Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function.

In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution of the obtained models is given. Moreover, the softmax function can be used as a discrete probability distribution function with a unity sum. Thus, applying those measures to the softmax function for simulated and real data is demonstrated. Besides, for real data, the softmax data are fit to a convenient ARIMA model.

Estimation of Parameters on Probability Density Function Using Enhanced GLUE Approach.

The most essential process in statistical image and signal processing is the parameter estimation of probability density functions (PDFs). The estimation of the probability density functions is a contentious issue in the domains of artificial intelligence and machine learning. The study examines challenges related to estimating density functions from random variables. Based on minimal predictions regarding densities, the study discusses a framework for evaluating probability density functions. During the Bayesian approach, which is to generate correct samplings that reflect the probability aspect of the variables, sampling is widely used to estimate as well as define the probabilistic model of unknown variables. Because of its effectiveness and extensive application, the generalized likelihood uncertainty estimation (GLUE) method has earned the most popularity among the various methodologies. The Bayesian technique allows parameters of the model to be estimated using prior expertise in the parameter results and experimental observations. The study uses a number of engineering issues that were lately looked into to illustrate the effectiveness of the upgraded GLUE. As the focus is on the examination of sampling effectiveness in view of engineering components, only a brief summary is provided to describe every challenge. The suggested GLUE method's outcomes are contrasted with those obtained using MCMC. Nevertheless, using the GLUE approach, the model's mean squared error of prediction is substantially higher than that of the previous algorithms. The methods' results are affected by the assumptions being made on parameter values in advance. The concepts of prediction accuracy, as well as the utility of geometric testing, are presented. Such notions are valuable in demonstrating that the GLUE approach defines an inconsistent and incoherent statistical inference process.

Exploring Parent's Satisfaction and the Effectiveness of Preformed Metal Crowns Fitting by Hall Technique for Carious Primary Molars in Jeddah Region, Saudi Arabia: Findings of a Prospective Cohort Study.

Purpose: The Hall technique (HT) is a non-invasive approach to treating carious primary teeth. Its acceptability by parents and effectiveness is not widely known in the Middle East. Therefore, we aimed to conduct this study to explore the effectiveness of preformed metal crowns (PMCs) fitting by HT and to what extent the parent's satisfaction for their children in Jeddah region. Materials and Methods: A prospective cohort study was conducted in the outpatient pediatric dental clinic at Jeddah Specialty Dental Center, in 2018. The cohort of children was exposed to the HT and was recalled 3 months to two years later to examine present or absence of: crown loss, open margin, signs or symptoms of reversible or irreversible pulpitis, and if the tooth exfoliated naturally. Parents who agreed to undergo the HT for their children completed a 5-point Likert questionnaire after treatment and after three months. Results: A total of 48 children (72 teeth) were initially enrolled, but only 25 children (49 teeth) completed two years of follow-up. At 2 years follow-up, one PMC was lost (2.04%) while no teeth fitted with the HT required any further intervention. Around 96% of parents were satisfied with this procedure and 92% wanted other carious teeth to be treated similarly. All parents were satisfied with this technique because it did not include local anesthesia and no drilling. It was found that parents of girls were satisfied more than parents of boys and on average their satisfaction score at the time of treatment was 3.04 units higher than parents of boys with a significant p-value of 0.02 and 95% CI for the beta coefficient to be 0.46 to 5.62. Conclusion: The HT is effective as a treatment of dental caries and it was generally accepted by parents initially and during their follow-up visits.

An Improved Estimation for Heterogeneous Datasets with Lower Detection Limits regarding Environmental Health.

Analysis of environmental data with lower detection limits (LDL) using mixture models has recently gained importance. However, only a particular type of mixture models under classical estimation methods have been used in the literature. We have proposed the Bayesian analysis for the said data using mixture models. In addition, an optimal mixture distribution to model such data has been explored. The sensitivity of the proposed estimators with respect to LDL, model parameters, hyperparameters, mixing weights, loss functions, sample size, and Bayesian estimation methods has also been proposed. The optimal number of components for the mixture has also been explored. As a practical example, we analyzed two environmental datasets involving LDL. We also compared the proposed estimators with existing estimators, based on different goodness of fit criteria. The results under the proposed estimators were more convincing as compared to those using existing estimators.

