In a generalized linear model with binary response, the role of a link function is important to find a model that fits data well. Aranda-Ordaz (1981) proposed a family of link functions that includes a logistic link function and a complementary log-log function. In this paper, we propose a new family of models on the basis of a family of link functions by extending the family proposed by Aranda-Ordaz (1981). We also consider tests to determine whether the new model fits data well. Examples of artificial and real data showing that our new model is more appropriate than the Aranda-Ordaz model are presented.
We consider a complete hierarchical multinomial probit (HMNP) model in which both the regression-coefficient vector and the covariance matrix are assumed to have hierarchical structure and propose an MCMC algorithm for numerically computing the Bayes estimates of the parameters. We show by simulation studies that the covariance matrix is estimated with higher accuracy using the method proposed in this paper than that using an HMNP model in which the covariance matrix is not assumed to have hierarchical structure.
In this paper we study the generalized lower(k)record values arising from the Fréchet distribution. Expressions for the moments and product moments of those generalized lower(k)record values are derived. Some properties of generalized lower(k) record values which characterize the Fréchet distribution have been established. Also some distributional properties of generalized lower(k)record values arising from the Fréchet distribution are considered and used for suggesting an estimator for the shape parameter of the Fréchet distribution. The location and scale parameters are estimated using the Best Linear Unbiased Estimation procedure. Prediction of a future record using the Best Linear Unbiased Predictor has been studied. A real life data set is used to illustrate the results generated in this work.
A new class of generalized two-piece skew normal distribution is introduced here as a two-piece version of the generalized skew normal distribution of Kumar and Anusree (2011). It is shown that the proposed class of distribution will be more suitable for modelling skewed, multimodal data sets. Several properties of the model are studied and the maximum likelihood estimation of the parameters of the distribution is discussed. Further, the practical usefulness of the model is illustrated with the help of certain real life data sets.
This paper addresses the problems of estimating the normal covariance and precision matrices. A commutator subgroup of lower triangular matrices is considered for deriving a class of invariant estimators. The class shows inadmissibility of the best invariant and minimax estimator of the covariance matrix relative to quadratic loss. Also, in estimation of the precision matrix, a dominance result is given for improvement on a minimax estimator relative to the Stein loss.
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