On bootstrap based variance estimation under fine stratification.

The primary focus of all sample surveys is on providing point estimates for the parameters of primary interest, and also estimating the variance associated with those point estimates to quantify the uncertainty. Larger samples and important measurement tools can help to reduce the point estimates' uncertainty. Numerous effective stratification criteria may be used in survey to reduce variance within stratum. In fine stratification design, the population is divided into numerous small strata, each containing a relatively small number of sampling units as one or two. This is done to ensure that certain characteristics or subgroups of the population are well-represented in the sample. But with many strata, the sample size within each stratum can become small, potentially resulting in higher errors and less stable estimates. The variance estimation process becomes difficult when we only have one unit per stratum. In that case, the collapsed stratum technique is the classical methods for estimating variance. This method, however, is biased and results in an overestimation of the variance. This paper proposes a bootstrap-based variance estimator for the total population under fine stratification, which overcomes the drawbacks of the previously explored estimation approach. Also, the estimator's properties were investigated. A simulation study and practical application on survey of mental health organizations data were done to investigate properties of the proposed estimators. The results show that the proposed estimator performs well.

General two-parameter distribution: Statistical properties, estimation, and application on COVID-19.

In this paper, we introduced a novel general two-parameter statistical distribution which can be presented as a mix of both exponential and gamma distributions. Some statistical properties of the general model were derived mathematically. Many estimation methods studied the estimation of the proposed model parameters. A new statistical model was presented as a particular case of the general two-parameter model, which is used to study the performance of the different estimation methods with the randomly generated data sets. Finally, the COVID-19 data set was used to show the superiority of the particular case for fitting real-world data sets over other compared well-known models.

Weighted power Maxwell distribution: Statistical inference and COVID-19 applications.

During the course of this research, we came up with a brand new distribution that is superior; we then presented and analysed the mathematical properties of this distribution; finally, we assessed its fuzzy reliability function. Because the novel distribution provides a number of advantages, like the reality that its cumulative distribution function and probability density function both have a closed form, it is very useful in a wide range of disciplines that are related to data science. One of these fields is machine learning, which is a sub field of data science. We used both traditional methods and Bayesian methodologies in order to generate a large number of different estimates. A test setup might have been carried out to assess the effectiveness of both the classical and the Bayesian estimators. At last, three different sets of Covid-19 death analysis were done so that the effectiveness of the new model could be demonstrated.

A New Model of Discrete-Continuous Bivariate Distribution with Applications to Medical Data.

The bivariate Poisson exponential-exponential distribution is an important lifetime distribution in medical data analysis. In this article, the conditionals, probability mass function (pmf), Poisson exponential and probability density function (pdf), and exponential distribution are used for creating bivariate distribution which is called bivariate Poisson exponential-exponential conditional (BPEEC) distribution. Some properties of the BPEEC model are obtained such as the normalized constant, conditional densities, regression functions, and product moment. Moreover, the maximum likelihood and pseudolikelihood methods are used to estimate the BPEEC parameters based on complete data. Finally, two data sets of real bivariate data are analyzed to compare the methods of estimation. In addition, a comparison between the BPEEC model with the bivariate exponential conditionals (BEC) and bivariate Poisson exponential conditionals (BPEC) is considered.