Journal of Probability and Statistics
Volume 2011 (2011), Article ID 863274, 10 pages
Research Article

A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit

Department of Statistics, Shivaji University, Kolhapur 416 004, India

Received 30 May 2011; Accepted 24 September 2011

Academic Editor: A. Thavaneswaran

Copyright © 2011 H. V. Kulkarni and S. K. Powar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a simple close-to-normal approximation to a Weibull random variable (r.v.) and consider the problem of estimation of upper prediction limit (UPL) that includes at least l out of m future observations from a Weibull distribution at each of r locations, based on the proposed approximation and the well-known Box-Cox normal approximation. A comparative study based on Monte Carlo simulations revealed that the normal approximation-based UPLs for Weibull distribution outperform those based on the existing generalized variable (GV) approach. The normal approximation-based UPLs have markedly larger coverage probabilities than GV approach, particularly for small unknown shape parameter where the distribution is highly skewed, and for small sample sizes which are commonly encountered in industrial applications. Results are illustrated with a real dataset for practitioners.