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In statistics, an ogive, also known as a cumulative frequency polygon, can refer to one of two things: any hand-drawn graphic of a cumulative distribution function [ 1 ] any empirical cumulative distribution function.
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
Cumulative distribution function for the exponential distribution Cumulative distribution function for the normal distribution. In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable, or just distribution function of , evaluated at , is the probability that will take a value less than or equal to .
Cumulative frequency distribution, adapted cumulative probability distribution, and confidence intervals. Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value.
A secant ogive of sharpness = / = The ogive shape of the Space Shuttle external tank Ogive on a 9×19mm Parabellum cartridge. An ogive (/ ˈ oʊ dʒ aɪ v / OH-jyve) is the roundly tapered end of a two- or three-dimensional object. Ogive curves and surfaces are used in engineering, architecture, woodworking, and ballistics.
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.
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula: [1] = + = + = ().
In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve). Main article: Central limit theorem The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution.