Next Article in Journal
New Analytic Solutions for the (N + 1)-Dimensional Generalized Boussinesq Equation
Previous Article in Journal
Free Vibration Analysis of Beams on Variable Winkler Elastic Foundation by Using the Differential Transform Method
Article Menu

Export Article

Open AccessArticle
Math. Comput. Appl. 2016, 21(2), 7; doi:10.3390/mca21020007

Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters

Department of Statistics, Faculty of Science, Anadolu University, 26470, Eskisehir, Turkey
Academic Editor: Mehmet Pakdemirli
Received: 13 January 2016 / Revised: 13 March 2016 / Accepted: 14 March 2016 / Published: 25 March 2016
View Full-Text   |   Download PDF [984 KB, uploaded 25 March 2016]   |  

Abstract

Many estimation methods have been proposed for the parameters of statistical distribution. The least squares estimation method, based on a regression model or probability plot, is frequently used by practitioners since its implementation procedure is extremely simple in complete and censoring data cases. However, in the procedure, heteroscedasticity is present in the used regression model and, thus, the weighted least squares estimation or alternative methods should be used. This study proposes an alternative method for the estimation of variance, based on a dependent variable generated via simulation, in order to estimate distributional parameters using the weighted least squares method. In the estimation procedure, the variances or weights are expressed as a function of the rank of the data point in the sample. The considered weighted estimation method is evaluated for the shape parameter of the log-logistic and Weibull distributions via a simulation study. It is found that the considered weighted estimation method shows better performance than the maximum likelihood, least-squares, and certain other alternative estimation approaches in terms of mean square error for most of the considered sample sizes. In addition, a real-life example from hydrology is provided to demonstrate the performance of the considered method. View Full-Text
Keywords: cumulative distribution function; variance estimation; heteroscedasticity; weighted least squares; simulation cumulative distribution function; variance estimation; heteroscedasticity; weighted least squares; simulation
Figures

Figure 1

This paper was processed and accepted under the editorial system of the ASR before its transfer to MDPI.

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Mert Kantar, Y. Estimating Variances in Weighted Least-Squares Estimation of Distributional Parameters. Math. Comput. Appl. 2016, 21, 7.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top