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  2. Method of moments (statistics) - Wikipedia

    en.wikipedia.org/wiki/Method_of_moments_(statistics)

    In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.

  3. Poisson distribution - Wikipedia

    en.wikipedia.org/wiki/Poisson_distribution

    In probability theory and statistics, the Poisson distribution (/ ˈ p w ɑː s ɒ n /; French pronunciation:) is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known constant mean rate and independently of the time since the last event. [1]

  4. Cumulant - Wikipedia

    en.wikipedia.org/wiki/Cumulant

    The Bell numbers are the moments of the Poisson distribution with expected value 1. ... k-statistic, a minimum-variance unbiased estimator of a cumulant;

  5. Moment-generating function - Wikipedia

    en.wikipedia.org/wiki/Moment-generating_function

    In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

  6. Moment (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Moment_(mathematics)

    In mathematics, the moments of a function are certain quantitative measures related to the shape of the function's graph.If the function represents mass density, then the zeroth moment is the total mass, the first moment (normalized by total mass) is the center of mass, and the second moment is the moment of inertia.

  7. Zero-truncated Poisson distribution - Wikipedia

    en.wikipedia.org/wiki/Zero-truncated_Poisson...

    This distribution is also known as the conditional Poisson distribution [1] or the positive Poisson distribution. [2] It is the conditional probability distribution of a Poisson-distributed random variable, given that the value of the random variable is not zero. Thus it is impossible for a ZTP random variable to be zero.

  8. Central moment - Wikipedia

    en.wikipedia.org/wiki/Central_moment

    The nth moment about the mean (or nth central moment) of a real-valued random variable X is the quantity μ n := E[(X − E[X]) n], where E is the expectation operator.For a continuous univariate probability distribution with probability density function f(x), the nth moment about the mean μ is

  9. Compound Poisson process - Wikipedia

    en.wikipedia.org/wiki/Compound_Poisson_process

    The jumps arrive randomly according to a Poisson process and the size of the jumps is also random, with a specified probability distribution. To be precise, a compound Poisson process, parameterised by a rate λ > 0 {\displaystyle \lambda >0} and jump size distribution G , is a process { Y ( t ) : t ≥ 0 } {\displaystyle \{\,Y(t):t\geq 0 ...