Exact intervals

Exact Confidence Intervals

Exact short Poisson confidence intervals

The authors propose a new method for constructing a confidence interval for the expectation θ of a Poisson random variable. The interval they obtain cannot be shortened without the infimum over θ of the coverage probability falling below 1 − α. In addition, the endpoints of the interval are strictly increasing functions of the observed variable. An easy-to-program algorithm is provided for comp...

Exact maximum coverage probabilities of confidence intervals with increasing bounds for Poisson distribution mean

 ‎A Poisson distribution is well used as a standard model for analyzing count data‎. ‎So the Poisson distribution parameter estimation is widely applied in practice‎. ‎Providing accurate confidence intervals for the discrete distribution parameters is very difficult‎. ‎So far‎, ‎many asymptotic confidence intervals for the mean of Poisson distribution is provided‎. ‎It is known that the coverag...

Exact real arithmetic using centred intervals and bounded error terms

Approximations based on dyadic centred intervals are investigated as a means for implementing exact real arithmetic. It is shown that the field operations can be implemented on these approximations with optimal or near optimal results. Bounds for the loss in quality of approximations for each of the field operations are also given. These approximations can be used as a more efficient alternativ...

Computation of exact bootstrap confidence intervals: complexity and deterministic algorithms

The bootstrap is a nonparametric approach for calculating quantities, such as confidence intervals, directly from data. Since calculating exact bootstrap quantities is believed to be intractable, randomized resampling algorithms are traditionally used. Motivated by the fact that the variability from randomization can lead to inaccurate outputs, we propose a deterministic approach. First, we est...