Bayes estimators of the lifetime parameters using the compound rayleigh model

The compound Rayleigh distribution, with its unimodal hazard function, makes it attractive for modelling lifetimes of patients with characteristics of a random hazard rate. The Bayes estimators for some lifetime parameters, as well as the parameters of the compound Rayleigh model, are derived for a right censored sample. The estimators for these parameters are obtained, using the squared error loss function, Varian's linear-exponential (linex) loss function and a weighted linex loss function. A discrete prior probability distribution is placed on the scale parameter and either the noninformative or the conjugate prior distribution is placed on the shape parameter. The prediction of a future lifetime is derived, using the noninformative and the conjugate prior distributions. An example illustrates the proposed estimators for the compound Rayleigh model.Articl

Bayesian analysis of survival data using the Rayleigh model and linex loss

Based on right censored data this paper presents the Bayes estimators for some lifetime distribution parameters such as the mean survival time, the hazard function and the survival distribution function, using the non-informative and informative prior distributions for θ. These estimators are derived using both the squared error loss function and Varian's asymmetric linear-exponential (linex) loss function. A hierarchical approach is followed when the hyperparameters of the conjugate gamma prior are unknown, which results in the use of the F-distribution as a prior for θ. A practical example illustrates the use of the non-informative and F priors under the two loss functions, as well as the prediction of the lifetime of a future observation/patient, for the case of unknown hyperparameters.Articl

Exact nonnull distribution of Wilks' statistic: The ratio and product of independent components

The study of the noncentral matrix variate beta type distributions has been sidelined because the final expressions for the densities depend on an integral that has not been resolved in an explicit way. We derive an exact expression for the nonnull distribution of Wilks' statistic and precise expressions for the densities of the ratio and product of two independent components of matrix variates where one matrix variate has the noncentral matrix variate beta type I distribution and the other has the matrix variate beta type I distribution. We provide the expressions for the densities of the determinant of the ratio and the product of these two components. These distributions play a fundamental role in various areas of statistics, for example in the criteria proposed by Wilks.Invariant polynomials Meijer's G-function Noncentral matrix variate beta type I distribution Product Ratio Wilks' statistic Zonal polynomial

Exact nonnull distribution of Wilks’ statistic: The ratio and product of independent components

The study of the noncentral matrix variate beta type distributions has been sidelined because the final expressions for the densities depend on an integral that has not been resolved in an explicit way. We derive an exact expression for the nonnull distribution of Wilks’ statistic and precise expressions for the densities of the ratio and product of two independent components of matrix variates where one matrix variate has the noncentral matrix variate beta type I distribution and the other has the matrix variate beta type I distribution. We provide the expressions for the densities of the determinant of the ratio and the product of these two components. These distributions play a fundamental role in various areas of statistics, for example in the criteria proposed by Wilks