Statistics of equivalent width data and new oscillator strengths for Si II, Fe II, and Mn II

Equivalent width data from Copernicus and IUE appear to have an exponential, rather than a Gaussian distribution of errors. This is probably because there is one dominant source of error: the assignment of the background continuum shape. The maximum likelihood method of parameter estimation is presented for the case of exponential statistics, in enough generality for application to many problems. The method is applied to global fitting of Si II, Fe II, and Mn II oscillator strengths and interstellar gas parameters along many lines of sight. The new values agree in general with previous determinations but are usually much more tightly constrained. Finally, it is shown that care must be taken in deriving acceptable regions of parameter space because the probability contours are not generally ellipses whose axes are parallel to the coordinate axes.