207,327 research outputs found
The Kumaraswamy-G Poisson Family of Distributions
For any baseline continuous G distribution, we propose a new generalized family called the Kumaraswamy-G Poisson (denoted with the prefix âKw-GPâ) with three extra positive parameters. Some special distributions in the new family such as the Kw-Weibull Poisson, Kw-gamma Poisson and Kw-beta Poisson distributions are introduced. We derive some mathematical properties of the new family including the ordinary moments, generating function and order statistics. The method of maximum likelihood is used to fit the distributions in the new family. We illustrate its potentiality by means of an application to a real data set
On PoissonâTweedie mixtures
Poisson-Tweedie mixtures are the Poisson mixtures for which the mixing measure is generated by those members of the family of Tweedie distributions whose support is non-negative. This class of non-negative integer-valued distributions is comprised of Neyman type A, back-shifted negative binomial, compound Poisson-negative binomial, discrete stable and exponentially tilted discrete stable laws. For a specific value of the âpowerâ parameter associated with the corresponding Tweedie distributions, such mixtures comprise an additive exponential dispersion model. We derive closed-form expressions for the related variance functions in terms of the exponential tilting invariants and particular special functions. We compare specific Poisson-Tweedie models with the corresponding Hinde-DemĂ©trio exponential dispersion models which possess a comparable unit variance function. We construct numerous local approximations for specific subclasses of Poisson-Tweedie mixtures and identify LĂ©vy measure for all the members of this three-parameter family
Conditional Probabilities of Multivariate Poisson Distributions
Multivariate Poisson distributions have numerous applications. Fast
computation of these distributions, holding constant a fixed set of linear
combinations of these variables, has been explored by Sontag and Zeilberger.
This elaborates on their work
Exponential families of mixed Poisson distributions
If I=(I1,âŠ,Id) is a random variable on [0,â)d with distribution ÎŒ(dλ1,âŠ,dλd), the mixed Poisson distribution MP(ÎŒ) on View the MathML source is the distribution of (N1(I1),âŠ,Nd(Id)) where N1,âŠ,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,â)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,âŠ,vq of [0,â)d with disjoint supports and for independent standard real gamma random variables Y1,âŠ,Yq
Compound Poisson and signed compound Poisson approximations to the Markov binomial law
Compound Poisson distributions and signed compound Poisson measures are used
for approximation of the Markov binomial distribution. The upper and lower
bound estimates are obtained for the total variation, local and Wasserstein
norms. In a special case, asymptotically sharp constants are calculated. For
the upper bounds, the smoothing properties of compound Poisson distributions
are applied. For the lower bound estimates, the characteristic function method
is used.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ246 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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