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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.
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 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.
Capability curve of an electrical generator describes the limits of the active and reactive power that the generator can provide. The curve represents a boundary of all operating points in the MW/MVAr plane; it is typically drawn with the real power on the horizontal axis, and, for the synchronous generator , resembles a letter D in shape, thus ...
The superformula is a generalization of the superellipse and was proposed by Johan Gielis in 2003. [1] Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature.
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In a power system, a load curve or load profile is a chart illustrating the variation in demand/electrical load over a specific time. Generation companies use this information to plan how much power they will need to generate at any given time. A load duration curve is similar to a load curve. The information is the same but is presented in a ...
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