The moments and central moments of a compound distribution

Grubbström, Robert W.; Tang, Ou

doi:10.1016/j.ejor.2004.06.012

Cited by 34 publications

(15 citation statements)

References 5 publications

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“…An in-depth analysis about compound distributions was recently done by Grubbström and Tang (2006). In this specific case we can extend the result reported in Kleinrock (1975), pp.…”

Section: Ps Movement Timesupporting

confidence: 56%

Fleet sizing of laser guided vehicles and pallet shuttles in automated warehouses

Ferrara

Gebennini

Grassi

2014

International Journal of Production Economics

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“…An in-depth analysis about compound distributions was recently done by Grubbström and Tang (2006). In this specific case we can extend the result reported in Kleinrock (1975), pp.…”

Section: Ps Movement Timesupporting

confidence: 56%

Fleet sizing of laser guided vehicles and pallet shuttles in automated warehouses

Ferrara

Gebennini

Grassi

2014

International Journal of Production Economics

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“…Proof. According to [8], since X t | X t−1 is a compound Poisson random variable where the compounding distribution is the Poisson law with parameter θ, its mth moment is given by…”

Section: Stationarity Ergodicity and Moments Existencementioning

confidence: 99%

A New Approach to Integer-Valued Time Series Modeling: The Neyman Type-A INGARCH Model*

2015

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The aim of this paper is to develop a probabilistic study of a wide class of conditionally heteroscedastic models recently introduced in the literature, the compound Poisson INGARCH processes [7]. This class includes, in particular, some well-known models like the Poisson INGARCH of Ferland, Latour, and Oraichi [4] or the negative binomial and generalized Poisson INGARCH introduced by Zhu in 2011 and 2012, respectively.Within this class, we analyze the existence and ergodicity of a strictly and weakly stationary solution. For a new particular model of that class, the Neyman type-A INGARCH model, we derive the autocorrelation function, analyze the existence of higher-order moments, and obtain an explicit form of their first four cumulants, from which we deduce the corresponding skewness and kurtosis.MSC: 62M10, 60G10, 60G12

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“…Taking the nth derivative and therefore , knowing , we find that (19) If the transform is developed into a series , then all coefficients below a n vanish when taking the derivative, and all terms above a n when taking the limit s → 0, leaving us with only So, given the transform of a density function, it suffices to examine the coefficients of its series expansion in order to determine all moments.…”

Section: Moment-generating Functionmentioning

confidence: 99%

“…The compound distribution is also a good example to illustrate the advantage of using Laplace transforms for moment-generating purposes for applications in inventory modelling [19], see also [36,37]. In the latter of these references, a more complicated distribution is handled by the Laplace transform.…”

Section: Robert W Grubbströmmentioning

confidence: 99%

Transform methodology applied to some inventory problems

Grubbström

2007

Z. Betriebswirtsch

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■ The Laplace transform is a mathematical methodology for solving differential equations, for studying stability properties of dynamic systems, as a moment-generating function in probability theory, for evaluating the Net Present Value (NPV), and for several other applications. It dates back to the early 18 th century.■ This article presents examples of few different applications to inventory problems: a delayed inventory control model, a simple stochastic model, saw-tooth patterned inventory cycles, and Material Requirements Planning (MRP). In particular, certain theorems of the Laplace transform have proved to be useful frequently, such as time translation, final value, and NPV.

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The moments and central moments of a compound distribution

Cited by 34 publications

References 5 publications

Fleet sizing of laser guided vehicles and pallet shuttles in automated warehouses

Fleet sizing of laser guided vehicles and pallet shuttles in automated warehouses

A New Approach to Integer-Valued Time Series Modeling: The Neyman Type-A INGARCH Model*

Transform methodology applied to some inventory problems

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