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 and Pooling in Nonlinear Flooding Event Scenarios with Bayesian Model.

Water-related tragedies are the highest common of all proven natural calamities and pose severe attacks on people and on socioeconomic status development. Due to the obvious controversy surrounding, their volume, location and time of incidence, geological swaths, and geophysical interrelations, flood events are difficult to completely control. Hence, complete flood prevention is always considered to be a viable choice. The specialized flood occurrences are investigated by developing a structural measure. In this paper, nonlinear flood event circumstance is determined by using a statistical Bayesian parametric approach for parameter estimation. A popular tool for estimating a flood design is model of nonlinear flood event. Nonlinear flood event models are subjected to a Bayesian technique for estimating parameter. The approach is based on the minimization function of square for models with nonlinear calculated peak discharges in terms of parameters. The observed and calculated peak discharges for numerous storms in the watershed, data on the pattern of error observed, and previous information on values of parameter all influence this objective function. The subsequent matrix for covariance is a measure of the calculated parameters' accuracy. Rainfall and runoff data from a Harvey River sample are used in this study to show the process.

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).

Fuzzy-interval inequalities for generalized preinvex fuzzy interval valued functions.

In this paper, firstly we define the concept of h-preinvex fuzzy-interval-valued functions (h-preinvex FIVF). Secondly, some new Hermite-Hadamard type inequalities (H-H type inequalities) for h-preinvex FIVFs via fuzzy integrals are established by means of fuzzy order relation. Finally, we obtain Hermite-Hadamard Fejér type inequalities (H-H Fejér type inequalities) for h-preinvex FIVFs by using above relationship. To strengthen our result, we provide some examples to illustrate the validation of our results, and several new and previously known results are obtained.

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.

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%.