An asymptotic normal approach for the variance exact confidence interval of a normal population

Daniel Furtado FERREIRA[1]

Denismar Alves NOGUEIRA1

§       ABSTRACT: The variance of a population is an important parameter to be estimated. There are many areas that require accurate estimates of the variance. The interval estimate has the purpose to express the precision of estimates of such parameter. This work aimed at presenting two confidence intervals for the normal variance that result from the transformation of Wilson and Hilferty (1931) and from the asymptotic chi-square approach of Bishop, Fienberg and Holland (1975). It alsoaims at evaluating their performances by means of Monte Carlo simulation using 2.000 iterations. The confidence interval based on Wilson and Hilferty (1931) approach showed basically the same accuracy as that of the exact confidence interval for confidence coefficient varying from 10% to 99.99% and should be recommended for n > 4, where n = n - 1 is the degrees of freedom of the sample. The interval based on the approach of Bishop, Fienberg and Holland (1975) can only be recommended for n > 30; however, the previous interval is considered to be better. The normal asymptotic interval presented robustness for non normal populations and it can be recommended to estimate variances for those populations in the absence of one or more efficient method for the situation in question The proposed confidence intervals do not need the estimate of chi-square quantiles and present similar results to those of the exact interval. For large values of n, these methods possess larger accuracy and although, in this situation,  numerical methods are unstable for obtaining chi-square quantiles; the didactic value of those approaches should be considered for thei uses and recommendations.

§       KEYWORDS: Asymptotic approach; chi-square; Monte Carlo simulation.

 



[1] Departamento de Ciências Exatas, Universidade Federal de Lavras - UFLA, Lavras, MG, CEP 37200-000. E‑mail: danielff@ufla.br. Bolsista CNPq.