ABSTRACT
In this chapter, necessary and sufficient conditions for the existence of a confidence interval of the minimum length l for a certain parameter are obtained in the two most frequently used cases: (1) l is proportional to the length of the probability interval of some random variable; (2) l is proportional to the difference between the inverse values of the ends of this interval. We have discussed the issues of possible applications of this result. In particular, we describe how to find the intervals for the degrees of freedom for the chi-square and Fisher distributions, which allow for reducing the length of the confidence interval on a certain (given) value. In other words, we discuss the effectiveness of the usage of confidence intervals of minimal length.
