On The Burr XII-Gamma Distribution: Development, Properties, Characterizations and Applications

We introduce a four-parameter lifetime model with flexible hazard rate called the Burr XII gamma (BXIIG) distribution. We derive the BXIIG distribution from (i) the T-X family technique and (ii) nexus between the exponential and gamma variables. The failure rate function for the BXIIG distribution is flexible as it can accommodate various shapes such as increasing, decreasing, decreasing-increasing, increasing-decreasing-increasing, bathtub and modified bathtub. Its density function can take shapes such as exponential, J, reverse-J, left-skewed, right-skewed and symmetrical. To illustrate the importance of the BXIIG distribution, we establish various mathematical properties such as random number generator, ordinary moments, generating function, conditional moments, density functions of record values, reliability measures and characterizations. We address the maximum likelihood estimation for the parameters. We estimate the adequacy of the estimators via a simulation study. We consider applications to two real data sets to prove empirically the potentiality of the proposed model.

Second-Order Least Squares Estimation in Nonlinear Time Series Models with ARCH Errors

Many financial and economic time series exhibit nonlinear patterns or relationships. However, most statistical methods for time series analysis are developed for mean-stationary processes that require transformation, such as differencing of the data. In this paper, we study a dynamic regression model with nonlinear, time-varying mean function, and autoregressive conditionally heteroscedastic errors. We propose an estimation approach based on the first two conditional moments of the response variable, which does not require specification of error distribution. Strong consistency and asymptotic normality of the proposed estimator is established under strong-mixing condition, so that the results apply to both stationary and mean-nonstationary processes. Moreover, the proposed approach is shown to be superior to the commonly used quasi-likelihood approach and the efficiency gain is significant when the (conditional) error distribution is asymmetric. We demonstrate through a real data example that the proposed method can identify a more accurate model than the quasi-likelihood method.

Mathematical modeling of pyroxene-magnetite crystalline shales elastic and acoustic properties

The analysis of the results of mathematical modeling of the influence of the format, mineral concentration and fracture of metamorphic crystalline shales of the Pishcha iron ore structure is presented. The aim of this work is to analyze the influence of mineral composition, types, orientation and concentration of mineral inclusions and microcracks on the acoustic and elastic properties of a group of samples of “quartz-magnetite-pyroxene” crystalline shales of Pishchans’ka iron ore structure. Based on the method of conditional moments, mathematical modeling of the influence of the format, orientation and content of mineral grains, as well as the concentration and format of cracking on the acoustic and elastic properties of rocks of the Pishchans`ka iron ore structure was performed. According to the obtained data, a weak effect of changes in the content of rock-forming minerals and a significant effect of different types of fractures on the value of elastic and acoustic anisotropy (10-40%) was proved. Elastic constants of models with layered and chaotic orientation of structural-textural elements are calculated. It is established that most models, as well as basic samples have a rhombic type of acoustic symmetry. When comparing the stereoprojections of the anisotropy parameters of real samples with the stereoprojections obtained during modeling, the authors found that in most samples there is a double system of cracking: chaotic and directed in the area of shale. The results of mathematical modeling showed that for models with ordered crack orientation, the change in the format and concentration of voids is a defining characteristic. This effect is significantly smaller for models with a chaotic arrangement of structural elements. It is proved that models with a combined (layered and chaotically oriented) type of fracture are the closest to real samples. The authors show that this technique allows you to create and operate models close to the real geological environment.

On the T-X Class of Topp Leone-G Family of Distributions: Statistical Properties and Applications

This article investigates the T-X class of Topp Leone- G family of distributions. Some members of the new family are discussed. The exponential-Topp Leone-exponential distribution (ETLED) which is one of the members of the family is derived and some of its properties which include central and non-central moments, quantiles, incomplete moments, conditional moments, mean deviation, Bonferroni and Lorenz curves, survival and hazard functions, moment generating function, characteristic function and R`enyi entropy are established. The probability density function (pdf) of order statistics of the model is obtained and the parameter estimation is addressed with the maximum likelihood method (MLE). Three real data sets are used to demonstrate its application and the results are compared with two other models in the literature.

Application to Engineering and Medical Data Using Three-Parameter Exponential Model

This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.

Cross-Hedging Portfolios in Emerging Stock Markets: Evidence for the LATIBEX Index

We consider alternative possibilities for hedging spot positions on the FTSE LATIBEX Index, the index of the only international market exclusively for Latin American firms that is denominated by the euro. Since there is not a futures market on the index, it is unclear whether a relatively successful hedge can be found. We explore the plausibility of employing futures on four stock market indices: EUROSTOXX 50, S&P500, BOVESPA, and IPC, and simulate the results that could be obtained by a hedge position based on either unconditional or conditional second order moments estimated from different asymmetric GARCH models. Several criteria for hedging effectiveness suggest that futures contracts on BOVESPA should be preferred, and that a salient reduction in risk can be achieved over the unhedged LATIBEX portfolio. The evidence in favor of a better performance of conditional moments is very clear, without significant differences among the alternative GARCH specifications.

Estimation of Sine Inverse Exponential Model under Censored Schemes

In this article, we introduce a new one-parameter model, which is named sine inverted exponential (SIE) distribution. The SIE distribution is a new extension of the inverse exponential (IE) distribution. The SIE distribution aims to provide the SIE model for data-fitting purposes. The SIE distribution is more flexible than the inverted exponential (IE) model, and it has many applications in physics, medicine, engineering, nanophysics, and nanoscience. The density function (PDFu) of SIE distribution can be unimodel shape and right skewed shape. The hazard rate function (HRFu) of SIE distribution can be J-shaped and increasing shaped. We investigated some fundamental statistical properties such as quantile function (QFu), moments (Mo), moment generating function (MGFu), incomplete moments (ICMo), conditional moments (CMo), and the SIE distribution parameters were estimated using the maximum likelihood (ML) method for estimation under censored samples (CS). Finally, the numerical results were investigated to evaluate the flexibility of the new model. The SIE distribution and the IE distribution are compared using two real datasets. The numerical results show the superiority of the SIE distribution.

Classical and Bayesian Inference of a Mixture of Bivariate Exponentiated Exponential Model

Exponentiated exponential (EE) model has been used effectively in reliability, engineering, biomedical, social sciences, and other applications. In this study, we introduce a new bivariate mixture EE model with two parameters assuming two cases, independent and dependent random variables. We develop a bivariate mixture starting from two EE models assuming two cases, two independent and two dependent EE models. We study some useful statistical properties of this distribution, such as marginals and conditional distributions and product moments and conditional moments. In addition, we study a dependent case, a new mixture of the bivariate model based on EE distribution marginal with two parameters and with a bivariate Gaussian copula. Different methods of estimation for the model parameters are used both under the classical and under the Bayesian paradigm. Some simulation studies are presented to verify the performance of the estimation methods of the proposed model. To illustrate the flexibility of the proposed model, a real dataset is reanalyzed.