum likelihood (ML) method is used to estimate the parameters of the proposed distribution. Moreover, the simulation study demonstrates how well the ML method performs when estimating the parameters of some submodels in the proposed family, such as the power Lomax-Weibull distribution. Finally, real data sets are utilized to showcase the practicality of this newly established family.
We introduce a novel distribution termed the half-Cauchy generalized Rayleigh distribution, characterized by three parameters, derived from the half-Cauchy family of distributions. Various statistical properties of this distribution are explored, encompassing explicit expressions for the survival function, median, hazard function, mode, moments, mean deviation, order statistics, cumulative hazard function, quantiles, and measures of dispersion based on quartiles and octiles. Parameter estimation for this model is conducted utilizing three widely employed techniques: maximum likelihood estimation (MLE), Cramer-Von-Mises (CVM), and least-square estimation (LSE) methods. To validate its applicability, we leverage two real datasets, subjecting the proposed model to a rigorous goodness-of-fittest. Results indicate a strong alignment between the proposed distribution and real-world data, showcasing its superior flexibility when compared to established models examined in the study. Additionally, we delve into a Bayesian analysis of the suggested model, employing the Hamiltonian Monte Carlo (HMC) algorithm with the No-U-Turn sampler (NUTS).
This paper introduces a new model selection criterion, SKIC(MLE), for simultaneous equations modelling based on the Kullback information criterion (KIC) using a maximum likelihood estimator (MLE). A comprehensive comparative simulation study demonstrates that when dealing with small sample sizes, SKIC(MLE) outperforms SKIC, a criterion proposed by Keerativibool and Jitthavech (2015). The results indicate that the proposed criterion, SKIC(MLE), has the potential to improve the accuracy of model selection significantly and exhibits higher observed L-2 efficiency than SKIC in such scenarios. The superiority of SKIC(MLE) in small sample sizes is attributed to the fact that the penalty term of SKIC increases exponentially as the number of parameters increases, causing the SKIC value to be higher than SKIC(MLE). As a result, SKIC is more likely to select underfitting models or few parameters than SKIC(MLE). However, this issue is not prevalent in medium to large sample sizes, so SKIC outperforms SKIC(MLE). This research has significant practical implications, potentially revolutionizing simultaneous equations modelling in cases with small sample sizes.
In real-world applications, collinearity can be problematic when modeling the link between the response variable and multiple explanatory variables. Collinearity in the Bell Regression Model (BRM), which is used for modeling count data with over-dispersion, presents a challenge because it makes the estimation unstable and inflates the variance of the parameter estimates. The Kibria and Lukman (K-L) estimator is one of shrinkage estimator. To model count data with over-dispersion, a variation of the K-L estimator is proposed in this paper for the BRM. The results of the Monte Carlo simulation and the Bell regression model application indicate that the suggested estimate significantly reduces the mean squared error when compared to other competing estimators.
This article explores the extension of Bayesian analysis through wrapped distributions. The study introduces the concept of posterior wrapped distributions derived under both uninformative and informative (gamma distribution) priors to obtain the posterior wrapped exponential distributions. Statistical measures such as mean, variance, skewness, kurtosis, and moment generating functions of the distributions are presented. Bayesian estimators and minimal posterior expected losses for the obtained distributions are derived. The probability density functions curves and their statistical properties are also investigated. Additionally, two examples of utilizing the posterior wrapped exponential distributions in real-life situations are demonstrated.
Identifying risk factors that exhibit significant associations with child growth and development is crucial for preventing unhealthy growth and supporting children's overall development. Given that children have a diverse range of growth patterns, it is particularly relevant to evaluate these associations across quantiles rather than simply focusing on the mean or median values. In this paper, we develop a Bayesian variable selection method within quantile regression (QR) and quantile mixed models (QMMs). In particular, these methods are designed to analyse longitudinal data, such as child growth data. This novel methodology combines several key components, including the Bayesian sparse group LASSO method, a likelihood function based on the scale mixture representation of the asymmetric Laplace (AL) distribution. It also incorporates spike-and-slab priors for regression coefficients and utilises linear mixed models based on a decomposition for the covariance matrix of random effects. By combining these elements, our approach offers a comprehensive solution for simultaneous selection and estimation of fixed and random effects in QMMs. We assess the performance of the proposed method through simulation studies, which demonstrate its strong variable selection and predictive capabilities. Furthermore, we illustrate its practical utility by applying it to the Growing Up in Scotland (GUS) dataset, providing practical insights into its real-world applicability.
