Construction of confidence limits, with the help of order statistics, for the bulk of the distribution of a general population. (English. Russian original) Zbl 0635.62034

Madreimov, I.; Petunin, Yu. I.

Theory Probab. Math. Stat. 32, 57-68 (1986); translation from Teor. Veroyatn. Mat. Stat. 32, 53-66 (1985).

The authors investigate the accuracy and reliability of confidence intervals containing the bulk of the distribution of the values of a general population with unimodal distribution. They prove that for a symmetric unimodal distribution, among all the confidence intervals \((x^{(i)},x^{(j)})\) constructed with the help of the order statistics \(x^{(i)}\) and \(x^{(j)}\) with given reliability, the interval \((x^{(k)},x^{(n-k+1)})\) has the greatest accuracy. The accuracy of linear confidence intervals in the case of a uniform distribution is examined.

MSC:

62G15	Nonparametric tolerance and confidence regions
62G30	Order statistics; empirical distribution functions

Keywords:

accuracy; reliability; symmetric unimodal distribution; confidence intervals; order statistics; linear confidence intervals; uniform distribution