Gaußfunktion

The Gaußfunktion, also known as the Gaussian function or bell curve, is a mathematical function that describes the normal distribution. Its general form is given by f(x) = a * exp(-(x-b)^2 / (2*c^2)), where 'a' is the amplitude, 'b' is the position of the center of the peak, and 'c' is related to the width or spread of the curve. The parameter 'c' is often referred to as the standard deviation in statistical contexts. As the name suggests, the shape of the graph of the Gaußfunktion is a symmetrical bell-shaped curve. The highest point of the curve occurs at x = b, and the function decreases as x moves away from b in either direction. The area under the curve of a normalized Gaußfunktion (where 'a' is chosen appropriately) is equal to 1, which is a crucial property in probability and statistics. The Gaußfunktion is fundamental in many scientific disciplines, including physics, engineering, image processing, and machine learning, where it is used to model phenomena that exhibit a tendency to cluster around a central value. Its smooth, continuous nature and its ability to approximate various data distributions make it a versatile tool.