Optimal Periods of Conducting Preventive Maintenance to Reduce Expected Downtime and Its Impact on Improving Reliability.

The present research mainly aims to use a mathematical formula to determine the optimal intervals for conducting preventive maintenance operations for machines to reduce the expected failure time when the malfunction data follow the Weibull distribution. The reliability function, failure rate, and the average time between machine failures were derived after performing preventive maintenance operations and before conducting preventive maintenance operations to state the amelioration that happens to machines. These rely on real data of performing preventive maintenance operations and the downtime required to repair machine or device faults that occur between preventive maintenance periods and the downtime necessary to perform preventive maintenance operations on the machine or device. Thus, the study concluded that preventive maintenance operations are working to increase the reliability of the machine and improve it, as well as to increase the average period of time for the machine to operate between faults.

Inferences for Stress-Strength Reliability Model in the Presence of Partially Accelerated Life Test to Its Strength Variable.

We focus on estimating the stress-strength reliability model when the strength variable is subjected to the step-stress partially accelerated life test. Based on the assumption that both stress and strength random variables follow Weibull distribution with a common first shape parameter, the inferences for this reliability system are constructed. The maximum likelihood, two parametric bootstraps, and Bayes estimates are obtained. Moreover, approximate confidence intervals, asymptotic variance-covariance matrix, and highest posterior density credible intervals are derived. A simulation study and application to real-life data are conducted to compare the proposed estimation methods developed here and also check the accuracy of the results.

Latent Growth Curve Modeling for COVID-19 Cases in Presence of Time-Variant Covariate.

For the past two years, the entire world has been fighting against the COVID-19 pandemic. The rapid increase in COVID-19 cases can be attributed to several factors. Recent studies have revealed that changes in environmental temperature are associated with the growth of cases. In this study, we modeled the monthly growth rate of COVID-19 cases per million infected in 126 countries using various growth curves under structural equation modeling. Moreover, the environmental temperature has been introduced as a time-varying covariate to enhance the performance of the models. The parameters of growth curve models have been estimated, and accordingly, the results are discussed for the affected countries from August 2020 to July 2021.

Assessing the Lifetime Performance Index with Digital Inferences of Power Hazard Function Distribution Using Progressive Type-II Censoring Scheme.

This paper deals with estimating the lifetime performance index. The maximum likelihood (ML) and Bayesian estimators for lifetime performance index C L X where L X is the lower specification limit are derived based on progressive type-II censored (Prog-Type-II-C) sample from two-parameter power hazard function distribution (PHFD). Knowing the lower specification limit, the MLE of C L X is applied to construct a new hypothesis testing procedure. Bayesian estimator of C L X is also utilized to develop a credible interval. Also, the relationship between the C L X and the conforming rate of products is investigated. Moreover, the Bayesian test to evaluate the lifetime performance of units is proposed. A simulation study and illustrative example based on a real dataset are discussed to evaluate the performance of the two tests.

The new discrete distribution with application to COVID-19 Data.

This research aims to model the COVID-19 in different countries, including Italy, Puerto Rico, and Singapore. Due to the great applicability of the discrete distributions in analyzing count data, we model a new novel discrete distribution by using the survival discretization method. Because of importance Marshall-Olkin family and the inverse Toppe-Leone distribution, both of them were used to introduce a new discrete distribution called Marshall-Olkin inverse Toppe-Leone distribution, this new distribution namely the new discrete distribution called discrete Marshall-Olkin Inverse Toppe-Leone (DMOITL). This new model possesses only two parameters, also many properties have been obtained such as reliability measures and moment functions. The classical method as likelihood method and Bayesian estimation methods are applied to estimate the unknown parameters of DMOITL distributions. The Monte-Carlo simulation procedure is carried out to compare the maximum likelihood and Bayesian estimation methods. The highest posterior density (HPD) confidence intervals are used to discuss credible confidence intervals of parameters of new discrete distribution for the results of the Markov Chain Monte Carlo technique (MCMC).

