A discrete mixed distribution: Statistical and reliability properties with applications to model COVID-19 data in various countries.

The aim of this paper is to introduce a discrete mixture model from the point of view of reliability and ordered statistics theoretically and practically for modeling extreme and outliers' observations. The base distribution can be expressed as a mixture of gamma and Lindley models. A wide range of the reported model structural properties are investigated. This includes the shape of the probability mass function, hazard rate function, reversed hazard rate function, min-max models, mean residual life, mean past life, moments, order statistics and L-moment statistics. These properties can be formulated as closed forms. It is found that the proposed model can be used effectively to evaluate over- and under-dispersed phenomena. Moreover, it can be applied to analyze asymmetric data under extreme and outliers' notes. To get the competent estimators for modeling observations, the maximum likelihood approach is utilized under conditions of the Newton-Raphson numerical technique. A simulation study is carried out to examine the bias and mean squared error of the estimators. Finally, the flexibility of the discrete mixture model is explained by discussing three COVID-19 data sets.

A new statistical approach for modeling the bladder cancer and leukemia patients data sets: Case studies in the medical sector.

Statistical methods are frequently used in numerous healthcare and other related sectors. One of the possible applications of the statistical methods is to provide the best description of the data sets in the healthcare sector. Keeping in view the applicability of statistical methods in the medical sector, numerous models have been introduced. In this paper, we also introduce a novel statistical method called, a new modified-G family of distributions. Several mathematical properties of the new modified-G family are derived. Based on the new modified-G method, a new updated version of the Weibull model called, a new modified-Weibull distribution is introduced. Furthermore, the estimators of the parameters of the new modified-G distributions are also obtained. Finally, the applicability of the new modified-Weibull distribution is illustrated by analyzing two medical sets. Using certain analytical tools, it is observed that the new modified-Weibull distribution is the best choice to deal with the medical data sets.

One- and Two-Sample Predictions Based on Progressively Type-II Censored Carbon Fibres Data Utilizing a Probability Model.

New Weibull-Pareto distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering and analysis of some physical properties of chemical compounds such as polymers and carbon fibres. In this paper, we construct the predictive interval of unobserved units in the same sample (one sample prediction) and the future sample based on the current sample (two-sample prediction). The used samples are generated from new Weibull-Pareto distribution due to a progressive type-II censoring scheme. Bayesian and maximum likelihood approaches are implemented to the prediction problems. In the Bayesian approach, it is not easy to simplify the predictive posterior density function in a closed form, so we use the generated Markov chain Monte Carlo samples from the Metropolis-Hastings technique with Gibbs sampling. Moreover, the predictive interval of future upper-order statistics is reported. Finally, to demonstrate the proposed methodology, both simulated data and real-life data of carbon fibres examples are considered to show the applicabilities of the proposed methods.

Asymmetric Power Hazard Distribution for COVID-19 Mortality Rate under Adaptive Type-II Progressive Censoring: Theory and Inferences.

This article investigates the estimation of the parameters for power hazard function distribution and some lifetime indices such as reliability function, hazard rate function, and coefficient of variation based on adaptive Type-II progressive censoring. From the perspective of frequentism, we derive the point estimations through the method of maximum likelihood estimation. Besides, delta method is implemented to construct the variances of the reliability characteristics. Markov chain Monte Carlo techniques are proposed to construct the Bayes estimates. To this end, the results of the Bayes estimates are obtained under squared error and linear exponential loss functions. Also, the corresponding credible intervals are constructed. A simulation study is utilized to assay the performance of the proposed methods. Finally, a real data set of COVID-19 mortality rate is analyzed to validate the introduced inference methods.

Poisson XLindley Distribution for Count Data: Statistical and Reliability Properties with Estimation Techniques and Inference.

In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating function, moment generating function, index of dispersion, Shannon entropy, Mills ratio, mean residual life function, and associated measures are investigated. All these properties can be expressed in explicit forms. It is found that the new probability mass function can be utilized to model positively skewed data with leptokurtic shape. Moreover, the new discrete distribution is considered a proper tool to model equi- and over-dispersed phenomena with increasing hazard rate function. The distribution parameter is estimated by different six estimation approaches, and the behavior of these methods is explored using the Monte Carlo simulation. Finally, two applications to real life are presented herein to illustrate the flexibility of the new model.

Bayesian and Frequentist Inferences on a Type I Half-Logistic Odd Weibull Generator with Applications in Engineering.

In this article, we have proposed a new generalization of the odd Weibull-G family by consolidating two notable families of distributions. We have derived various mathematical properties of the proposed family, including quantile function, skewness, kurtosis, moments, incomplete moments, mean deviation, Bonferroni and Lorenz curves, probability weighted moments, moments of (reversed) residual lifetime, entropy and order statistics. After producing the general class, two of the corresponding parametric statistical models are outlined. The hazard rate function of the sub-models can take a variety of shapes such as increasing, decreasing, unimodal, and Bathtub shaped, for different values of the parameters. Furthermore, the sub-models of the introduced family are also capable of modelling symmetric and skewed data. The parameter estimation of the special models are discussed by numerous methods, namely, the maximum likelihood, simple least squares, weighted least squares, Cramér-von Mises, and Bayesian estimation. Under the Bayesian framework, we have used informative and non-informative priors to obtain Bayes estimates of unknown parameters with the squared error and generalized entropy loss functions. An extensive Monte Carlo simulation is conducted to assess the effectiveness of these estimation techniques. The applicability of two sub-models of the proposed family is illustrated by means of two real data sets.

Adjunctive treatment of chronic periodontitis with daily dietary supplementation with omega-3 Fatty acids and low-dose aspirin.

BACKGROUND: Host modulatory therapy has been proposed as a treatment for periodontal diseases. Omega-3 (ω-3) polyunsaturated fatty acids (PUFAs), including docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), were shown to have therapeutic anti-inflammatory and protective actions in inflammatory diseases including periodontitis. The goal of this study was to test an innovative strategy for periodontal treatment in a clinical experiment. METHODS: Eighty healthy subjects (40 in each group) with advanced chronic periodontitis were enrolled in Mansoura, Egypt, in a parallel-design, double-masked clinical study. The control group was treated with scaling and root planing (SRP) and a placebo, whereas the ω-3 group was treated with SRP followed by dietary supplementation of fish oil (900 mg EPA + DHA) and 81 mg aspirin daily. Saliva samples were obtained from all patients at baseline and 3 and 6 months for evaluation of receptor activator of nuclear factor-kappa B ligand (RANKL) and matrix metalloproteinase-8 (MMP-8). Plaque and gingival indices, bleeding on probing, probing depths, and attachment levels were recorded at the same time points. RESULTS: Statistical analyses demonstrated a significant reduction in probing depths and a significant attachment gain after 3 and 6 months in the ω-3 group compared to baseline and the control group (P <0.05). Salivary RANKL and MMP-8 levels showed significant reductions in the ω-3 group in response to treatment at 3 and 6 months and compared to the control group at 6 months (P <0.01). Supplementation with ω-3 + aspirin resulted in a significant shift in the frequency of pockets with probing depths <4 mm (P <0.05). CONCLUSION: The results of this preliminary clinical study suggest that dietary supplementation with ω-3 PUFAs and 81 mg aspirin may provide a sustainable, low-cost intervention to augment periodontal therapy.