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The width of the sloped parts corresponds to the width of the narrowest uniform distribution. If the uniform distributions have the same width w, the result is a triangular distribution , symmetric about its mean, on the support [a+c,a+c+2w].
Its complementary cumulative distribution function is a stretched exponential function. The Weibull distribution is related to a number of other probability distributions; in particular, it interpolates between the exponential distribution (k = 1) and the Rayleigh distribution (k = 2 and = [5]).
The problem of estimating the maximum of a discrete uniform distribution on the integer interval [,] from a sample of k observations is commonly known as the German tank problem, following the practical application of this maximum estimation problem, during World War II, by Allied forces seeking to estimate German tank production.
The convolution of a function with a Gaussian is also known as a Weierstrass transform. A Gaussian function is the wave function of the ground state of the quantum harmonic oscillator. The molecular orbitals used in computational chemistry can be linear combinations of Gaussian functions called Gaussian orbitals (see also basis set (chemistry)).
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
Uniform distribution may refer to: Continuous uniform distribution; Discrete uniform distribution; Uniform distribution (ecology) Equidistributed sequence; See also.
A distribution has a density function if its cumulative distribution function F(x) is absolutely continuous. In this case: F is almost everywhere differentiable , and its derivative can be used as probability density: d d x F ( x ) = f ( x ) . {\displaystyle {\frac {d}{dx}}F(x)=f(x).}
The Dirichlet distribution is the conjugate prior distribution of the categorical distribution (a generic discrete probability distribution with a given number of possible outcomes) and multinomial distribution (the distribution over observed counts of each possible category in a set of categorically distributed observations).