Approximate confidence interval for the new extreme value distribution

Abstract

Purpose

Exact confidence interval estimation for the new extreme value model is often impractical. This paper seeks to evaluate the accuracy of approximate confidence intervals for the two‐parameter new extreme value model.

Design/methodology/approach

The confidence intervals of the parameters of the new model based on likelihood ratio, Wald and Rao statistics are evaluated and compared through the simulation study. The criteria used in evaluating the confidence intervals are the attainment of the nominal error probability and the symmetry of lower and upper error probabilities.

Findings

This study substantiates the merits of the likelihood ratio, the Wald and the Rao statistics. The results indicate that the likelihood ratio‐based intervals perform much better than the Wald and Rao intervals.

Originality/value

Exact interval estimates for the new model are difficult to obtain. Consequently, large sample intervals based on the asymptotic maximum likelihood estimators have gained widespread use. Intervals based on inverting likelihood ratio, Rao and Wald statistics are rarely used in commercial packages. This paper shows that the likelihood ratio intervals are superior to intervals based on the Wald and the Rao statistics.

Citation

Hurairah, A., Akma Ibrahim, N., Bin Daud, I. and Haron, K. (2006), "Approximate confidence interval for the new extreme value distribution", Engineering Computations, Vol. 23 No. 2, pp. 139-153. https://doi.org/10.1108/02644400610644513