On hysteretic vector autoregressive model with applications

This paper proposes a new hysteretic vector autoregressive (HVAR) model in which the regime switching may be delayed when the hysteresis variable lies in a hysteresis zone. We integrate an adapted multivariate Student-t distribution from amending the scale mixtures of normal distributions. This HVAR model allows for a higher degree of flexibility in the degrees of freedom for each time series. We use the proposed model to test for a causal relationship between any two target time series. Using posterior odds ratios, we overcome the limitations of the classical approach to multiple testing. Both simulated and real examples herein help illustrate the suggested methods. We apply the proposed HVAR model to investigate the causal relationship between the quarterly growth rates of gross domestic product of United Kingdom and United States. Moreover, we check the pairwise lagged dependence of daily PM2.5 levels in three districts of Taipei.     

Accurate computation of single and product moments of order statistics under progressive censoring

An accurate procedure is proposed to calculate approximate moments of progressive order statistics in the context of statistical inference for lifetime models. The study analyses the performance of power series expansion to approximate the moments for location and scale distributions with high precision and smaller deviations with respect to the exact values. A comparative analysis between exact and approximate methods is shown using some tables and figures. The different approximations are applied in two situations. First, we consider the problem of computing the large sample variance–covariance matrix of maximum likelihood estimators. We also use the approximations to obtain progressively censored sampling plans for log-normal distributed data. These problems illustrate that the presented procedure is highly useful to compute the moments with precision for numerous censoring patterns and, in many cases, is the only valid method because the exact calculation may not be applicable.     

Progressive censoring with fixed censoring times

In this paper, we revisit the progressive Type-I censoring scheme as it has originally been introduced by Cohen [Progressively censored samples in life testing. Technometrics. 1963;5(3):327–339]. In fact, original progressive Type-I censoring proceeds as progressive Type-II censoring but with fixed censoring times instead of failure time based censoring times. Apparently, a time truncation has been added to this censoring scheme by interpreting the final censoring time as a termination time. Therefore, not much work has been done on Cohens's original progressive censoring scheme with fixed censoring times. Thus, we discuss distributional results for this scheme and establish exact distributional results in likelihood inference for exponentially distributed lifetimes. In particular, we obtain the exact distribution of the maximum likelihood estimator (MLE). Further, the stochastic monotonicity of the MLE is verified in order to construct exact confidence intervals for both the scale parameter and the reliability.     

On the power of goodness-of-fit tests for the exponential distribution under progressive Type-II censoring

The aim of this article is to review existing goodness-of-fit tests for the exponential distribution under progressive Type-II censoring and to provide some new ideas and adjustments. In particular, we consider two-parameter exponentially distributed random variables and adapt the proposed test procedures to our scenario if necessary. Then, we compare their power by an extensive simulation study. Furthermore, we propose five new test procedures that provide reasonable alternatives to those already known.     

On MLEs of the parameters of a modified Weibull distribution based on record values

The modified Weibull distribution can be used quite effectively to model complex data from mechanical engineering or survival analysis studies that posses a monotonic or a bathtub-shape hazard rate. In this paper, we study the MLEs of the parameters of a modified Weibull distribution model in the presence of upper kth record values. The existence and uniqueness of the MLEs are proven in this case. Real data analysis is performed for illustrative purposes.     

Inference and optimal design of multiple constant-stress testing for generalized half-normal distribution under type-II progressive censoring

The generalized half-normal (GHN) distribution and progressive type-II censoring are considered in this article for studying some statistical inferences of constant-stress accelerated life testing. The EM algorithm is considered to calculate the maximum likelihood estimates. Fisher information matrix is formed depending on the missing information law and it is utilized for structuring the asymptomatic confidence intervals. Further, interval estimation is discussed through bootstrap intervals. The Tierney and Kadane method, importance sampling procedure and Metropolis-Hastings algorithm are utilized to compute Bayesian estimates. Furthermore, predictive estimates for censored data and the related prediction intervals are obtained. We consider three optimality criteria to find out the optimal stress level. A real data set is used to illustrate the importance of GHN distribution as an alternative lifetime model for well-known distributions. Finally, a simulation study is provided with discussion.     

Confidence regions for Pareto parameters from a single and independent samples

[Abstract] Based on a single and on two independent samples, joint confidence regions for parameters of Pareto distributions are proposed with minimum volume properties and without assigning the confidence level to dimensions. In the one-sample case, comparisons are made to former simultaneous confidence sets for Pareto parameters by means of simulation and a real data set. The two-sample case is studied in various set-ups and comprises simultaneous confidence regions for the shape parameters, the scale parameters, and higher-dimensional vectors of these parameters, where common shape and common scale models are also considered.     

Tempered Mittag-Leffler Lévy processes

In this article, we introduce tempered Mittag-Leffler Lévy processes (TMLLP). TMLLP is represented as tempered stable subordinator delayed by a gamma process. Its probability density function and Lévy density are obtained in terms of infinite series and Mittag-Leffler function, respectively. Asymptotic forms of the tails and moments are given. A step-by-step procedure of the parameters estimation and simulation of sample paths is given. We also provide main results available for Mittag-Leffler Lévy processes (MLLP) and some extensions which are not available in a collective way in a single article. Our results generalize and complement the results available on Mittag-Leffler distribution and MLLP in several directions. Further, the asymptotic forms of the moments of the first-exit times of the TMLLP are also discussed.     

知识分布、衰减程度与产业集群创新模式的内在机制研究

以知识流动为研究视角，将集群创新过程中的知识溢出、吸收能力内生化，构建包含三种创新模式下的产业集群演化模型，重点分析集群知识分布和知识衰减程度与集群创新模式的内在机制及其对创新产出的影响，并进行仿真实验。研究表明：不同知识分布下，混合创新模式的创新产出表现最好，外部吸收创新模式与内部自主创新模式呈现出不同的创新产出演化路径；在外部吸收创新和混合创新模式下，均匀分布型产业集群的创新产出表现最好，集中分布型表现次之，异质分布型表现最差，而在内部自主创新模式下，集中分布型则表现最好；不同创新模式对知识衰减的敏感程度呈现阶段性差异特征。这些结论对产业集群创新和可持续发展具有很好的理论和实践指导意义。