Preservation of the aging intensity order and the preservation of the monotonic aging intensity classes under distorted distributions.

This paper presents preservation property of the aging intensity order and the preservation property of the monotonic aging intensity classes under distorted distributions. Several sufficient conditions are given to get the preservation properties. It is shown that the imposed conditions are achievable as we examine in some examples. The preservation of the aging intensity order and the preservation of the decreasing aging intensity class under the structure of a parallel system with independent and identically distributed components' lifetime are made. A lower bound for the aging intensity function of a random lifetime with an increasing failure rate in average distribution is derived. The results are applied to some semiparametric model as a particular standard family of distorted distribution.

Epidemiological modeling of COVID-19 data with Advanced statistical inference based on Type-II progressive censoring.

This research proposes the Kavya-Manoharan Unit Exponentiated Half Logistic (KM-UEHL) distribution as a novel tool for epidemiological modeling of COVID-19 data. Specifically designed to analyze data constrained to the unit interval, the KM-UEHL distribution builds upon the unit exponentiated half logistic model, making it suitable for various data from COVID-19. The paper emphasizes the KM-UEHL distribution's adaptability by examining its density and hazard rate functions. Its effectiveness is demonstrated in handling the diverse nature of COVID-19 data through these functions. Key characteristics like moments, quantile functions, stress-strength reliability, and entropy measures are also comprehensively investigated. Furthermore, the KM-UEHL distribution is employed for forecasting future COVID-19 data under a progressive Type-II censoring scheme, which acknowledges the time-dependent nature of data collection during outbreaks. The paper presents various methods for constructing prediction intervals for future-order statistics, including maximum likelihood estimation, Bayesian inference (both point and interval estimates), and upper-order statistics approaches. The Metropolis-Hastings and Gibbs sampling procedures are combined to create the Markov chain Monte Carlo simulations because it is mathematically difficult to acquire closed-form solutions for the posterior density function in the Bayesian framework. The theoretical developments are validated with numerical simulations, and the practical applicability of the KM-UEHL distribution is showcased using real-world COVID-19 datasets.

A generalized Gompertz promotion time cure model and its fitness to cancer data.

The cure models based on standard distributions like exponential, Weibull, lognormal, Gompertz, gamma, are often used to analyze survival data from cancer clinical trials with long-term survivors. Sometimes, the data is simple, and the standard cure models fit them very well, however, most often the data are complex and the standard cure models don't fit them reasonably well. In this article, we offer a novel generalized Gompertz promotion time cure model and illustrate its fitness to gastric cancer data by three different methods. The generalized Gompertz distribution is as simple as the generalized Weibull distribution and is not computationally as intensive as the generalized F distribution. One detailed real data application is provided for illustration and comparison purposes.

Some properties of stop-loss moments under biased sampling.

The stop-loss moments have generally been used as useful summary measures for analyzing the data which exceeds specific threshold levels. In many scientific studies, the investigator cannot record the sampling units with equal probability, and in such a scenario, the selected sample units appear with unequal probability, in other words with different weights, which leads to a biased or weighted sampling. In the present study, we examine the usefulness of stop-loss moments in biased sampling. The application of the weighted stop-loss moments in analyzing biased data has been investigated and compared using different empirical estimators through simulated and real data sets.

Inference of multicomponent stress-strength reliability following Topp-Leone distribution using progressively censored data.

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods.

More efficient estimators of the area under the receiver operating characteristic curve in paired ranked set sampling.

Receiver operating characteristic is a beneficial technique for evaluating the performance of a binary classification. The area under the curve of the receiver operating characteristic is an effective index of the accuracy of the classification process. While nonparametric point estimation has been well-studied under the ranked set sampling, it has received little attention under ranked set sampling variations. In order to set out to fill this gap, this article deals with the problem of estimating the area under the curve of the receiver operating characteristic based on paired ranked set sampling. New estimators of the area under the curve of the receiver operating characteristic based on paired ranked set sampling are proposed. Using the information supported by the concomitant variable, the additional area under the curve of the receiver operating characteristic estimators based on ranked set sampling as well as paired ranked set sampling are also introduced. It is shown either theoretically or numerically that the proposed estimators are consistent under the perfectness situation. It emerges that the concomitant-based estimators are shown to be superior to their competitors provided that the perfect assumption is not sharply violated. In contrast, kernel-based estimators are significantly superior relative to their rivals regardless of the quality of ranking. Finally, the application of the proposed procedures is also demonstrated by using empirical datasets in the context of medicine.

