A “Reverse Order” Elementary Statistics Course

A family of coefficients for measuring monotone association is presented. These include measures of association of ordinal or interval variables such as gamma of Goodman and Kruskal, Somers's d_yx , Kendall's tau, or Spearman's rho as special cases. The article shows how a large number of measures of association can be put into a single general form. These coefficients are used as a basis for defining a variety of data analysis techniques.     

The beta Weibull-geometric distribution

A new five-parameter distribution called the beta Weibull-geometric (BWG) distribution is proposed. The new distribution is generated from the logit of a beta random variable and includes the Weibull-geometric distribution of Barreto-Souza et al. [The Weibull-geometric distribution, J. Stat. Comput. Simul. 81 (2011), pp. 645–657], beta Weibull (BW), beta exponential, exponentiated Weibull, and some other lifetime distributions as special cases. A comprehensive mathematical treatment of this distribution is provided. The density function can be expressed as an infinite mixture of BW densities and then we derive some mathematical properties of the new distribution from the corresponding properties of the BW distribution. The density function of the order statistics and also estimation of the stress–strength parameter are obtained using two general expressions. To estimate the model parameters, we use the maximum likelihood method and the asymptotic distribution of the estimators is also discussed. The capacity of the new distribution are examined by various tools, using two real data sets.     

Testing exponentiality based on Type-I censored data

The problem of goodness-of-fit for the exponential distribution when the available data are subject to Type-I censoring is discussed here. A test procedure is proposed in this case that exhibits more power as compared to existing methods. The power of the proposed test is assessed for several alternative distributions by means of Monte Carlo simulations. Finally, the proposed test is illustrated with a real data set.     

Multivariate Birnbaum–Saunders regression model

In this paper, we propose a multivariate log-linear Birnbaum–Saunders regression model. We discuss maximum-likelihood estimation of the model parameters and provide closed-form expressions for the score function and for Fisher's information matrix. Hypothesis testing is performed using approximations obtained from the asymptotic normality of the maximum-likelihood estimator. Some influence methods, such as the local influence and generalized leverage are discussed and the normal curvatures for studying local influence are derived under some perturbation schemes. Further, a test for the homogeneity of the shape parameter of the multivariate regression model is investigated. A real data set is presented for illustrative purposes.     

Generation of d–optimal designs in a finite design space

This paper presents some considerations about the numerical procedures for generating D–optimal design in a finite design space. The influence of starting procedures and the finite set of points on the design efficiency is considered. Some modifications of the existing procedures for D–optimal designs generation are described. It is shown that for large number of factors the sequential procedures are more appropriate than the nonsequential ones     

On the Restricted Liu Estimator in the Gauss–Markov Model

In this paper, we compare two estimators, the RLE (restricted Liu estimator) and the RLSE (restricted least squares estimator) of parameters in linear models under Gauss–Markov models. Using generalized inverse of matrices, we found some equivalency conditions for the superiority of the RLE with respect to the MSE criterion.     

A Note on Bayesian Analyses of Capture–Recapture Data with Perfect Recaptures

The present article deals with the problem of misspecifying the disturbance-covariance matrix as scalar, when it is locally non scalar. We consider a family of shrinkage estimators based on OLS estimator and compare its asymptotic properties with the properties of OLS estimator. We proposed a similar family of estimators based on FGLS and compared its asymptotic properties with the shrinkage estimator based on OLS under a Pitman's drift process. The effect of misspecifying the disturbances covariance matrix was analyzed with the help of a numerical simulation.     

Goodness-of-Fit Tests for the Skew-Normal Distribution When the Parameters Are Estimated from the Data

In this article, tests are developed which can be used to investigate the goodness-of-fit of the skew-normal distribution in the context most relevant to the data analyst, namely that in which the parameter values are unknown and are estimated from the data. We consider five test statistics chosen from the broad Cramér–von Mises and Kolmogorov–Smirnov families, based on measures of disparity between the distribution function of a fitted skew-normal population and the empirical distribution function. The sampling distributions of the proposed test statistics are approximated using Monte Carlo techniques and summarized in easy to use tabular form. We also present results obtained from simulation studies designed to explore the true size of the tests and their power against various asymmetric alternative distributions.     

Weighted Multivariate Tests of Independence

We present new tests of marginal independence for ?^d-valued random vectors. Our tests rely upon weighted Cramér–von Mises-type statistics, which are functionals of the empirical copula process based upon a random sample of size n. We establish a decomposition of this process into asymptotically independent components, and describe the tests which follow from these arguments.