Nadiminti Nagamani
@vitap.ac.in
Assistant professor and Department of Mathematics
VIT AP University
RESEARCH INTERESTS
Estimation Theory, Statistical Inference.
Scopus Publications
Scholar Citations
Scholar h-index
Scopus Publications
Abbarapu Ashok and Nadiminti Nagamani
Faculty of Engineering, University of Kragujevac
Nadiminti Nagamani and Manas Ranjan Tripathy
Informa UK Limited
Abstract Estimation of quantiles from two normal populations is considered under the assumption of common mean and ordered variances. Several new estimators have been proposed using certain estimators of the common mean, including the plug-in type restricted MLE. A sufficient condition for improving equivariant estimators is proved and as a result improved estimators are derived. The percentage of risk improvements for each of the improved estimators have been computed numerically, which are quite significant. All the improved estimators have been compared numerically using Monte-Carlo simulation method. Finally, recommendations have been made for the use of estimators in practice.
Nadiminti Nagamani, Manas Ranjan Tripathy, and Somesh Kumar
Informa UK Limited
Abstract Estimation under equality restrictions is an age old problem and has been considered by several researchers in the past due to practical applications and theoretical challenges involved in it. Particularly, the problem has been extensively studied from classical as well as decision theoretic point of view when the underlying distribution is normal. In this paper, we consider the problem when the underlying distribution is non-normal, say, logistic. Specifically, estimation of the common scale parameter of two logistic populations has been considered when the location parameters are unknown. It is observed that closed forms of the maximum likelihood estimators (MLEs) for the associated parameters do not exist. Using certain numerical techniques the MLEs have been derived. The asymptotic confidence intervals have been derived numerically too, as these also depend on the MLEs. Approximate Bayes estimators are proposed using non-informative as well as conjugate priors with respect to the squared error (SE) and the LINEX loss functions. A simulation study has been conducted to evaluate the proposed estimators and compare their performances through mean squared error (MSE) and bias. Finally, two real life examples have been considered in order to show the potential applications of the proposed model and illustrate the method of estimation.
Nadiminti Nagamani and Manas Ranjan Tripathy
Informa UK Limited
SYNOPTIC ABSTRACT The problem of estimating the common scale parameter of two gamma populations has been considered when the shape parameters are unknown and possibly different. The performance of an estimator is evaluated using both bias and mean squared error. The maximum likelihood estimator (MLE) has been obtained numerically using the Monte-Carlo simulation, as the closed form does not exist. The Fisher information matrix has been obtained for our model and, consequently, asymptotic confidence intervals have been constructed. Certain Bayes estimators, using various priors, have been obtained. Like the MLE, the closed form of these Bayes estimators does not exist. An approximation due to Lindley (1980) has been used to obtain these Bayes estimators approximately. Finally, the bias and the mean squared error of all these estimators have been numerically compared through the Monte-Carlo simulation method.