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The Dirac comb of period 2 π, although not strictly a function, is a limiting form of many directional distributions. It is essentially a wrapped Dirac delta function. It represents a discrete probability distribution concentrated at 2 π n — a degenerate distribution — but the notation treats it as if it were a continuous distribution.
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Two statistical models are nested if the first model can be transformed into the second model by imposing constraints on the parameters of the first model. As an example, the set of all Gaussian distributions has, nested within it, the set of zero-mean Gaussian distributions: we constrain the mean in the set of all Gaussian distributions to get ...
In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite. A simulation-based alternative to this approximation is the application of Monte Carlo simulations.
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [ 1 ] [ 2 ] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events ( subsets of the sample space).
This is still quick to compute, and much more accurate for smooth functions such as the sine function. Here is an example using linear interpolation: Here is an example using linear interpolation: function lookup_sine ( x ) x1 = floor ( x * 1000 / pi ) y1 = sine_table [ x1 ] y2 = sine_table [ x1 + 1 ] return y1 + ( y2 - y1 ) * ( x * 1000 / pi ...
Thus, rational functions can easily be incorporated into a rational function model. Rational function models can often be used to model complicated structure with a fairly low degree in both the numerator and denominator. This in turn means that fewer coefficients will be required compared to the polynomial model. Rational function models are ...
In probability theory and statistics, the Weibull distribution / ˈ w aɪ b ʊ l / is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure or time between events. Examples are maximum one-day rainfalls and the time a user spends on a web page.