General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G.M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883–898], proposed a new generalized distribution (denoted here with the prefix ‘Kw-G’ (Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-G density function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155–161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279–285] and Kw-Flexible Weibull [M. Bebbington, C.D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719–726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Rényi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.     

高校思想政治教育网络教育手段的理性分析

网络技术运用于高校思想政治教育,不仅丰富了思想政治教育的途径和方式,而且也有效地拓展了思想政治教育的空间。但是由于思想观念、技术水平的差异性,网络为思想政治教育提供的手段并没有得到充分地开发利用。因此,大胆实施改革创新,不断完善网络教育手段和方式,是促使思想政治教育功能得以最大程度发挥的重要基础。     

Estimation of weibull location

A simulation study was carried out to compare the performances of two different simple estimators of the location parameter for a three-parameter Weibull distribution Both Estimators have been suggested by recent paper in the literature. Bras and mean square error are examined for many different sample-size and shape-parameter-value combinations. Strong evidence of the domination of one estimator over the other is found.     

Generalized information matrix tests for copulas

We propose a family of goodness-of-fit tests for copulas. The tests use generalizations of the information matrix (IM) equality of White and so relate to the copula test proposed by Huang and Prokhorov. The idea is that eigenspectrum-based statements of the IM equality reduce the degrees of freedom of the test’s asymptotic distribution and lead to better size-power properties, even in high dimensions. The gains are especially pronounced for vine copulas, where additional benefits come from simplifications of score functions and the Hessian. We derive the asymptotic distribution of the generalized tests, accounting for the nonparametric estimation of the marginals and apply a parametric bootstrap procedure, valid when asymptotic critical values are inaccurate. In Monte Carlo simulations, we study the behavior of the new tests, compare them with several Cramer–von Mises type tests and confirm the desired properties of the new tests in high dimensions.     

Testing equality of variances for several normal populations

In this study, we develop a test based on computational approach for the equality of variances of several normal populations. The proposed method is numerically compared with the existing methods. The numeric results demonstrate that the proposed method performs very well in terms of type I error rate and power of test. Furthermore we study the robustness of the tests by using simulation study when the underlying data are from t, exponential and uniform distributions. Finally we analyze a real dataset that motivated our study using the proposed test.     

Tail Behavior and Limit Distribution of Maximum of Logarithmic General Error Distribution

Logarithmic general error distribution, an extension of the log-normal distribution, is proposed. Some interesting properties of the log GED are derived. These properties are applied to establish the asymptotic behavior of the ratio of probability densities and the ratio of the tails of the logarithmic general error and log-normal distributions, and to derive the asymptotic distribution of the partial maximum of an independent and identically distributed sequence obeying the log GED.     

A note on the mean residual life of a coherent system with a cold standby component

In this paper, we investigate the effect of a cold standby component on the mean residual life (MRL) of a system. When the system fails, a cold standby component is immediately put in operation. We particularly focus on the coherent systems in which, after putting the standby component into operation, the failure of the system is due to the next component failure. For these systems, we define MRL functions and obtain their explicit expressions. Also some stochastic ordering results are provided. Such systems include k-out-of-n systems. Hence, our results extend some results in literature.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.     

A new estimator of proportion with a linear function using data from two-decks randomized response model

A new estimator for estimating the proportion of a potentially sensitive attribute in survey sampling has been introduced by solving a linear equation. The proposed estimator has been compared with the estimator proposed by Odumade and Singh (2009) with equal protection to all of the respondents. The asymptotic properties of the proposed estimator are investigated through exact numerical illustrations for different choices of parameters. A non randomized response approach has been suggested. A scope for further research has also been pointed out.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.