  This paper discusses the amplitude estimation using data originating from a
sine-like function as probability density function. If a simple least squares
fit is used, a significant bias is observed for small amplitudes. It is shown
that a proper treatment using the Feldman-Cousins algorithm of likelihood
ratios allows one to construct improved confidence intervals. Using Bayes'
theorem a probability density function is derived for the amplitude. It is used
in an application to show that it leads to better estimates compared to a
simple least squares fit.