By incorporating the unit Gompertz (UG) distribution into the framework of artificial neural network (ANN) modelling, we present a novel approach in this paper. We include the UG distribution in our ANN modelling framework to improve the precision and interpretability of predictions. Through this integration, we hope to learn new things, strengthen forecast accuracy, and better understand the mechanisms at work in our data. After performing computations for a number of situations using the Hazard Rate Function (HRF), Cumulative Density Function (CDF), Probability Density Function (PDF), and Reliability (R) functions, a data collection has been developed. With this UG distribution and ANN modelling combo, it is expected that the ability to analyze and predict these functions would improve. Two separate artificial neural network models have been created using a total of 32 data sets gathered. The generated multi-layer perceptron network models utilized 15% for model validation, 70% of data for model training, and 15% for model testing. The findings demonstrate that ANNs are highly accurate at predicting the PDF, CDF, HRF, and R functions of the UG model.
The main objective of this paper is to tackle the issue of bias in linear mixed models that utilize ridge estimates, particularly in the presence of measurement error in the fixed-effects variables. To achieve this, we first describe a ridge estimator for linear mixed models and then introduce a new estimator called the jackknife ridge estimator. We compare the jackknife ridge estimator with the ridge estimator, highlighting its bias and mean square error advantages. Furthermore, we derive the asymptotic properties of both estimators. Finally, we conduct a simulation study and provide a numerical example to assess the effectiveness of the jackknife ridge estimator in linear ridge mixed measurement error models.
In this article, we introduce a new distribution named, Topp-Leone Heavy-Tailed Gompertz-G (TL-HT-Gom-G) family of distributions. Several mathematical and statistical properties of the new TL-HT-Gom-G family of distributions including quantile function, moments, moment generating function, Renyi entropy, distribution of order statistics, stochastic orderings are derived. Risk measures and a numerical simulation study are also presented for this family of distributions. To estimate the model parameters, we use six different estimation methods, namely, maximum likelihood, Anderson-Darling, Right-Tail Anderson-Darling, Ordinary Least Squares, Weighted Least Squares, and Cramer-von Mises. A simulation study is further performed to assess these estimation techniques and finally we demonstrate the applicability of the new family of distributions using applications to three real data sets.
Interval estimation is one of the important concepts in statistics. There are different methods to find a confidence interval for distribution parameters, but finding an optimal confidence interval is always a concern. On the other hand, it is important to find a confidence interval for the Shannon information of the ith order statistic when the distribution parameters are unknown. In the present paper, using information measures, we introduce an asymptotic confidence interval for scale parameter and the Shannon information of the ith order statistic related to the location-scale family. Via simulation study, we study the coverage probability and length of confidence intervals. Finally, some examples for hypothesis testing related to the Shannon information of the ith order statistic and the scale parameter are provided.
A novel family of distribution has been introduced, named as "exponent-Generator family of statistical distribution", designed for optimal univariate modeling. We explored the structural and characterizing properties of a newly proposed distribution, the exponent power function (EPF) distribution. We provide explicit expressions for the probability density function (PDF), cumulative distribution function (CDF), reliability function (RF), and hazard rate function (HRF). Also the r-th moment, moment generating function (MGF), and the order statistics are obtained. The manuscript also includes a detailed discussion on the shapes of PDF and HRF for selected parameter values, providing valuable insights into the behavior of distribution. Moreover, we discussed maximum likelihood estimation (MLE) and Bayesian estimation method. The adaptability of the proposed distribution is evaluated by analyzing the three real data sets related to lifetime of cancer patients as well as a simulated dataset.
Existence of a well defined and perfect sampling frame is the fundamental requirement of any sample survey. But there is enough evidence to support the fact that a perfect sampling frame that captures all the individual units of the population is rarely available, especially for a dynamic population where a constant movement of the units of the population is observed. In such cases, the sample collected can not be considered as a good representative of the population and the problem of incomplete frame arises. The results so drawn can immensely change the survey results and influence the legitimacy of the research. This study deals with the incomplete frame problem using ratio method of estimation, where the information on the auxiliary or ancillary variable is collected in the first phase and a second phase sample is then drawn to obtain estimates of the population mean of the characteristic under study and its mean square error up to first order approximation. Two different estimators, viz., combined ratio estimator and separate ratio estimators have been used and their efficiencies are compared. Further, the results are illustrated numerically with the help of Monte-Carlo simulations.
Excessive zero counts are one of the causes of over-dispersion in count data that is often observed in different fields. In this paper, we propose a new zero-inflated model namely 'the zero-inflated Poisson Garima distribution' to handle excessive zero counts. Various structural properties including reliability characteristics, generating functions, moments, etc. are obtained. Also, the parametric estimation of the proposed model is obtained using maximum likelihood method of estimation. Furthermore, a simulation study is carried out to check the behaviour of maximum likelihood estimators. Moreover, the proposed model and the baseline model are distinguished using two different test procedures. Finally, two real-life data sets taken from different domains are considered to validate the empirical applications of the proposed model.
