A Simple Normal Approximation for Weibull Distribution with Application to Estimation of Upper Prediction Limit. (20th November 2011)

• Record Type: Journal Article
• Authors: Kulkarni, H. V.; Powar, S. K.
• Other Names: Thavaneswaran A. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2011(2011)
• Publication Date: 2011-11-20
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2011/863274
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : 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.