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131.
Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes
Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine the performance of these methods of inference. Finally, a numerical example is presented in order to illustrate all the methods of inference developed here. 相似文献
132.
Change-over designs with independently distributed errors in the model have been studied extensively in the literature. Martin and Eccleston (2001) gave an algorithm for the generation of efficient change-over designs when the errors are correlated. This article proposes an algorithm for the generation of efficient change-over designs for estimation of direct effects of treatments in the presence of first-order residual effects in the model and when the errors are correlated. 相似文献
133.
Katarzyna Budny 《统计学通讯:理论与方法》2013,42(17):5220-5223
ABSTRACTWe extend Chebyshev's inequality to a random vector with a singular covariance matrix. Then we consider the case of a multivariate normal distribution for this generalization. 相似文献
134.
Wilfrido J. Paredes-García 《统计学通讯:理论与方法》2013,42(23):5877-5888
AbstractIn choice experiments the process of decision-making can be more complex than the proposed by the Multinomial Logit Model (MNL). In these scenarios, models such as the Nested Multinomial Logit Model (NMNL) are often employed to model a more complex decision-making. Understanding the decision-making process is important in some fields such as marketing. Achieving a precise estimation of the models is crucial to the understanding of this process. To do this, optimal experimental designs are required. To construct an optimal design, information matrix is key. A previous research by others has developed the expression for the information matrix of the two-level NMNL model with two nests: Alternatives nest (J alternatives) and No-Choice nest (1 alternative). In this paper, we developed the likelihood function for a two-stage NMNL model for M nests and we present the expression for the information matrix for 2 nests with any amount of alternatives in them. We also show alternative D-optimal designs for No-Choice scenarios with similar relative efficiency but with less complex alternatives which can help to obtain more reliable answers and one application of these designs. 相似文献
135.
Sanpei Kageyama 《统计学通讯:理论与方法》2013,42(6):559-580
We present a number of methods of constructing efficiency-balanced binary block designs which are design patterns for simplification of statistical analysis. Furthermore, a method of construction of an efficiency-balanced block design with v+1 treatments from one with v treatments is generally characterized. 相似文献
136.
In this paper two equivalent sets of necessary and sufficient conditions are derived for dependent quadratic forms to be distributed as multivariate gamma distribution. The procedure also gives a set of necessary and sufficient conditions for principal minors of generalized quadratic forms to be jointly distributed as the joint distribution of principal minors of a Kishart matrix. 相似文献
137.
This paper finds a general form of the correlation matrix that may be used to provide unbiased F tests in a.k-way factorial experiment. 相似文献
138.
Uniformly minimum variance unbiased estimators of several parameters of the multivariate lognormal distribution are expressed by using the hypergeometric functions of matrix argument. And the variances are given in special cases. 相似文献
139.
T.W.F. Stroud 《统计学通讯:理论与方法》2013,42(17):2085-2109
For a linear regression model over m populations with separate regression coefficients but a common error variance, a Bayesian model is employed to obtain regression coefficient estimates which are shrunk toward an overall value. The formulation uses Normal priors on the coefficients and diffuse priors on the grand mean vectors, the error variance, and the between-to-error variance ratios. The posterior density of the parameters which were given diffuse priors is obtained. From this the posterior means and variances of regression coefficients and the predictive mean and variance of a future observation are obtained directly by numerical integration in the balanced case, and with the aid of series expansions in the approximately balanced case. An example is presented and worked out for the case of one predictor variable. The method is an extension of Box & Tiao's Bayesian estimation of means in the balanced one-way random effects model. 相似文献
140.
Two equivalent methods (gene counting and maximum likelihood) for estimating gene frequencies in a general genetic marker system based on observed phenotype data are derived. Under the maximum likelihood approach, an expression is given for the estimated covariance matrix from which estimated standard errors of the estimators can be found. In addition, consideration is given to the problem of estimating gene frequencies when there are available several independent population data sets. 相似文献