The Pareto distribution is a commonly used model for heavy tailed data. Pareto distribution is a useful modeling and predicting tool in a wide variety of socioeconomic contexts. In the present study, we model heterogeneous population by using two component mixture model and two parameter Pareto mixture is considered for this purpose. The expressions for Bayes estimators and their posterior risk...

The present paper considers modified extension of the exponential distribution with three parameters. The main properties of this new distribution is studied, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modifiedextension exponential distribution (MEXED) have been obtained the Bayes Estimators of scale and shape para...

The present paper considers modified extension of the exponential distribution with three parameters. The main properties of this new distribution is studied, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modifiedextension exponential distribution (MEXED) have been obtained the Bayes Estimators of scale and shape para...

The present paper considers modified extension of the exponential distribution with three parameters. The main properties of this new distribution is studied, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modifiedextension exponential distribution (MEXED) have been obtained the Bayes Estimators of scale and shape para...

In this paper, we consider Bayesian point estimation and predictive density in the binomial case. After presenting preliminary results on these problems, compare risk functions of Bayes estimators based truncated untruncated beta priors obtain dominance conditions when probability parameter is less than or equal to a known constant. The case where there are both lower bound restriction an upper...

We describe two methodologies for obtaining segmented regression estimators from massive training data sets. The first methodology, called Linear Regression Tree (LRT), is used for continuous response variables, and the second and complementary methodology, called Naive Bayes Tree (NBT), is used for categorical response variables. These are implemented in the IBM ProbE (Probabilistic Estimation...

Let y = Aβ + ε, where y is an N × 1 vector of observations, β is a p× 1 vector of unknown regression coefficients, A is an N × p design matrix and ε is a spherically symmetric error term with unknown scale parameter σ. We consider estimation of β under general quadratic loss functions, and, in particular, extend the work of Strawderman [J. Amer. Statist. Assoc. 73 (1978) 623–627] and Casella [A...

The present paper considers modified extension of the exponential distribution with three parameters. The main properties of this new distribution is studied, with special emphasis on its median, mode and moments function and some characteristics related to reliability studies. For Modifiedextension exponential distribution (MEXED) have been obtained the Bayes Estimators of scale and shape para...

Empirical Bayes' (EB) estimation is a widely used procedure to calculate teacher value-added. It is primarily viewed as a way to make imprecise estimates more reliable. In this paper we review the theory of EB estimation and use simulated data to study its ability to properly rank teachers. We compare the performance of EB estimators with that of other widely used value-added estimators under d...

Let X ∼ Np(θ, σIp) and W ∼ σχm, where both θ and σ are unknown, and X is independent of W . Optimal estimation of θ with unknown σ is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are adm...