Histogram Fits

This tab is used to define general settings for histogram fits, as well as to specify particular settings for E and S histogram fits.

Fits are performed on the visible part of a plot. In other words, to limit the fit to only part of a plot, simply adjust the graph boundaries to the min and max values of data points to be included in the fit.

1. General Settings

These settings apply to any histograms (or curves) in graphs supporting fits.

• Fit Method

All fits are performed using an iterative non-linear minimization approach, but the quantity minimized depends on both the method and the weighting chosen. Three methods are currently implemented: Least Square, Least Absolute Residuals and Bisquare.

• Weighted Fit

The quantity minimized by the chosen algorithm is a sum of terms, each involving a function of the difference between the histogram value h_i and the fit function value f_i at that point, multiplied by a weight w_i. There is currently no way for the user to  specify the weights, which are defined as:

                                                                        w_i = max(1/h_i, 1)

This definition ensures that histogram values of 0 do not artificially bias the fit (but are included in it).

• Use Same Number of Points as Histogram

If checked and the fitting algorithm provides a valid output, the corresponding plot is displayed using the same abscissa as the original histogram. If unchecked, the number of points used for the plot is that defined by the next parameter:

• # Points

Number of data points to use to represent the fitted curve. The first and last value correspond to the graph boundaries.

• Data Spacing

Either Linear (default) or Logarithmic. The latter is useful for correlation functions, for instance, whose time lags are generally distributed pseudo-logarithmically.

• Show All Fit Components

If checked, and the fit model is a sum of multiple functions, each term is represented as a separate plot (in addition to a plot representing their sum).

2. E, S Histogram Settings

These settings only apply to E and S Histograms (in the ALEX Analysis page), where it might be useful to attempt a multi-component fit, while constraining one of the components. Note that while the name of these parameters refer to the D-only peak, in practice, they refer to the peak referenced by the first (green) cursor of the graph. Cursors are indeed used to provide guess values for multi-component fits, the first one (in the cursor list) defining the guess position of the first peak, and so on.

• Fix D-only Peak Location

If checked, the location of the first peak (defined by the first cursor location) will not be fitted, but instead will be fixed to the value specified in D-only Peak.

• Fix D-only Peak FWHM

If checked, the full-width at half-maximum of the first peak (defined by the first cursor location) will not be fitted, but instead will be fixed to the value specified in D-Only FWHM.