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Tests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions

František Rublík (2001)

Kybernetika

Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level provided that the population characteristic roots are distinct and the covariance matrices of certain quadratic...

The shortest confidence interval for the probability of success in a negative binomial model

Wojciech Zieliński (2012)

Applicationes Mathematicae

The existence of the shortest confidence interval for the probability of success in a negative binomial distribution is shown. The method of obtaining such an interval is presented as well. The interval obtained is compared with the Clopper-Pearson shortest confidence interval for the probability in the binomial model.

The shortest randomized confidence interval for probability of success in a negative binomial model

Wojciech Zieliński (2014)

Applicationes Mathematicae

Zieliński (2012) showed the existence of the shortest confidence interval for a probability of success in a negative binomial distribution. The method of obtaining such an interval was presented as well. Unfortunately, the confidence interval obtained has one disadvantage: it does not keep the prescribed confidence level. In the present article, a small modification is introduced, after which the resulting shortest confidence interval does not have that disadvantage.

Three-Stage Estimation Procedures for the Negative Exponential Distributions.

N. Mukhopadhyay, A. Mauromoustakos (1987)

Metrika

Two-sided Tolerance Intervals in a Simple Linear Regression

Martina Chvosteková (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Numerical results for a simple linear regression indicate that the non-simultaneous two-sided tolerance intervals nearly satisfy the condition of multiple-use confidence intervals, see Lee and Mathew (2002), but the numerical computation of the limits of the multiple-use confidence intervals is needed. We modified the Lieberman–Miller method (1963) for computing the simultaneous two-sided tolerance intervals in a simple linear regression with independent normally distributed errors. The suggested...