On the principle of equivariance: concepts and applications.
On the problem of the means of weighted normal populations.
An analytical problem, which arises in the statistical problem of comparing the means of two normal distributions, the variances of which -as well as their ratio- are unknown, is well known in the mathematical statistics as the Behrens-Fisher problem. One generalization of the Behrens-Fisher problem and different aspect concerning the estimation of the common mean of several independent normal distributions with different variances are considered and one solution is proposed.
On the quadratic derivative of exponential probabilities
In the paper it is shown that exponential families of probabilities have the quadratic derivative of the likelihood ratio, and explicit formulas for this derivative are derived.
On the Rao-Blackwell Theorem for fuzzy random variables
In a previous paper, conditions have been given to compute iterated expectations of fuzzy random variables, irrespectively of the order of integration. In another previous paper, a generalized real-valued measure to quantify the absolute variation of a fuzzy random variable with respect to its expected value have been introduced and analyzed. In the present paper we combine the conditions and generalized measure above to state an extension of the basic Rao–Blackwell Theorem. An application of this...
On the relation between gnostical and probability theories
On the Resolution of a Mixture of Observations from two Gamma Distributions by the Method of Maximum Likelihood.
On The Resolution Of A Mixture Of Observations From Two Modified Power Series Distributions.
On the restricted range in the samples from the gamma population
Samples from the gamma population are considered which are censored both above and below, that is, observations below and observations above are missing among observations. The range in such censored samples is taken up and the distribution of this restricted range is obtained, which can be compared with that in the complete sample case given in a previous paper.
On the robustness of multiple regression coefficient estimators obtained by the p-point method
On the theory of ratio estimates
On the translated exponential model with censoring.
On the two-sided multiparameter control
On the two-sided quality control
Let the random variable have the normal distribution . Explicit formulas for maximum likelihood estimator of are derived under the hypotheses , where are arbitrary fixed numbers. Asymptotic distribution of the likelihood ratio statistic for testing this hypothesis is derived and some of its quantiles are presented.
On the uniqueness of the M. L. estimates in curved exponential families
On the Variance of the Ratio Estimator.
On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function.
Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ-r of unknown parameter λ of gamma distribution with density f(x|λ, b) = λb-1 e-λx xb-1 / Γ(b), x>0, where b is a known parameter, for loss function L(λ-r, λ-r) = (λ-r - λ-r)2 / λ-2r.Goodman in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ2 of the normal distribution....
On Uniformly Minimum Variance Unbiased Estimation when no Complete Sufficient Statistics Exist.
On variance of the two-stage estimator in variance-covariance components model
The paper deals with a linear model with linear variance-covariance structure, where the linear function of the parameter of expectation is to be estimated. The two-stage estimator is based on the observation of the vector and on the invariant quadratic estimator of the variance-covariance components. Under the assumption of symmetry of the distribution and existence of finite moments up to the tenth order, an approach to determining the upper bound for the difference in variances of the estimators...
On variance-covariance components estimation in linear models with AR(1) disturbances.
On Weak Convergence of Parameter Estimators of General Statistical Parametric Models