In Statistical theory, inclusion of an additional parameter to standard distributions is a usual practice. In this study, a new distribution referred to as Alpha-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution, including moment generating function, mode, quantiles, entropies, mean residual life function, stochastic orders and order statistics are obtained. Parameters of the proposed distribution have been estimated using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that the proposed distribution outperforms different variants of Pareto distribution on the basis of model selection criteria.

Educational researchers, psychologists, social, epidemiological and medical scientists are often dealing with multilevel data. Sometimes, the response variable in multilevel data is categorical in nature and needs to be analyzed through Multilevel Logistic Regression Models. The main theme of this paper is to provide guidelines for the analysts to select an appropriate sample size while fitting multilevel logistic regression models for different threshold parameters and different estimation methods. Simulation studies have been performed to obtain optimum sample size for Penalized Quasi-likelihood (PQL) and Maximum Likelihood (ML) Methods of estimation. Our results suggest that Maximum Likelihood Method performs better than Penalized Quasi-likelihood Method and requires relatively small sample under chosen conditions. To achieve sufficient accuracy of fixed and random effects under ML method, we established ''50/50" and ''120/50" rule respectively. On the basis our findings, a ''50/60" and ''120/70" rules under PQL method of estimation have also been recommended.

In this paper, we produced a new family of distribution called Gull Alpha Power Family of distributions (GAPF). A Special case of GAPF is derived by considering the Weibull distribution as a baseline distribution called Gull Alpha Power Weibull distribution (GAPW). The suitability of the proposed distribution derives from its ability to model both the monotonic and nonmonotonic hazard rate functions which are a common practice in survival analysis and reliability engineering. Various statistical properties were derived in addition to their special cases. The unknown parameters of the model are estimated using the maximum likelihood method. Moreover, the usefulness of the proposed distribution is supported by using two real lifetime data sets as well as simulated data.

In this paper, we have focused on machine learning (ML) feature selection (FS) algorithms for identifying and diagnosing multidrug-resistant (MDR) tuberculosis (TB). MDR-TB is a universal public health problem, and its early detection has been one of the burning issues. The present study has been conducted in the Malakand Division of Khyber Pakhtunkhwa, Pakistan, to further add to the knowledge on the disease and to deal with the issues of identification and early detection of MDR-TB by ML algorithms. These models also identify the most important factors causing MDR-TB infection whose study gives additional insights into the matter. ML algorithms such as random forest, k-nearest neighbors, support vector machine, logistic regression, leaset absolute shrinkage and selection operator (LASSO), artificial neural networks (ANNs), and decision trees are applied to analyse the case-control dataset. This study reveals that close contacts of MDR-TB patients, smoking, depression, previous TB history, improper treatment, and interruption in first-line TB treatment have a great impact on the status of MDR. Accordingly, weight loss, chest pain, hemoptysis, and fatigue are important symptoms. Based on accuracy, sensitivity, and specificity, SVM and RF are the suggested models to be used for patients’ classifications.

The medical data are often filed for each patient in clinical studies in order to inform decision-making. Usually, medical data are generally skewed to the right, and skewed distributions can be the appropriate candidates in making inferences using Bayesian framework. Furthermore, the Bayesian estimators of skewed distribution can be used to tackle the problem of decision-making in medicine and health management under uncertainty. For medical diagnosis, physician can use the Bayesian estimators to quantify the effects of the evidence in increasing the probability that the patient has the particular disease considering the prior information. The present study focuses the development of Bayesian estimators for three-parameter Frechet distribution using noninformative prior and gamma prior under LINEX (linear exponential) and general entropy (GE) loss functions. Since the Bayesian estimators cannot be expressed in closed forms, approximate Bayesian estimates are discussed via Lindley’s approximation. These results are compared with their maximum likelihood counterpart using Monte Carlo simulations. Our results indicate that Bayesian estimators under general entropy loss function with noninformative prior (BGENP) provide the smallest mean square error for all sample sizes and different values of parameters. Furthermore, a data set about the survival times of a group of patients suffering from head and neck cancer is analyzed for illustration purposes.