An Exponential-Cum-Sine-Type Hybrid Imputation Technique for Missing Data.

In this study, a new exponential-cum-sine-type hybrid imputation technique has been proposed to handle missing data when conducting surveys. The properties of the corresponding point estimator for population mean have been examined in terms of bias and mean square errors. An extensive simulation study using data generated from normal, Poisson, and Gamma distributions has been conducted to evaluate how the proposed estimator performs in comparison to several contemporary estimators. The results have been summarized, and discussion regarding real-life applications of the estimator follows.

Logit model in prospective coronary heart disease (CHD) risk factors prediction in Saudi population.

Analysis through logistic regression explored to investigate the relationship between binary or multivariable ordinal response probability and in one or more explanatory variables. The main objectives of this study to investigate advanced prediction risk factor of Coronary Heart Disease (CHD) using a logit model. Attempts made to reduce risk factors, increase public or professional awareness. Logit model used to evaluate the probability of a person develop CHD, considering any factors such as age, gender, high low-density lipoprotein (LDL) cholesterol, low high-density lipoprotein (HDL) cholesterol, high blood pressure, family history of CHD younger than 45, diabetes, smoking, being post-menopausal for women and being older than 45 for men. Logit concept of brief statistics described with slight modification to estimate the parameters testing for the significance of the coefficients, confidence interval fits the simple, multiple logit models. Besides, interpretation of the fitted logit regression model introduced. Variables showing best results within the scientific context, good explanation data assessed to fit an estimated logit model containing chosen variables, this present experiment used the statistical inference procedure; chi-square distribution, likelihood ratio, Score, or Wald test and goodness-of-fit. Health promotion started with increased public or professional awareness improved for early detection of CHD, to reduce the risk of mortality, aimed to be Saudi vision by 2030.

Artificial neural networks and statistical models for optimization studying COVID-19.

The biggest challenge facing the world in 2020 was the pandemic of the coronavirus disease (COVID-19). Since the start of 2020, COVID-19 has invaded the world, causing death to people and economic damage, which is cause for sadness and anxiety. Since the world has passed from the first peak with relative success, this should be evaluated by statistical analysis in preparation for potential further waves. Artificial neural networks and logistic regression models were used in this study, and some statistical indicators were extracted to shed light on this pandemic. WHO website data for 32 European countries from 11th of January 2020 to 29th of May 2020 was utilized. The rationale for choosing the stated methodological tools is that the classification accuracy rate of artificial neural networks is 85.6% while the classification accuracy rate of logistic regression models 80.8%.

The Influence of Sweet Taste Perception on Dietary Intake in Relation to Dental Caries and BMI in Saudi Arabian Schoolchildren.

OBJECTIVES: The aim of the study was to evaluate the influence of sweet taste perception on dietary habits in Saudi schoolchildren. In addition, the relationship between dietary habits and both caries and BMI was studied. METHODS: A cross-sectional observational study comprising 225 schoolchildren aged 13-15 years from Jeddah, Saudi Arabia, was conducted. The consumption frequency of certain food items was analysed from a beverage and snack questionnaire and a three-day estimated dietary record was obtained. The sweet taste perception level was determined as sweet taste threshold (TT) and sweet taste preference (TP). Children were grouped into low, medium, and high, according to their sweet taste perception level. ICDAS and DMFS indices were used for caries registration and anthropometric measurements using BMI were collected. RESULTS: Sweet taste perception was found to be negatively correlated to the number of main meals and positively correlated to both snack and sweet intake occasions. Statistically significant differences were found between the TT and TP groups with regard to the number of main meals and sweet intake (p ≤ 0.01). No significant correlation between the dietary variables and caries or BMI was found. CONCLUSIONS: The dietary habits and sweet intake were found to be influenced by the sweet taste perception level, while the relation between the dietary habits and the caries and BMI was found insignificant.

