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

Daniel Furtado FERREIRA[1]

Denismar
Alves NOGUEIRA^{1}^{ }

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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.

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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.