The unit log-log distribution: a new unit distribution with alternative quantile regression modeling and educational measurements applications.

In this paper, we propose a new distribution, named unit log-log distribution, defined on the bounded (0,1) interval. Basic distributional properties such as model shapes, stochastic ordering, quantile function, moments, and order statistics of the newly defined unit distribution are studied. The maximum likelihood estimation method has been pointed out to estimate its model parameters. The new quantile regression model based on the proposed distribution is introduced and it has been derived estimations of its model parameters also. The Monte Carlo simulation studies have been given to see the performance of the estimation method based on the new unit distribution and its regression modeling. Applications of the newly defined distribution and its quantile regression model to real data sets show that the proposed models have better modeling abilities than competitive models. The proposed unit quantile regression model has targeted to explain linear relation between educational measurements of both OECD (Organization for Economic Co-operation and Development) countries and some non-members of OECD countries, and their Better Life Index. The existence of the significant covariates has been seen on the real data applications for the unit median response.

A new alternative quantile regression model for the bounded response with educational measurements applications of OECD countries.

This article introduces a new distribution with two tuning parameters specified on the unit interval. It follows from a 'hyperbolic secant transformation' of a random variable following the Weibull distribution. The lack of research on the prospect of hyperbolic transformations providing flexible distributions over the unit interval is a motivation for the study. The main distributional structural properties of the new distribution are established. The different estimation methods and two simulation works have been derived for model parameters. Subsequently, we develop a related quantile regression model for further statistical perspectives. We consider two real data applications based on the educational measurements of both OECD and some non-members of OECD countries. Our regression model aims to relate the desire to get top grades on certain young students in the OECD countries with some of their Education and School Life Index such as reading performance, work environment at home, and paid work experience. It is shown that the elaborated quantile regression model has a better fitting power than famous regression models when the unit response variable possesses skewed distribution as well as two independent variables are significant in the statistical sense at any standard significance level for the median response.

Estimation of parameters of inverse Weibull distribution and application to multi-component stress-strength model.

The problem of estimation of the parameters of two-parameter inverse Weibull distributions has been considered. We establish existence and uniqueness of the maximum likelihood estimators of the scale and shape parameters. We derive Bayes estimators of the parameters under the entropy loss function. Hierarchical Bayes estimator, equivariant estimator and a class of minimax estimators are derived when shape parameter is known. Ordered Bayes estimators using information about second population are also derived. We investigate the reliability of multi-component stress-strength model using classical and Bayesian approaches. Risk comparison of the classical and Bayes estimators is done using Monte Carlo simulations. Applications of the proposed estimators are shown using real data sets.

A one-parameter discrete distribution for over-dispersed data: statistical and reliability properties with applications.

In the literature of distribution theory, a vast proportion is acquired by discrete distributions and their applications in real-world phenomena. However, in a rapidly changing technological era, the data generated is becoming increasingly complex day by day, making it difficult for us to capture various aspects of this real data through existing discrete models. In view of this, we propose a new flexible discrete distribution with one parameter. Some statistical and reliability are derived. These properties can be expressed as closed-forms. One of the important virtues of this newly evolved model is that it can model not only over-dispersed, positively skewed and leptokurtic data sets, but it can also be utilized for modeling increasing, decreasing and unimodal failure rate. Various estimation approaches are utilized to estimate the model parameter. A simulation study is carried out to examine the performance of the estimators for different sample size. The flexibility of the new model for analyzing different types of data is explained by utilizing four real data sets in different fields. Finally, the proposed model can serve as an alternative model to other distributions in the existing literature for modeling positive real data in several areas.

Acceptance sampling plans from truncated life test based on Tsallis q-exponential distribution.

In this study, we propose a new single acceptance sampling plan from truncated life test assuming that the quality characteristics follow the Tsallis q-exponential distribution. The proposed plan is given, and then we derived the operation characteristics function and calculate the optimal sample size and producer''s risk for some given parameter values to measure the performance of this plan. Also, a comparative study with other sampling plan is discussed to show the benefit of the proposed plan, and real data analysis is given to illustrate the applicability of the proposed plan in the industry.