A copula-based bivariate unit power-Weibull distribution is proposed using the Farlie-Gumbel-Morgenstern copula. The construction preserves the marginal distributions and leads to an explicit expression for the joint density on (0,1)2 . We study dependence properties and derive closed-form expressions for mixed moments, which are represented by absolutely convergent Meijer G -function series. An entropy decomposition involving the copula entropy is obtained, together with a convergent series representation for the latter. Identifiability and asymptotic properties of the maximum likelihood estimator are established. The analysis provides a mathematically explicit bivariate extension of the UPWD distribution and complements existing univariate results through tractable dependence modeling, moment representations, entropy analysis, and likelihood-based inference.
The latent Weibull model has recently been reported to be a superior testing tool for comparing two treatments with ordinal responses. Response-adaptive procedures were also developed for the design of these clinical studies. The test statistic is constructed on the basis of the latent Weibull model. Due to the need for model identification, the estimation procedure relies on the selection of one of the treatments as a reference, which is modeled by a standard Weibull distribution. However, it is unclear whether the choice of the reference affects the test procedure. The objective of this short paper is to provide a theoretical proof of this crucial invariance property, under which the test conclusion is invariant to the choice of the reference. A clinical example is also used to illustrate the invariance property.
In this paper, we study series and parallel systems composed of m dependent subsystems consisting of dependent and heterogeneous components. The components of the system follow additive or multiplicative hazard models, and their dependence structure is modeled by Archimedean copula. We derive sufficient conditions for comparing two series (parallel) systems stochastically under three different scenarios. We first assume that the vector of the additive or multiplicative hazard parameters of the first system majorizes to that of the second one. Secondly, we assume that the vector of the number of components in each subsystem of the first system majorizes to that of the second one. Thirdly, we assume that two systems have different numbers of subsystems formed by different numbers of components. At the end, we provide some numerical examples to illustrate the developed results of this paper.
Uniform design in constrained experimental domains (UDCED) poses significant challenges due to the complexity of constraints and high dimensionality. Although the advanced two-phase differential evolution (ToPDE) algorithm has shown improvements in search capabilities, it still suffers from low evolutionary efficiency and limited solution granularity. To address these limitations, this paper proposes the Charge Repulsion Algorithm (CRA), a novel algorithm specifically designed for uniform design in constrained experimental domains for UDCEDs. In CRA, sample points within the constrained domain are modeled as equal-mass spheres carrying identical charges. The algorithm leverages the physical principle that like-charged objects repel each other, thereby promoting uniform distribution by maximizing the minimum inter-point distance. To enhance global search performance, CRA integrates the iterative point deletion strategy from ToPDE and dynamically relocates sample points to sparser regions using the minimum distance (MD) criterion. This hybrid mechanism enables the algorithm to escape local optima and effectively handle complex constraints and high-dimensional search spaces. Experimental results demonstrate that CRA consistently outperforms ToPDE under both the MD and minimum distance maximization criteria, exhibiting superior solution quality and robustness.
The study of the generating function approach to entropy has gained popularity due to its ability to produce several well-known entropy measures found in the literature. In this work, we define the weighted cumulative residual entropy generating function (WCREGF) and study its properties. We then introduce the dynamic weighted cumulative residual entropy generating function (DWCREGF). It is shown that the DWCREGF uniquely determines the distribution. We study some characterization results using the relationship between the DWCREGF and the hazard rate and/or the mean residual life function. Using a characterization based on DWCREGF, we propose a new goodness-of-fit test for the Rayleigh distribution. A Monte Carlo simulation study is conducted to evaluate the performance of the proposed test. Finally, the test is illustrated by means of two real data sets.
This paper proposes a novel and flexible framework for constructing bivariate distribution models in the mixed setting where one variable is discrete and the other is continuous. The proposed approach enables the systematic development of analytically tractable joint distributions with explicit marginals and conditional structures. To illustrate its applicability, two bivariate models are developed and fitted to a real-world dataset on average credit card expenditure and number of derogatory reports. Explicit closed-form expressions for the joint moments are derived, and the dependence structure is rigorously examined through conditional behavior, local dependence properties, and stochastic ordering. Furthermore, important distributional properties of the concomitants of order statistics arising from the proposed models are established.
In this paper, linear Bayesian estimator for parameter vector of linear model with an inequality constraint is considered. Firstly, linear Bayesian estimator is constructed based on the inequality constrained least-squared estimator of parametric vector. Secondly, the dominance properties for proposed estimator are analyzed by mean square error matrix. Finally, a simulation study and real data analysis are performed to illustrate the theoretical results, respectively. It is shown that linear Bayesian estimator dominates the inequality constrained least-squared estimator and approaches Bayesian estimator.
Let {X,Xn;n >= 1} be a sequence of identically distributed random variables in a sub-linear expectation space (Omega,H,E). Suppose that Xk is independent of (Xk+1,& mldr;,Xn) for each k=1,& mldr;,n-1,n >= 1. We establish Baum-Katz-type complete and complete moment convergence theorems for the maximum of weighted sums under optimal moment condition in a sub-linear expectation space. As an application of our complete convergence theorem, strong laws for weighted sums is obtained. Our results generalize and improve the corresponding results of the probability space.
Sliced inverse regression (SIR) is a popular framework for supervised dimension reduction, which projects high-dimensional covariates onto a low-dimensional linear subspace without information loss. In this article, we extend SIR to a semi-supervised setting with limited labeled data and abundant unlabeled data, and we explicitly exploit machine learning predictions to guide slice assignment. The proposed Prediction-Assisted Sliced Inverse Regression (PASIR) uses outcome predictions to determine whether unobserved responses fall into predefined slices, rather than imputing their exact values, and leverages the slice structure of SIR, which only depends on subgroup membership. We formulate the selection of unlabeled points as a convex quadratic program that jointly optimizes kernel-based diversity and slice-wise false selection rate (FSR) control under a fixed measurement budget for labels. Numerical simulations and a real-data example validate the superior performance of the proposed strategy.
The pricing problem of Asian options is investigated under the generalized fractional Brownian motion model. The analytical formula for pricing geometric Asian option with fixed strike price is derived. An approximate analytical formula for valuing arithmetic Asian option is obtained. Moreover, We validate the accuracy of the analytical formula through Monte Carlo simulation, and provide some numerical analysis results.
This paper investigates a statistical inference issue concerning two drift parameter estimators in the complex-valued Vasicek model influenced by fractional Brownian motion. We develop a moment estimator specifically for the mean-reversion parameter and construct the least squares estimators for two drift parameters. Furthermore, they are demonstrated to be of strong consistency and asymptotic normality. This extends the findings of Shen et al. to the case of Hurst index H is an element of(14,12) , as well as generalizes the results of Alazemi et al. from the Ornstein-Uhlenbeck process to the Vasicek model. The key way of our computations is a novel inner product formula on the canonical Hilbert space associated with fractional Brownian motion in Alazemi et al. for H is an element of(0,12) . The main results involve the utilization of the complex fourth moment theorems and the Garsia-Rodemich-Rumsey inequality.
