In this paper, we address the challenging problem of statistical inference for unknown parameters in generalized lifetime distributions under double censoring. We propose classical and Bayesian estimation approaches for these parameters, incorporating a range of loss functions in the Bayesian framework to improve flexibility and estimate accuracy. The Bayesian inference is implemented using the Metropolis-Hastings algorithm within a Markov Chain Monte Carlo setting to generate posterior samples. These samples are subsequently utilized to compute Bayes estimates and construct credible intervals, thereby providing a comprehensive measure of parameter uncertainty. The performance of the proposed methods is systematically evaluated through simulation studies, which assess their accuracy under various censoring schemes. Additionally, we present two real-data examples to illustrate the practical applicability and utility of the methods in addressing doubly censored data. Furthermore, we explore optimal experimental design considerations, proposing experimental plans specifically tailored to the double-censoring structure. This study offers new insights into the design and analysis of experiments where double censoring is prevalent, with the potential to optimize both time and resource allocation in such studies.
A proper k-total coloring c of a graph G is a mapping c from V(G) U E(G) to [k] = {1, 2, & centerdot; & centerdot; & centerdot;, k} such that c(x) =/ c(y) where x, y E V(G) U E(G) and x is adjacent to or incident with y. Let jJ(v) denote the product of c(v) and the colors on all the edges incident with v. For each edge uv E E(G), if jJ(u) = jJ(v), then the coloring c is called a neighbor product distinguishing total coloring of G. By chi '' jJ(G), we denote the minimal value of k in such a coloring of G. In this paper, we considered the corona graph G of two arbitrary sub cubic graphs and confirmed that chi '' jJ(G) <= triangle(G) + 3.
The purpose of this work is to study the conformal geometry of vacuum static spaces with a constant scalar curvature, which corresponds to an interesting generalization of the critical point of the equation. We prove that a vacuum static space admitting a non-trivial gradient conformal vector field is isometric to a Euclidean space or to a warped product I & times;phi (m-1) pound of an interval I and an Einstein manifold (m-1) pound, provided that scalar curvature of (m-1) pound is constant.
In this paper, we undertake a deeper study of self-conjugate reciprocal (SCR) polynomials, which ultimately contributes to the construction of new classes of permutation polynomials of simpler forms over Fq2. The primary focus is on identifying the conditions under which certain degree 2 and degree 3 SCR polynomials have no roots in & micro;q+1, the set of (q + 1)th roots of unity-which plays a key role in determining polynomials that permute Fq2. Along the way, we also examine certain higher-degree SCR polynomials that can be reduced to degree 2 SCR polynomials over both odd and even characteristic fields. Furthermore, we investigate SCR polynomials of the form axq+1 + bxq + bx + aq, considering both cases where a E Fq and where a E Fq2 \ Fq.
This study develops a statistical inference framework for a cure fraction based on a competing risks model from the Kumaraswamy-G family of distributions under the Unified Progressive Hybrid Censoring scheme. The latent failure times are assumed to be independent and identically distributed, where each individual is classified as either cured or susceptible to failure from competing causes. Classical and Bayesian inferential procedures are developed for parameter estimation. Maximum likelihood estimation is employed to obtain point estimates and asymptotic confidence intervals, while Bayesian estimation is performed using the Metropolis-Hastings Markov chain Monte Carlo algorithm to obtain posterior estimates and highest posterior density credible intervals. The finite-sample performance of the proposed estimators is evaluated through extensive Monte Carlo simulation studies under various sample sizes and censoring schemes, and levels of partially masking. The methods are compared in terms of bias, mean squared error, coverage probability, and average widths under both restricted and unrestricted parameter spaces. The proposed methodology is illustrated using the publicly available METABRIC breast cancer clinical dataset containing competing risks and long-term survivors. The proposed cure model sufficiently models the Cumulative incidence functions of two causes, particularly under moderate to heavy censoring. Moreover, it highlights the flexibility and effectiveness of the proposed framework for analyzing cure-fraction competing-risks data.
