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A normal distribution is sometimes informally called a bell curve. [8] However, many other distributions are bell-shaped (such as the Cauchy , Student's t , and logistic distributions). (For other names, see Naming .)
The Gaussian function is the archetypal example of a bell shaped function. A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous or smooth, asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at ...
The term "curve" refers to the bell curve, the graphical representation of the probability density of the normal distribution, but this method can be used to achieve any desired distribution of the grades – for example, a uniform distribution.
The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".
Figure 1: The left graph shows a probability density function. The right graph shows the cumulative distribution function. The value at a in the cumulative distribution equals the area under the probability density curve up to the point a. Absolutely continuous probability distributions can be described in several ways.
The shape of a distribution will fall somewhere in a continuum where a flat distribution might be considered central and where types of departure from this include: mounded (or unimodal), U-shaped, J-shaped, reverse-J shaped and multi-modal. [1]
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Bathtub curve; Bell curve; Calibration curve; Curve of growth (astronomy) Fletcher–Munson curve; Galaxy rotation curve; Gompertz curve; Growth curve (statistics) Kruithof curve; Light curve; Logistic curve; Paschen curve; Robinson–Dadson curves; Stress–strain curve; Space-filling curve