Communications in Statistics: Theory and Methods

Hsu, Yu-Sheng; Wu, Cheng-Hsun

doi: 10.1080/03610921003764167pmid: N/A

Although geometric Brownian motion has a great variety of applications, it can not cover all the random phenomena. The purpose of this article is to propose a model that generalizes geometric Brownian motion. We present some interesting applications of this model in financial engineering and statistical inferences for the unknown parameters.

Govindaraju, K.

doi: 10.1080/03610921003764191pmid: N/A

Zero acceptance number sampling inspection plans are commonly employed for compliance sampling and audit inspection purposes. The discriminatory power of zero acceptance number sampling plans is rather poor. This article remedies this disadvantage by chaining past lot results within a quick switching system.

Parsi, S.; Ganjali, M.; Farsipour, N. Sanjari

doi: 10.1080/03610921003764175pmid: N/A

Comparative lifetime experiments are important when the object of a study is to determine the relative merits of two competing duration of life products. This study considers the interval estimation for two Weibull populations when joint Type-II progressive censoring is implemented. We obtain the conditional maximum likelihood estimators of the two Weibull parameters under this scheme. Moreover, simultaneous approximate confidence region based on the asymptotic normality of the maximum likelihood estimators are also discussed and compared with two Bootstrap confidence regions. We consider the behavior of probability of failure structure with different schemes. A simulation study is performed and an illustrative example is also given.

Kim, Hea-Jung

doi: 10.1080/03610921003764183pmid: N/A

This article proposes a class of multivariate bilateral selection t distributions useful for analyzing non-normal (skewed and/or bimodal) multivariate data. The class is associated with a bilateral selection mechanism, and it is obtained from a marginal distribution of the centrally truncated multivariate t. It is flexible enough to include the multivariate t and multivariate skew-t distributions and mathematically tractable enough to account for central truncation of a hidden t variable. The class, closed under linear transformation, marginal, and conditional operations, is studied from several aspects such as shape of the probability density function, conditioning of a distribution, scale mixtures of multivariate normal, and a probabilistic representation. The relationships among these aspects are given, and various properties of the class are also discussed. Necessary theories and two applications are provided.

Rychlik, Tomasz

doi: 10.1080/03610921003764241pmid: N/A

For the distributions with decreasing density and decreasing failure rate, and decreasing density and decreasing failure rate on the average, the quantiles are less than the mean if their orders do not exceed fixed levels. We determine the sharp negative upper bounds on the differences of the small quantiles and means for the distributions from the respective families in terms of scale units generated by pth absolute central moments. We show that the bounds amount trivially to zero when p > 1, and are strictly negative for p = 1.

Yang, Jun; Xie, Min; Goh, Thong Ngee

doi: 10.1080/03610921003746685pmid: N/A

In statistical process control (SPC), if the traditional 3-sigma control limits or probability limits are adopted, some points with relatively high occurrence possibility may be excluded; however, some points with relatively small occurrence possibility may be accepted for asymmetrical or multimodal distributions. Motivated by the highest posterior density credibility interval, we propose control limits based on the narrowest confidence interval to solve the problem, where the narrowest confidence interval denotes the confidence interval with the shortest width. The proposed control limits will not only meet the false alarm requirement, but also ensure that each in-control data point has relatively high occurrence possibility. Some properties of the proposed control limits and its relation to the existing two control limits are presented in the end.

Liu, Xu-Qing; Gao, Feng

doi: 10.1080/03610921003746693pmid: N/A

In this article, we aim to study the linearized ridge regression (LRR) estimator in a linear regression model motivated by the work of Liu (1993). The LRR estimator and the two types of generalized Liu estimators are investigated under the PRESS criterion. The method of obtaining the optimal generalized ridge regression (GRR) estimator is derived from the optimal LRR estimator. We apply the Hald data as a numerical example and then make a simulation study to show the main results. It is concluded that the idea of transforming the GRR estimator as a complicated function of the biasing parameters to a linearized version should be paid more attention in the future.

Miao, Yu; Chen, Ying-Xia

doi: 10.1080/03610921003764209pmid: N/A

Let {X n , n ≥ 1} be a stationary sequence of m-dependent random variables with survival function . The empirical survival function based on X 1,…, X n is proposed as an estimator for . In this article, we obtain some asymptotic results of the survival function estimator, which include uniform moderate deviations, Berry-Esséen bound, Cramér type large deviation, and so on.

Ramos, Alexandra; Ledford, Anthony

doi: 10.1080/03610921003764233pmid: N/A

An alternative limiting point process to that of de Haan (1985) is studied that holds regardless of whether the underlying data generation mechanism is asymptotically dependent or asymptotically independent. We characterize its intensity function in terms of the coefficient of tail dependence and an angular measure which satisfies a normalisation condition. We use this point process to derive a generalisation of standard componentwise maxima results that holds for both asymptotic dependence and asymptotic independence. We illustrate our results using a flexible parametric example and provide methods for simulating from both the limiting point process and the limiting componentwise maxima distribution.

Yenigün, C. D.; Székely, G. J.; Rizzo, M. L.

doi: 10.1080/03610921003764274pmid: N/A

Maximal correlation has several desirable properties as a measure of dependence, including the fact that it vanishes if and only if the variables are independent. Except for a few special cases, it is hard to evaluate maximal correlation explicitly. We focus on two-dimensional contingency tables and discuss a procedure for estimating maximal correlation, which we use for constructing a test of independence. We compare the maximal correlation test with other tests of independence by Monte Carlo simulations. When the underlying continuous variables are dependent but uncorrelated, we point out some cases for which the new test is more powerful.