Parameter and quantile estimation for the three-parameter gamma distribution based on statistics invariant to unknown location

The three-parameter gamma distribution is widely used as a model for distributions of life spans, reaction times, and for other types of skewed data. In this paper, we propose an efficient method of estimation for the parameters and quantiles of the three-parameter gamma distribution, which avoids the problem of unbounded likelihood, based on statistics invariant to unknown location. Through a Monte Carlo simulation study, we then show that the proposed method performs well compared to other prominent methods in terms of bias and mean squared error. Finally, we present two illustrative examples.     

The Moment-Generating Function and Negative Integer Moments

It does not appear to be widely known that the moment-generating function M_x (t) contains information about negative as well as positive integer moments. Proofs of this are provided, extensions are indicated, and earlier literature deriving and using this type of result is briefly noted. Some examples are given.     

Estimation of parameters of 1-out-of-n:g repairable system

A single unit system supported by N-l inactive standbys and a repair facility is considered when λ,μ are unknown, λand μbeing failure and repair rates of the unit respectively. Three sampling schemes are considered to obtain moment estimators λ^?:and μ _?:when the performance of the unit have to be observed in the system only. Asymptotic variances of the estimates are supplied.     

Asymptotic bayesian inference in some nonstandard cases: Bernstein–von Mises Results and regular bayes' estimators

Asymptotically with probability close to one, the convergence in variation (also in distribution) to the multivariate normal, of the aposteriori density function of a parameter agains an apriori density, viz. the BERNSTEIN–VON MISES results are established when observations are not necessarily indenpendent or identically distributed but satisfy weak regularity assumptions on their joint density function. Regular BAYES' estimators are defined with respect to regular loss functions and a positive apriori density and proved consistent, asymptotically efficient and asymptotically normal. Examples and applications to conjugate families of densities, to inference in MARKOV Chains and other nonstandard cases illustrate results     

Missing data estimators in the general linear model: an evaluation of simulated data as an experimental design

Previous simulations have reported second order missing data estimators to be superior to the more straightforward first order procedures such as mean value replacement. These simulations however were based on deterministic comparisonsbetween regression criteria even though simulated sampling is a random procedure. In this paper a simulation structured asan experimental design allows statistical testing of the various missing data estimators for the various regression criteria as well as different regression specifications. Our results indicate that although no missing data estimator is globally best many of the computationally simpler first order methods perform as well as the more expensive higher order estimators, contrary to some previous findings.     

A bayesian approach to prediction in the presence of spurious observations for several models

The problem of spuriousity has been dealt with from a Bayesian perspective by, among others, Box and Taio (1968) and in several papers by Guttman with various co-authors, beginning with Guttman (1973), The main objective of these papers has been to obtain posterior distributions of parameters, and to base inference on these distributions. In the current paper, the Bayesian argument is carried one step further by deriving predictive distributions of future observations. Inferences are then based on these distributions. We will obtain predictive results for several models, First, we consider the univariate normal case with one spurious observation, This is then generalized to several spurious observations. The multivariate normal situation is studied next. Finally, we consider the general linear model with normal errors.     

Exact moments of lawless and wang's operational ridge regression estimator

Assuming the disturbances are normally distributed, we derive expressions for, and simple conditions for the existence of the exact bias and matrix of second order moments of the Lawless and Wang Operational Ridge Regression estimator.     

Estimation of population mean based on dual use of auxiliary information in non response

Whenever there is auxiliary information available in any form, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. When there exists enough amount of correlation between the study and the auxiliary variables, and parallel to these associations, the ranks of the auxiliary variables are also correlated with the study variable, which can be used a valuable device for enhancing the precision of an estimator accordingly. This article addresses the problem of estimating the finite population mean that utilizes the complementary information in the presence of (i) the auxiliary variable and (ii) the ranks of the auxiliary variable for non response. We suggest an improved estimator for estimating the finite population mean using the auxiliary information in the presence of non response. Expressions for bias and mean squared error of considered estimators are derived up to the first order of approximation. The performance of estimators is compared theoretically and numerically. A numerical study is carried out to evaluate the performances of estimators. It is observed that the proposed estimator is more efficient than the usual sample mean and the regression estimators, and some other families of ratio and exponential type of estimators.     

A simulation study of least squares and ridge estimaors for normal and nonnormal autocorrelated disturbances

The purpose of this paper is to examine the small sample properties of various ridge estimators along with least squares, in some special settings.Specifically, we consider a first order autoregressive structuure for normal and nonnormal disturbances, and report on a Monte Carlo study the small sample behavior of these estimators according to the criteria of bias and dispersion.The results suggest that under all the examined settings and for all the criteria used the HKB estimator exhibited a superior performance compared to the other estimators, while the LS and LW estimators gave consistently poor results.Also if the error term is only moderately autocorrelated the performance of the ridge estimators that do not account for autocorrelation outperform their counterparts as well as least squares that account for autocorrelation.     

Empirical power study of a multi-sample test of exponentiality based on spacings

We present the results of an empirical power study of a new multi-sample test of exponentiality due to (1980)and show that this test is on the whole considerably more powerful than the other prominent tests considered by Dyer and Harbin (1981).