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This paper is focused on the research an improved version of the Boltzmann-Poisson model for BaTiO3-ceramics. In the approximation of one relaxation time, for constant external electrical field, this approach included correct quadratic relation for varistor effect in the case of the Heywang model. Within meso-kinetics, quantum corrected Boltzmann-Poisson model, contains space-time correlations for the probability distribution density function f(r, k, t), lead to correct fractional relaxation velocity description. These new results corresponds to our other research based on electronic particles Brownian motion within its fractal nature. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter lifetime model called the Weibull Burr XII distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, and order statistics. The new density function can be expressed as a linear mixture of Burr XII densities. We propose a log-linear regression model using a new distribution so-called the log-Weibull Burr XII distribution. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling various types of data. [ABSTRACT FROM AUTHOR]

This paper provides Bayesian analysis of absolute continuous Marshall–Olkin bivariate Pareto distribution. We consider only three parameters for this Marshall–Olkin bivariate Pareto distribution. We take two types of prior—reference prior and gamma prior for our analysis. Bayesian estimate of the parameters are calculated based on slice cum Gibbs sampler and Lindley approximation. Credible intervals are also provided for all methods and all prior distributions. A real-life data analysis is shown for illustrative purpose. [ABSTRACT FROM AUTHOR]

This paper studies the stationary bootstrap applicability for realized covariations of high frequency asynchronous financial data. The stationary bootstrap method, which is characterized by a block-bootstrap with random block length, is applied to estimate the integrated covariations. The bootstrap realized covariance, bootstrap realized regression coefficient and bootstrap realized correlation coefficient are proposed, and the validity of the stationary bootstrapping for them is established both for large sample and for finite sample. Consistencies of bootstrap distributions are established, which provide us valid stationary bootstrap confidence intervals. The bootstrap confidence intervals do not require a consistent estimator of a nuisance parameter arising from nonsynchronous unequally spaced sampling while those based on a normal asymptotic theory require a consistent estimator. A Monte-Carlo comparison reveals that the proposed stationary bootstrap confidence intervals have better coverage probabilities than those based on normal approximation. [ABSTRACT FROM AUTHOR]

In the wood industry, it is common practice to compare in terms of the ratio of the same-strength properties for lumber of two different dimensions, grades, or species. Because United States lumber standards are given in terms of population fifth percentile, and strength problems arise from the weaker fifth percentile rather than the stronger mean, so the ratio should be expressed in terms of the fifth percentiles rather than the means of two strength distributions. Percentiles are estimated by order statistics. This paper assumes small samples to derive new non parametric methods such as percentile sign test and percentile Wilcoxon signed rank test, construct confidence intervals with covergage rate 1 –αxfor single percentiles, and compute confidence regions for ratio of percentiles based on confidence intervals for single percentiles. Small 1 –αxis enough to obtain good coverage rates of confidence regions most of the time. [ABSTRACT FROM AUTHOR]

This paper deals with Renyi information properties of mixed systems when lifetimes of components are independent and identically distributed. The provided results are obtained by using the concept of Samaniego’s signature. Stochastic comparisons of Renyi entropy for mixed systems are discussed provided that both systems have the same signature. To approximate the behavior of the Renyi entropy, some bounds are also given. In the rest, Renyi discrimination information between the distribution of system’s lifetime and component lifetime are obtained and proved that they are distribution free and depends only on the system signature. [ABSTRACT FROM PUBLISHER]

In the expectation–maximization (EM) algorithm for maximum likelihood estimation from incomplete data, Markov chain Monte Carlo (MCMC) methods have been used in change-point inference for a long time when the expectation step is intractable. However, the conventional MCMC algorithms tend to get trapped in local mode in simulating from the posterior distribution of change points. To overcome this problem, in this paper we propose a stochastic approximation Monte Carlo version of EM (SAMCEM), which is a combination of adaptive Markov chain Monte Carlo and EM utilizing a maximum likelihood method. SAMCEM is compared with the stochastic approximation version of EM and reversible jump Markov chain Monte Carlo version of EM on simulated and real datasets. The numerical results indicate that SAMCEM can outperform among the three methods by producing much more accurate parameter estimates and the ability to achieve change-point positions and estimates simultaneously. [ABSTRACT FROM PUBLISHER]

In practice, it is often not possible to find an appropriate family of distributions which can be used for fitting the sample distribution with high precision. In these cases, it seems to be opportune to search for the best approximation by a family of distributions instead of an exact fit. In this paper, we consider the Anderson–Darling statistic with plugged-in minimum distance estimator for the parameter vector. We prove asymptotic normality of the Anderson–Darling statistic which is used for a test of goodness of approximation. Moreover, we introduce a measure of discrepancy between the sample distribution and the model class. [ABSTRACT FROM AUTHOR]

The performance of attributes control charts is usually evaluated under the assumption of known process parameters (i.e., the nominal proportion of non conforming units or the nominal average number of nonconformities). However, in practice, these process parameters are rarely known and have to be estimated from an in-control Phase I data set. The major contributions of this paper are (a) the derivation of the run length properties of the Run Rules Phase IIcandnpcharts with estimated parameters, particularly focusing on theARL,SDRL, and 0.05, 0.5, and 0.95 quantiles of the run length distribution; (b) the investigation of the numbermof Phase I samples that is needed by these charts in order to obtain similar in-controlARLs to the known parameters case; and (c) the proposition of new specific chart parameters that allow these charts to have approximately the same in-controlARLs as the ones obtained in the known parameters case. [ABSTRACT FROM AUTHOR]

In this paper, when a jointly Type-II censored sample arising fromkindependent exponential populations is available, the conditional MLEs of thekexponential mean parameters are derived. The moment generating functions and the exact densities of these MLEs are obtained using which exact confidence intervals are developed for the parameters. Moreover, approximate confidence intervals based on the asymptotic normality of the MLEs and credible confidence regions from a Bayesian viewpoint are also discussed. An empirical comparison of the exact, approximate, bootstrap, and Bayesian intervals is also made in terms of coverage probabilities. Finally, an example is presented in order to illustrate all the methods of inference developed here. [ABSTRACT FROM AUTHOR]

Sung [On inverse moments for a class of nonnegative random variables. J Inequal Appl. 2010;2010:1–13. Article ID 823767, doi:10.1155/2010/823767] obtained the asymptotic approximation of inverse moments for a class of nonnegative random variables with finite second moments and satisfying a Rosenthal-type inequality. In the paper, we further study the asymptotic approximation of inverse moments for a class of nonnegative random variables with finite first moments, which generalizes and improves the corresponding ones of Wu et al. [Asymptotic approximation of inverse moments of nonnegative random variables. Statist Probab Lett. 2009;79:1366–1371], Wang et al. [Exponential inequalities and inverse moment for NOD sequence. Statist Probab Lett. 2010;80:452–461; On complete convergence for weighted sums of ϕ mixing random variables. J Inequal Appl. 2010;2010:1–13, Article ID 372390, doi:10.1155/2010/372390], Sung (2010) and Hu et al. [A note on the inverse moment for the nonnegative random variables. Commun Statist Theory Methods. 2012. Article ID 673677, doi:10.1080/03610926.2012.673677]. [ABSTRACT FROM PUBLISHER]