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The hazard function (also known as the failure rate, hazard rate, or force of mortality) h(x) is the ratio of the probability density function P(x) to the survival function ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

An extended form of Bürmann's theorem. Let f(z) be a function of z analytic in a ring-shaped region A, bounded by another curve C and an inner curve c. Let theta(z) be a ...

A plot of a function expressed in spherical coordinates, with radius r as a function of angles theta and phi. Polar plots can be drawn using SphericalPlot3D[r, {phi, phimin, ...

The most general form of "an" exponential function is a power-law function of the form f(x)=ab^(cx+d), (1) where a, c, and d are real numbers, b is a positive real number, ...

The Ackermann function is the simplest example of a well-defined total function which is computable but not primitive recursive, providing a counterexample to the belief in ...

The rectangle function Pi(x) is a function that is 0 outside the interval [-1/2,1/2] and unity inside it. It is also called the gate function, pulse function, or window ...

The survival function describes the probability that a variate X takes on a value greater than a number x (Evans et al. 2000, p. 6). The survival function is therefore ...

Given a subset A of a larger set, the characteristic function chi_A, sometimes also called the indicator function, is the function defined to be identically one on A, and is ...

For a fractal process with values y(t-Deltat) and y(t+Deltat), the correlation between these two values is given by the Brown function r=2^(2H-1)-1, also known as the ...