60 research outputs found
Modeling the Amount of Carbon Dioxide Emissions Application: New Modified Alpha Power Weibull-X Family of Distributions
No full textThe use of statistical distributions to model life phenomena has received considerable attention in the literature. Recent studies have shown the potential of statistical distributions in modeling data in applied sciences, especially in environmental sciences. Among them, the Weibull distribution is one of the most well-known models that can be used very effectively for modeling data in the fields of pollution and gas emissions, to name a few. In this paper, we introduce a family of distributions, which we call the modified Alpha-Power Weibull-X family of distributions. Based on the proposed family, we introduce a new model with five parameters, the modified Alpha-Power Weibull–Weibull distribution. Some mathematical properties were determined. Bayesian and maximum likelihood estimates for the model parameters were derived. The MLEs, bootstrap and Bayesian HPD credibility intervals for the unknown parameters were performed. A Monte Carlo simulation study was performed to evaluate the performance of the estimates. A simulation study was performed based on the parameters of the proposed model. An application to the carbon dioxide emissions dataset was performed to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the model. For this data set, the proposed model is compared with the modified alpha power Weibull exponential distribution and the two-parameter Weibull distribution. To show which of the competing distributions is the best, we draw on certain analytical tools such as the Kolmogorov–Smirnov test. Based on these analytical measures, we found that the new model outperforms the competing models
On Predictive Modeling Using a New Three-Parameters Modification of Weibull Distribution and Application
No full textIn this article, a new modification of the Weibull model with three parameters, the new exponential Weibull distribution (E-WD), is defined. The new model has many statistical advantages, the heavy-tailed behavior and the regular variation property were offered. Many of the important statistical functions of the modified model are presented in closed forms. The flexibility of E-WD has been improved. The proposed model can be used to fit data with different shapes, it can be right-skewed, left-skewed, decreasing, curved and symmetric. Some distribution properties of the proposed model, including moment generating function, characteristic function, moment, quantile and identifiability property, have been derived. In addition to the information generating function, the Shannon entropy and information energy are also discussed. The maximum likelihood approach and Bayesian estimation are used to estimate the distribution parameters. In the Bayesian method, three different loss functions are used. The calculations show the biases and estimated risks to obtain the best estimator. The bootstrap confidence intervals, the asymptotic confidence intervals and the observed variance-covariance matrix are obtained. Metropolis Hastings’ MCMC procedure is used for the calculations. We apply the composite distribution to stock data for four variables. The goodness-of-fit results show that the model performs well compared to its competitors. The proposed model can be used for forecasting and decision making
The Arcsine Kumaraswamy-Generalized Family: Bayesian and Classical Estimates and Application
No full textIn this paper, by including a trigonometric function, we propose a family of heavy-tailed distribution called the arcsine Kumaraswamy generalized-X family of distributions. Based on the proposed approach, a four-parameter extension of the Lomax distribution called the arcsine Kumaraswamy generalized Lomax (ASKUG-LOMAX) distribution is discussed in detail. Maximum likelihood, bootstrap, and Bayesian estimation are used to estimate the model parameters. A simulation study is used to evaluate ASKUG-LOMAX performance. The flexibility and usefulness of the proposed ASKUG-LOMAX distribution to predict unique symmetric and asymmetric patterns is demonstrated by analyzing real data. The results show that the ASKUG-LOMAX model is a good candidate for analyzing claims based on heavy-tailed data
Weighted Extropy for Concomitants of Upper k-Record Values Based on Huang–Kotz Morgenstern of Bivariate Distribution
No full textIn this paper, the marginal distribution of concomitants of k−record values (CKR) based on the Huang–Kotz Farlie–Gumbel–Morgenstern (HK-FGM) family of bivariate distributions is derived. In addition, we obtained the joint distribution of CKR for this family. Also, we obtained the hazard rate, reversed hazard rate, and residual life functions of CKR using the HK-FGM family. The weighted extropy and the weighted cumulative past extropy (WCPJ) are acquired for CKR under the HK-FGM family. In addition, we look into the issue of estimating the WCPJ by combining the empirical method with the concurrent use of KR in the HK-FGM family. Finally, we analyzed real-world data for illustration purposes, and the outcomes are rather striking
Khalil New Generalized Weibull Distribution Based on Ranked Samples: Estimation, Mathematical Properties, and Application to COVID-19 Data
No full textIn this paper, a five-parameter distribution, Khalil’s new generalized Weibull distribution, is defined and studied in detail. Some mathematical and statistical functions are studied. The effects of shape parameters on skewness and kurtosis are studied. Extensions for density and distribution functions are provided. Estimation of the intended model parameters based on ranked samples is investigated. The behavior of the maximum likelihood estimators is examined using a Monte Carlo simulation. In order to predict unique symmetric and asymmetric patterns and illustrate the applicability and potential of the intended distribution, a COVID-19 dataset is analyzed. The goodness-of-fit results of the new generalized Weibull model of Khalil are compared with some other models. Finally, we make some concluding remarks
Memory type general class of estimators for population variance under simple random sampling
No full textWith an emphasis on memory-type approaches, this study presents a class of estimators specifically designed for estimating population variation in simple random sampling (SRS). The term ‘memory-type’ pertaining to the use of exponentially weighted moving averages (EWMA) statistic for the estimation, which utilizes the current and past information in temporal surveys. The study provides expressions for the bias and mean square error (MSE) of these estimators and establishes conditions under which their efficiency represses the conventional and other memory-type estimators. The theoretical findings are reinforced through a comprehensive simulation study conducted on hypothetically sampled populations. Additionally, the effectiveness of the proposed estimators is demonstrated utilizing real-life population data. The findings of simulation and real data application show the superiority of the proposed memory type estimator over the existing usual and memory type estimators
Bivariate and Bilateral Gamma Distributions
No full textThis article review some known bivariate and bilateral (difference) gamma distributions. Some properties, advantages and limitations are pointed out. Two new bivariate gamma distributions using self-decomposability property are introduced. The corresponding bilateral gamma distributions are derived.</jats:p
On Some Quasi-Curves in Galilean Three-Space
No full textIn this paper, the quasi-frame and quasi-formulas are introduced in Galilean three-space. In addition, the quasi-Bertrand and the quasi-Mannheim curves are studied. It is proven that the angle between the tangents of two quasi-Bertrand or quasi-Mannhiem curves is not constant. Furthermore, the quasi-involute is studied. Moreover, we prove that there is no quasi-evolute curve in Galilean three-space. Also, we introduce quasi-Smarandache curves in Galilean three-space. Finally, we demonstrate an illustrated example to present our findings
Negative Binomial Regression Model Estimation Using Stein Approach: Methods, Simulation, and Applications
No full textThe negative binomial regression model (NBRM) is popular for modeling count data and addressing overdispersion issues. Generally, the maximum likelihood estimator (MLE) is used to estimate the NBRM coefficients. However, when the explanatory variables in the NBRM are correlated, the MLE yields inaccurate estimates. To tackle this challenge, we propose a James–Stein estimator for the NBRM. The matrix mean squared error (MSE) and the scalar MSE properties are derived and compared with other estimators, including the ridge estimator (RE), Liu estimator (LE), and the MLE. We assess the performance of the suggested estimator using two real applications and a simulation study, with MSE serving as the assessment criterion. Results from both simulations and real applications demonstrate the superior performance of the proposed estimator over the RE, LE, and MLE
Bayesian Subset Selection of Seasonal Autoregressive Models
No full textSeasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture–normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm
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