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Sigmoid curves are also common in statistics as cumulative distribution functions (which go from 0 to 1), such as the integrals of the logistic density, the normal density, and Student's t probability density functions. The logistic sigmoid function is invertible, and its inverse is the logit function.
The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
XLfit is a Microsoft Excel add-in that can perform regression analysis, curve fitting, and statistical analysis. It is approved by the UK National Physical Laboratory and the US National Institute of Standards and Technology [1] XLfit can generate 2D and 3D graphs and analyze data sets. XLfit can also analyse the statistical data.
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
Diffusional transformations like austenite transforming to a cementite and ferrite mixture can be explained using the sigmoidal curve; for example the beginning of pearlitic transformation is represented by the pearlite start (P s) curve. This transformation is complete at P f curve. Nucleation requires an incubation time.
The Van Genuchten–Gupta model is an inverted S-curve applicable to crop yield and soil salinity relations. [1] It is named after Martinus Theodore van Genuchten and Satyandra K. Gupta's work from the 1990s. Van Genuchten-Gupta model for crop response to soil salinity.