Deficient cytokine control modulates temporomandibular joint pain in rheumatoid arthritis.

The aim was to investigate how endogenous cytokine control of tumor necrosis factor (TNF) influences temporomandibular joint (TMJ) pain in relation to the role of anti-citrullinated peptide antibodies (ACPA) in patients with rheumatoid arthritis (RA). Twenty-six consecutive patients with TMJ RA were included. Temporomandibular joint pain intensity was assessed at rest, on maximum mouth opening, on chewing, and on palpation. Mandibular movement capacity and degree of anterior open bite (a clinical sign of structural destruction of TMJ tissues) were also assessed. Systemic inflammatory activity was assessed using the Disease Activity Score in 28 joints (DAS28) for rheumatoid arthritis. Samples of TMJ synovial fluid and blood were obtained and analyzed for TNF, its soluble receptor, soluble TNF receptor II (TNFsRII), and ACPA. A high concentration of TNF in relation to the concentration of TNFsRII in TMJ synovial fluid was associated with TMJ pain on posterior palpation on maximum mouth opening. The ACPA concentration correlated significantly to the TNF concentration, but not to the TNFsRII concentration, indicating that increased inflammatory activity is mainly caused by an insufficient increase in anti-inflammatory mediators. This study indicates that TMJ pain on palpation in patients with RA is related to a deficiency in local cytokine control that contributes to increased inflammatory activity, including sensitization to mechanical stimuli over the TMJ.

Tumor necrosis factor mediates temporomandibular joint bone tissue resorption in rheumatoid arthritis.

OBJECTIVE: To investigate if TNF, IL-1 or their endogenous controls, in relation to ACPA, are associated with radiological signs of ongoing temporomandibular joint (TMJ) bone tissue resorption and disc displacement in RA patients. METHODS: Twenty-two consecutive outpatients with TMJ of RA were included. Systemic inflammatory activity was assessed by DAS28. The number of painful regions in the body and ESR, CRP, RF and ACPA were analyzed. TMJ synovial fluid and blood samples were obtained and analyzed for TNF, TNFsRII, IL-1ra, IL-1sRII and ACPA. The ratios between the mediators and their endogenous control receptors were used in the statistical analysis. Magnetic resonance imaging was performed in closed- and open-mouth positions and evaluated regarding disc position and presence of condylar and temporal erosions of the TMJ. RESULTS: A high TNF level in relation to TNFsRII in TMJ synovial fluid correlated to the degree of TMJ condylar erosion. A high IL-1ra level in relation to TNF in TMJ synovial fluid was also correlated to the degree of TMJ condylar erosion. The total degree of TMJ condylar erosion was correlated with the number of painful regions. CONCLUSION: This study indicates that TNF in TMJ synovial fluid mediates TMJ cartilage and bone tissue resorption in RA. The study also suggests that the degree of endogenous cytokine control is of importance for development of bone tissue destruction.

Impact of temporomandibular joint pain in rheumatoid arthritis.

To investigate the impact of temporomandibular joint (TMJ) pain on daily activities and quality of life in relation to systemic inflammatory activity in patients with rheumatoid arthritis (RA), thirty-three consecutive outpatients with RA were included. TMJ pain intensity at rest, on maximum mouth opening, and on chewing was assessed on a 0-10 numerical rating scale. TMJ palpatory tenderness, degree of anterior open bite, the impact of TMJ pain on daily activities and quality of life were also assessed. The systemic inflammatory activity was estimated by the disease activity score 28 (DAS28), blood levels of inflammatory markers and number of painful musculoskeletal regions. TMJ pain at rest, on maximum mouth opening, and on chewing as well as DAS28 was correlated with the impact of the TMJ pain on daily activities and quality of life. Partial correlations showed a significant interaction between TMJ pain on movement and DAS28 that explained the TMJ pain impact on daily activities and quality of life to a significant degree. This study indicates that both current TMJ pain intensity and systemic inflammatory activity play roles in the impact of TMJ pain on daily living and quality of life in RA.