Search results
Results from the WOW.Com Content Network
Sigmoid functions have domain of all real numbers, with return (response) value commonly monotonically increasing but could be decreasing. Sigmoid functions most often show a return value (y axis) in the range 0 to 1. Another commonly used range is from −1 to 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent ...
The probability density function is the partial derivative of the cumulative distribution function: (;,) = (;,) = / (+ /) = (() / + / ()) = ().When the location parameter μ is 0 and the scale parameter s is 1, then the probability density function of the logistic distribution is given by
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.
Created with gnuplot using the following input file: set terminal svg font "Bitstream Vera Sans,18" size 600,400 set output "Logistic-curve.svg" set xrange [-6:6] set xzeroaxis linetype -1 set yzeroaxis linetype -1 set xtics axis nomirror set ytics axis nomirror 0,0.5,1 set key off set grid set border 1 set samples 400 plot exp(x)/(1 + exp(x)) with line linetype rgbcolor "orange" linewidth 2
Smoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics, [1] [2] video game engines, [3] and machine learning. [ 4 ] The function depends on three parameters, the input x , the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.
I stumbled over the second of the two algebraic functions in the example section: x^n/(x^n + (1-x)^n). as far as I see this is not a sigmoid function. It violates the definition of a sigmoid given in the section Definition. Notably, the derivative is not non-negative and it has multiple inflection points.
The Gudermannian function is a sigmoid function, and as such is sometimes used as an activation function in machine learning. The (scaled and shifted) Gudermannian function is the cumulative distribution function of the hyperbolic secant distribution. A function based on the Gudermannian provides a good model for the shape of spiral galaxy arms ...
Sigmoid means resembling the lower-case Greek letter sigma (uppercase Σ, lowercase σ, lowercase in word-final position ς) or the Latin letter S. Specific uses include: Sigmoid function, a mathematical function; Sigmoid colon, part of the large intestine or colon; Sigmoid sinus, two structures that drain blood from the bottom of the brain