Finding the “best-fitting” circle to describe a set of points in two dimensions is discussed in terms of maximum likelihood estimation. Several combinations of distributions are proposed to describe the stochastic nature of points in the plane, as the points are considered to have a common,...

This paper calculates response surface models for a large range of quantiles of the Leybourne (Oxf Bull Econ Stat 57:559–571, <CitationRef CitationID="CR9">1995</CitationRef>) test for the null hypothesis of a unit root against the alternative of (trend) stationarity. The response surface models allow the estimation of critical values...</citationref>

We derive a new algorithm for calculating an exact confidence interval for a parameter of location or scale family, based on a two-sided hypothesis test on the parameter of interest, using some pivotal quantities. We use this algorithm to calculate approximate confidence intervals for the...