<p>A trinomial difference distribution is defined and its distributional properties are illustrated. This distribution present the binomial difference distribution as a special case. The moment estimators and maximum likelihood estimators of the trinomial difference distribution are compared via simulation study. Two applications are modeled with the trinomial difference distribution and compared with other possible distributions.</p>
The Pareto distribution is widely used to model industrial, biological, engineering, and other various types of data. A new generalized model, namely the neutrosophic Pareto distribution (NPD), is developed in this article. The proposed model is a neutrosophic variant of the classical Pareto distribution, potentially useful for analyzing vague, unclear, indeterminate, or imprecise data. The structure form of the proposed distribution is skewed to the right and determined to be unimodal. Several characteristics of the NPD are investigated under the neutrosophic framework. The expressions for basic properties such as mean, variance, raw moments, and shape coefficients are obtained. The maximum likelihood approach is presented for estimating the imprecise distributional parameters of the proposed model. The extended notions of the NPD are explained with various key functions in the domain of applied statistical methods. Finally, the practical benefits of NPD are proven by analyzing two real datasets.
In this work, we presented the type I half logistic Burr-Weibull distribution, which is a unique continuous distribution. It offers several superior benefits in fitting various sorts of data. Estimates of the model parameters based on classical and nonclassical approaches are offered. Also, the Bayesian estimates of the model parameters were examined. The Bayesian estimate method employs the Monte Carlo Markov chain approach for the posterior function since the posterior function came from an uncertain distribution. The use of Monte Carlo simulation is to assess the parameters. We established the superiority of the proposed distribution by utilising real COVID-19 data from varied countries such as Saudi Arabia and Italy to highlight the relevance and flexibility of the provided technique. We proved our superiority using both real data.
This paper is devoted to study the problem of stability, chaos behavior and parameters estimation of the habitat destruction model with three-species (prey, predator and top-predator). The mathematical formula of the model and its proposed interactions are presented. Some important special solutions of systems are discussed. The stationary states of the model are derived. Local stability conditions for the stationary states are derived. Furthermore, the chaotic behavior of the model is discussed and presented graphically. Using Liapunov stability technique, the dynamic estimators of the unknown probabilities and their updating rules are derived. It is found that, the control laws are non-linear functions of the species densities. Numerical illustrative examples are carried out and presented graphically.
Proposing new families of probability models for data modeling in applied sectors is a prominent research topic. This paper also proposes a new method based on the trigonometric function to derive the updated form of the existing probability models. The proposed family is called the cotangent trigonometric-G family of distributions. Based on the cotangent trigonometric-G method, a new version of the Weibull model, namely, the cotangent trigonometric Weibull distribution, is studied. Certain mathematical properties of the cotangent trigonometric-G family are derived. The estimators of the cotangent trigonometric-G distributions are obtained via the maximum likelihood method. The Monte Carlo simulation study is conducted to assess the performances of the estimators. Finally, two applications from the health sector are considered to illustrate the cotangent trigonometric-G method. Based on seven evaluating criteria, it is observed that the cotangent trigonometric-G significantly improves the fitting power of the existing models.
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