Analytical PDFs

Analytic PDFs are counted after array PDFs.For example if there are three binned PDFs and one analytical one, the analytical PDF will be the fourth distribution. The information on each analytical PDF is stored in the titles bank MXFQ. If analytical PDFs are to be used a switch must also be set in MXFC or with the command.

  $mxf_do_analytic $on

The number of analytic PDFs to be fit for is set with the command

  $num_anal_pdfs  3  ! use 3 analytic PDFs

For each analytic PDF the shape in each fitting parameter must be specified within the limits set for that parameter in the bank MXFP. A number of generic shapes have been coded. A flag is assigned to the PDF to indicate which shape should be used. Up to 5 input parameters are permitted to describe the shape.

Flat

Flag$=$1. The distribution has no dependence on this fitting parameter. No input parameters are required, and the shape is given by the routine mxf_anal_flat.for.

Gaussian

flag$=$2. The distribution has dependence

$${f(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{\frac{(x-\mu)^2}{2\sigma^2}}}$$ (30.1)

on parameter x. The two input parameters are the mean, $\mu$ and width $\sigma$ of the distribution respectively. The routine mxf_anal_gaussian.for is used.

Polynomial

flag$=$3. The distribution has dependence

$${f(x) = p_1+p_2.x+p_3.x^2+p_4.x^3+p_5.x^4}$$ (30.2)

on parameter x. Up to five input parameters, $p_1, p_2, p_3, p_4, p_5$ can be supplied.

Exponential Polynomial

flag$=$4. The distribution has dependence

$${f(x) = p_1+e^{(p_2+p_3.x^2)}}$$ (30.3)

on parameter x. Three input parameters, $p_1, p_2$ and $p_3$ respectively are required.

Spare

flag$=$5. This routine, mxf_anal_spare.for, as yet does nothing but can be adapted to make a new analytical shape.

In order to include a new analytical shape, the user should assign it the next flag number and add a new fortran function following the outline of mxf_anal_spare.for. The routine mxf_choose_anal.for which determines which function to call, should be editted accordingly.