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  2. Pareto distribution - Wikipedia

    en.wikipedia.org/wiki/Pareto_distribution

    The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, [2] is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend ...

  3. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    The Dirac delta function, although not strictly a probability distribution, is a limiting form of many continuous probability functions. It represents a discrete probability distribution concentrated at 0 — a degenerate distribution — it is a Distribution (mathematics) in the generalized function sense; but the notation treats it as if it ...

  4. Normal distribution - Wikipedia

    en.wikipedia.org/wiki/Normal_distribution

    In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is [ 2 ] [ 3 ] f ( x ) = 1 2 π σ 2 e − ( x − μ ) 2 2 σ 2 . {\displaystyle f(x)={\frac {1}{\sqrt {2\pi \sigma ^{2 ...

  5. Generalized Pareto distribution - Wikipedia

    en.wikipedia.org/wiki/Generalized_Pareto...

    In statistics, the generalized Pareto distribution (GPD) is a family of continuous probability distributions. It is often used to model the tails of another distribution. It is specified by three parameters: location , scale , and shape .

  6. Power law - Wikipedia

    en.wikipedia.org/wiki/Power_law

    The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...

  7. Long tail - Wikipedia

    en.wikipedia.org/wiki/Long_tail

    Given enough choice, a large population of customers, and negligible stocking and distribution costs, the selection and buying pattern of the population results in the demand across products having a power law distribution or Pareto distribution. It is important to understand why some distributions are normal vs. long tail (power) distributions.

  8. Relationships among probability distributions - Wikipedia

    en.wikipedia.org/wiki/Relationships_among...

    If X 1 and X 2 are independent geometric random variables with probability of success p 1 and p 2 respectively, then min(X 1, X 2) is a geometric random variable with probability of success p = p 1 + p 2 − p 1 p 2. The relationship is simpler if expressed in terms probability of failure: q = q 1 q 2.

  9. Seven states of randomness - Wikipedia

    en.wikipedia.org/wiki/Seven_states_of_randomness

    The seven states of randomness in probability theory, fractals and risk analysis are extensions of the concept of randomness as modeled by the normal distribution. These seven states were first introduced by Benoît Mandelbrot in his 1997 book Fractals and Scaling in Finance , which applied fractal analysis to the study of risk and randomness ...