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Pseudo-Voigt approximation. The pseudo-Voigt profile (or pseudo-Voigt function) is an approximation of the Voigt profile V (x) using a linear combination of a Gaussian curve G (x) and a Lorentzian curve L (x) instead of their convolution. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes.
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 ...
Gaussian function. In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape.
The closer this value is to 1.0, the better the data fit to a hyperplane representing the relationship between the response variable and a set of covariate variables. A value equal to 1.0 indicates all data fit perfectly within the hyperplane. λ: Gas mean free path (cm) D 50: Mass-median-diameter (MMD). The log-normal distribution mass median ...
EMG. In probability theory, an exponentially modified Gaussian distribution (EMG, also known as exGaussian distribution) describes the sum of independent normal and exponential random variables. An exGaussian random variable Z may be expressed as Z = X + Y, where X and Y are independent, X is Gaussian with mean μ and variance σ2, and Y is ...
Kernel smoother. A kernel smoother is a statistical technique to estimate a real valued function as the weighted average of neighboring observed data. The weight is defined by the kernel, such that closer points are given higher weights. The estimated function is smooth, and the level of smoothness is set by a single parameter.
Probability distribution fitting. 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 ...
v. t. e. Non-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations.