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Curve fitting [1] [2] is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, [3] possibly subject to constraints. [ 4 ] [ 5 ] Curve fitting can involve either interpolation , [ 6 ] [ 7 ] where an exact fit to the data is required, or smoothing , [ 8 ] [ 9 ] in which a "smooth ...
The convolution of a function with a Gaussian is also known as a Weierstrass transform. A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
Probability distribution fitting or simply distribution fitting is the fitting of a probability distribution to a series of data concerning the repeated measurement of a variable phenomenon. The aim of distribution fitting is to predict the probability or to forecast the frequency of occurrence of the magnitude of the phenomenon in a certain ...
F = the cumulative distribution function for the probability distribution being tested. Y u = the upper limit for bin i, Y l = the lower limit for bin i, and; N = the sample size; The resulting value can be compared with a chi-square distribution to determine the goodness of fit.
MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
Fitting a phase type distribution to heavy-tailed distributions has been shown to be practical in some situations. [9] PhFit a C script for fitting discrete and continuous phase type distributions to data [10] EMpht is a C script for fitting phase-type distributions to data or parametric distributions using an expectation–maximization ...
In this example we try to fit the function = + using the Levenberg–Marquardt algorithm implemented in GNU Octave as the leasqr function. The graphs show progressively better fitting for the parameters a = 100 {\displaystyle a=100} , b = 102 {\displaystyle b=102} used in the initial curve.
In geochronology, the MSWD is a measure of goodness of fit that takes into account the relative importance of both the internal and external reproducibility, with most common usage in isotopic dating.