CALL: FIT_POLYA


reference

  The histogram is referenced via a global variable that has usually
  been returned by a call to BOOK_HISTOGRAM or GET_HISTOGRAM. This
  argument may also be an expression that results in a histogram.

  The argument is not modified on return.

x

  A 1-dimensional array that contains the ordinates of the
  points to be fitted.

  The vectors x, y and err_y must have the same length,
  unless err_y is given as a scalar.

  Not changed on exit.

y

  A 1-dimensional array that contains the coordinates of the
  points to be fitted.

  The vectors x, y and err_y must have the same length,
  unless err_y is given as a scalar.

  In the initial estimate, the data points where y <= 0 are
  skipped. If there are many such points which should
  be taken into account for the fit, then convergence is
  not guaranteed.

  Not changed on exit.

err_y

  A 1-dimensional array that contains the errors on the
  coordinates of the points to be fitted.

  This argument can also be a scalar, which is then used as
  error for all points. If this argument is a vector, then
  it must have the same length as x and y.

  Not changed on exit.

parameters

  The function that is fitted to the data points is given by

  function = factor*slope *
             ((theta+1)**(theta+1)/Gamma(theta+1) *
             (offset+slope*X)**theta *
             exp(-(theta+1)*(offset+slope*X))

  i.e. a Polya distribution with argument   offset+slope*X   and
  with Polya parameter theta.

  The input values for the terms are used as initial values for
  the fit if the MANUAL option is used (this is not default).
  The parameters "offset" and "slope" are fitted if the option
  FIT is specified, otherwise the values have to be specified on
  input.

  Parameters of which the value on input is to be used, must be
  of type Number.

  All arguments except "offset" and "slope" when using the FIX
  option, must be modifiable, i.e. it can not be a constant nor
  an expression.

errors

  The errors returned are the square roots of the diagonal elements
  of the covariance matrix, multiplied by a correction factor equal
  to:

       sqrt(chi**2/(#points - #parameters))

  This correction factor is equal to 1 if the errors to the data
  points have been assigned correctly.

  These arguments must be modifiable, that is, they can neither be
  constants nor expressions.

options

  The options string may contain the keywords listed in the table
  below. The keywords should be separated by blanks or commas.
  Additional text may be added - no error message will be issued
  if unrecognised keywords are used.

  ---------------------------------------------------------------------
  Option     Meaning                                 Defaults
  ---------------------------------------------------------------------
  AUTO       Determine suitable starting values      Default
  EQUAL      Assume equal weight of all points       Not default
  FIT        Fit the scale of the distribution       Default
  FIX        Don't modify the scale parameters       Not default
  MANUAL     Start from given initial values         Not default
  NOPLOT     Don't plot the histogram and fit        Default
  NOPRINT    Don't print details during the fit      Default
  PLOT       Plot the histogram with fit             Not default
  POISSON    Assume Poisson errors                   Default
  PRINT      Print details during the fit            Not default
  ---------------------------------------------------------------------

  Note: The EQUAL and POISSON options are ignored for matrix fits since
        the errors on the points are explicitely provided in that case.

        The plot is always made on a linear-logaritmic scale.

Keyword index. Formatted on 10/11/98.