MODA V1.52

- for the HP49 -






MODA provides an environment for non-linear chi-square and/or least-square fitting and
it gives access to the goodness-of-fit, to the covariance matrix and to confidence limits.
The fit functions can be archived and maintained in a catalog and the results can be plotted
in several ways. See the introduction for some general remarks on curve fitting.
 


I'd like to thank
    Dave Scott for his encouragement and Ralf Fritzsch for his support as well
    as for his readiness to discuss the pros&cons of various catalog-related ideas.
    Special thanks go to Daniel G. Hyams who gave the permission to use and adapt
    the catalog of fit functions from CurveExpert.

Comments & suggestions,
as well as bug reports are welcome!
StevenAhlig



Introduction


The two basic ingredients of any fitting procedure are the data and a function.
The data are typically the result of some measurements in which pairs of
values (x_i, y_i)  (independent, dependent) i=1,...,N are recorded.
The results of the measurements, i.e. the dependent variables y_i will usually
have a certain measurement error. The function f is supposed to encode the
mechanism that produced the data.
f depends on X and on the parameters a_i, i=1,...,M.

The aim of the fitting procedure is to find those values of the parameters a_i
which do best describe the 'experimental values'.

The fitting is 'nonlinear' since the parameters a_i may enter the function f in a
linear and/or in a nonlinear way.

The difference between chi-square and least-square fitting lies in the inclusion
or neglection of the measurement errors of the y_i. These measurement errors are
taken into account in the chi-square fitting algorithms and they are assumed
to be equal to 1 in the least-square fitting algorithms.
MODA can handle both cases.



Installation


The installation is very simple; transfer (in binary mode) the file modav*.lib
to your HP49. Place the content of the variable modav*.lib on the stack.
Make sure that the calc is in RPN mode, then enter:

      :0:768 [ENTER] [STO]
      768 ATTACH [ENTER]

MODA should now be installed.

MODA can now be started in two ways:

If you want to use the default catalog than you have to transfer (in binary
mode) the file MDCAT to your HP49.