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)\<SUP\>\&theta;+1\</SUP\>/\&Gamma;(\&theta;+1) (offset+slope*x)\<SUP\>\&theta;\</SUP\> e\<SUP\>-(\&theta;+1)*(offset+slope*x)\</SUP\>

i.e. a Polya distribution with argument offset+slope*x and with Polya parameter \θ.

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.

error

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

\&radic;(\&chi;\&sup2;/(#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 commata. 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

Notes:

The EQUAL and POISSON options are ignored for matrix fits since the errors on the points are explicitly provided in that case.
The plot is always made on a linear-logarithmic scale.

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Formatted on 21/01/18 at 16:55.