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
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.
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: