In probability theory and statistics, the geometric Poisson distribution (also called the Pólya–Aeppli distribution) is used for describing objects that come in clusters, where the number of clusters follows a Poisson distribution and the number of objects within a cluster follows a geometric distribution.[1] It is a particular case of the compound Poisson distribution.[2]
The probability mass function of a random variable N distributed according to the geometric Poisson distribution is given by
where λ is the parameter of the underlying Poisson distribution and θ is the parameter of the geometric distribution.[2]
The distribution was described by George Pólya in 1930. Pólya credited his student Alfred Aeppli's 1924 dissertation as the original source. It was called the geometric Poisson distribution by Sherbrooke in 1968, who gave probability tables with a precision of four decimal places.[3]
The geometric Poisson distribution has been used to describe systems modelled by a Markov model, such as biological processes[2] or traffic accidents.[4]
^Johnson, Kotz & Kemp 2005, p. 410.
^ abcNuel 2008.
^Johnson, Kotz & Kemp 2005, p. 412.
^Özel & İnal 2010.
and 27 Related for: Geometric Poisson distribution information
probability theory and statistics, the geometricPoissondistribution (also called the Pólya–Aeppli distribution) is used for describing objects that come...
In probability theory, a compound Poissondistribution is the probability distribution of the sum of a number of independent identically-distributed random...
exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process...
and statistics, the geometricdistribution is either one of two discrete probability distributions: The probability distribution of the number X {\displaystyle...
mixed Poissondistribution is a univariate discrete probability distribution in stochastics. It results from assuming that the conditional distribution of...
the Poisson. The negative binomial distribution has a variance μ / p {\displaystyle \mu /p} , with the distribution becoming identical to Poisson in the...
has a Poissondistribution, and assumes the logarithm of its expected value can be modeled by a linear combination of unknown parameters. A Poisson regression...
the geometricdistribution to the nth success. The discrete compound Poissondistribution The parabolic fractal distribution The Poissondistribution, which...
distributions, the purely discrete scaled Poissondistribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but...
random points form a Poisson process, then the number of points in a region of finite size is a random variable with a Poissondistribution. The process and...
is a geometricdistribution with parameter p. A gamma distribution with shape parameter α = 1 and rate parameter β is an exponential distribution with...
probability distributions used in statistical modeling include the Poissondistribution, the Bernoulli distribution, the binomial distribution, the geometric distribution...
A geometric stable distribution or geo-stable distribution is a type of leptokurtic probability distribution. Geometric stable distributions were introduced...
{\displaystyle +1/2} " coming courtesy of the half-forms. Geometric quantization of Poisson manifolds and symplectic foliations also is developed. For...
Weibull distribution can be compared with other common discrete distributions such as the Poisson, geometric, and negative binomial distributions, each...
moments exist. The Cauchy distribution has no moment generating function. In mathematics, it is closely related to the Poisson kernel, which is the fundamental...
to PoissonDistribution". Stat.ucla.edu. Retrieved March 3, 2017. Das, Abhranil (2021). "A method to integrate and classify normal distributions". Journal...
Pólya–Aeppli distribution, now also known as the geometricPoissondistribution, is a particular case of the compound Poissondistribution, and is used...
a field in mathematics, a Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises that of...
our example, if we pick the Gamma distribution as our prior distribution over the rate of the Poissondistributions, then the posterior predictive is...
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their...
distributions are in fact best described by their mean, including the exponential and Poissondistributions. The mean of a probability distribution is...
In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values...
mathematical object. The Poisson process is named after Siméon Poisson, due to its definition involving the Poissondistribution, but Poisson never studied the...
Exponential distribution Gamma distributionGeometricdistribution Hypoexponential distribution Lévy distributionPoissondistribution Stable distribution Mixture...
In mathematics, a Poisson algebra is an associative algebra together with a Lie bracket that also satisfies Leibniz's law; that is, the bracket is also...
Beta distribution is the conjugate prior of the Bernoulli distribution. The geometricdistribution models the number of independent and identical Bernoulli...