Three Classes of Univariate Discrete Distributions

Khatri, C. G.; Patel, Ishan

doi:10.2307/2527856

Cited by 27 publications

(8 citation statements)

References 4 publications

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“…the convergence is linear,19) so the computational cost of evaluating n probabilities is O ( n ). Khatri and Patel (1961) provide recurrences for distributions, needed for the deterministic initial condition setting.The generating function can also be used directly for parameter estimation, without calculating the distribution first. Marcheselli et al.…”

Section: Appendixmentioning

confidence: 99%

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

2018

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Multimodality is a phenomenon which complicates the analysis of statistical data based exclusively on mean and variance. Here, we present criteria for multimodality in hierarchic first-order reaction networks, consisting of catalytic and splitting reactions. Those networks are characterized by independent and dependent subnetworks. First, we prove the general solvability of the Chemical Master Equation (CME) for this type of reaction network and thereby extend the class of solvable CME’s. Our general solution is analytical in the sense that it allows for a detailed analysis of its statistical properties. Given Poisson/deterministic initial conditions, we then prove the independent species to be Poisson/binomially distributed, while the dependent species exhibit generalized Poisson/Khatri Type B distributions. Generalized Poisson/Khatri Type B distributions are multimodal for an appropriate choice of parameters. We illustrate our criteria for multimodality by several basic models, as well as the well-known two-stage transcription–translation network and Bateman’s model from nuclear physics. For both examples, multimodality was previously not reported.Electronic supplementary materialThe online version of this article (10.1007/s00285-018-1205-2) contains supplementary material, which is available to authorized users.

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Section: Appendixmentioning

confidence: 99%

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

2018

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“…1 ' 12 ' 19 have derived a general recurrence relationship for the probabilities by repeatedly differentiating the PGF w.r.t. s and then placing s = 0.…”

Section: Several Authorsmentioning

confidence: 99%

Stuttering Poisson Distributions

Kemp¹

2014

Wiley StatsRef: Statistics Reference Online

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“…The distribution of Z j is one of the zero-modified distributions and in particular it is the binomial-with-added zeros; it is a special case of the binomial-binomial distribution of Khatri and Pattel (1961). If conditional on infection, lobe type independence is assumed, then for a pig receiving vaccine v, write…”

Section: Model: Bilateral Symmetry With Non-identical Lobe Type Probamentioning

confidence: 99%

Allowing for Two Different Mechanisms by which Lesion Free Lung Lobes Occur in Pigs After an Experimental Challenge: Vaccine Performance Comparisons

Trajstman

2001

Biom. J.

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Three Classes of Univariate Discrete Distributions

Cited by 27 publications

References 4 publications

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

General solution of the chemical master equation and modality of marginal distributions for hierarchic first-order reaction networks

Stuttering Poisson Distributions

Allowing for Two Different Mechanisms by which Lesion Free Lung Lobes Occur in Pigs After an Experimental Challenge: Vaccine Performance Comparisons

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