In this paper, we treat estimation and prediction problems where negative multinomial variables are observed and, in particular, consider unbalanced settings. First, the problem of estimating multiple parameter vectors under standardized squared error loss is treated a new empirical Bayes estimator which dominates uniformly minimum variance unbiased (UMVU) suitable conditions derived. Next, joi...

We present a general result giving us families of incomplete and boundedly complete families of discrete distributions. For such families, the classes of unbiased estimators of zero with finite variance and of parametric functions which will have uniformly minimum variance unbiased estimators with finite variance are explicitly characterized. The general result allows us to construct a large nu...

The ratio-type estimators have been introduced for estimating the mean and total population, but in recent years based on the ratio methods several estimators for population variance have been proposed. In this paper two families of estimators have been suggested and their approximation mean square error (MSE) have been developed. In addition, the efficiency of these variance estimators are com...

Random samples are extensively used to summarize massive data sets and facilitate scalable analytics. Coordinated sampling, where samples of different data sets “share” the randomization, is a powerful method which facilitates more accurate estimation of many aggregates and similarity measures. We recently formulated a model of Monotone Estimation Problems (MEP), which can be applied to coordin...

In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any assumptions on the direct feedthrough matrix. We also provide the connection between the stability of the estimator and a system property known as strong detec...

In this paper, we present a unified optimal and exponentially stable filter for linear discrete-time stochastic systems that simultaneously estimates the states and unknown inputs in an unbiased minimum-variance sense, without making any assumptions on the direct feedthrough matrix. We also provide the connection between the stability of the estimator and a system property known as strong detec...

Problem Statement: The two-parameter exponentiated Rayleigh distribution has been widely used especially in the modelling of life time event data. It provides a statistical model which has a wide variety of application in many areas and the main advantage is its ability in the context of life time event among other distributions. The uniformly minimum variance unbiased and maximum likelihood es...

Variance components (VCs) in linear adjustment models are usually successfully computed by unbiased estimators. However, for many unbiased VC techniques estimated variance components might be negative, a result that cannot be tolerated by the user. This is, for example, the case with the simple additive VC model aσ2 1 + bσ2 2 with known coefficients a and b, where either of the unbiasedly estim...

This paper will study the estimation of parameter of Topp-Leone distribution based on lower record values. First, the minimum variance unbiased estimator and maximum likelihood estimator are obtained. Then the Bayes estimator is derived under symmetric loss function and further the empirical Bayes estimators is also obtained based on marginal probability density of record sample and maximum lik...