Nicholas Makumi

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.

Smooth non-parametric quantile function estimators on basis of symmetric kernels exhibit boundary bias due to spill-over near the edges. An improved non-parametric estimator of a quantile function under simple random sampling without replacement is proposed, based on a multiplicative bias corrected distribution function. There is no spill-over around the edges with our new quantile estimator. The proposed quantile estimator's asymptotic properties are investigated. The suggested method is compared to existing estimators using real data set findings, demonstrating the improved performance.

This article introduces a new statistical distribution called the power unit Burr-XII distribution, which is an extension of the Burr XII distribution obtained through a power transform. This paper investigates several statistical properties of this new model, including mode, moments, moment generating and characteristic functions, entropy, and Bonferroni and Lorenz curves. In addition, various classical estimators for the parameters of the power unit Burr-XII distribution are evaluated, including maximum likelihood estimates, ordinary least squares estimates, maximum product of interval estimates, Anderson–Darling, right and left tail Anderson–Darling, and Cramer–von Mises estimators. This study provides tables and graphs to illustrate the performance of these methods under different scenarios and sample sizes. The results of the proposed distribution in different fields of application are shown using the mortality rates of COVID-19 patients in Spain and flood data from 20 observations. As a result of both applications, it was observed that the proposed distribution gave better results compared to other well-known distributions, such as the beta distribution, transformed gamma distribution, log-weighted power distribution, transmuted power distribution, Kumaraswamy distribution, Topp–Leone distribution, exponentiated reduce Kies distribution, and exponentiated Topp–Leone distribution.

This article aims to introduce the inverse new XLindley distribution, a further extension of the new XLindley distribution. The article explores various properties of the proposed model, such as the quantile function, stochastic orders, entropies, fuzzy reliability, moments, and stress–strength estimation. The paper also compares different methods of estimating the parameters of the proposed model and evaluates their performance using a simulation study. Moreover, the paper demonstrates the usefulness of the proposed model by applying it to two real datasets. The article shows that the proposed model fits the data better than seven existing models based on model selection criteria, goodness-of-fit test statistics, and graphical visualizations. The paper concludes that the new model can be a valuable tool for modeling and analyzing hazard functions or survival data in various fields and contributing to probability theory and statistical inferences.

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.

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.

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.

Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic‐X (NFLog‐X) family. The suggested NFLog‐X family is obtained by applying the T‐X method together with the exponential model having the PDF m(t) = e^−t. Based on the NFLog‐X approach, a three parameters probability distribution, namely, a new flexible logarithmic‐Weibull (NFLog‐Wei) distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog‐X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog‐Wei distribution. Comparisons are made between the analytical goodness‐of‐fit metrics of the suggested distribution. We made comparison with the (i) alpha power transformed Weibull, (ii) exponentiated Weibull, (iii) Weibull, (iv) flexible reduced logarithmic‐Weibull, and (v) Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions.

The problem in nonparametric estimation of finite population total particularly when dealing with high‐dimensional datasets is addressed in this paper. The coverage properties of a robust finite population total estimator based on a feedforward backpropagation neural network developed with the help of a superpopulation model are computed, and a comparison with existing model‐based estimators that can handle high‐dimensional datasets is conducted to evaluate the estimator’s performance using simulated datasets. The results presented in this paper show good performance in terms of bias, MSE, and mean absolute error for the feedforward backpropagation neural network estimator as compared to other identified existing estimators of finite population total in high‐dimensional datasets. In this regard, the paper recommends the use of the proposed estimator in estimating population parameters such as population total in the presence of high‐dimensional datasets.

In the context of stratified sampling, we develop a nonparametric regression technique to estimating finite population quantiles in model‐based frameworks using a multiplicative bias correction strategy. Furthermore, the proposed estimator’s asymptotic behavior is presented, and when certain conditions are met, the estimator is observed to be asymptotically unbiased and asymptotically consistent. Simulation studies were conducted to determine the proposed estimator’s performance for the three quartiles of two fictitious populations under varied distributional assumptions. Based on relative biases, mean‐squared errors, and relative root‐mean‐squared errors, the proposed estimator can be extremely satisfactory, according to these findings.