96,274 research outputs found
New Bounds on the Distance Distribution of Extended Goppa Codes
AbstractWe derive new estimates for the error term in the binomial approximation to the distance distribution of extended Goppa codes. This is an improvement on the earlier bounds by Vladuts and Skorobogatov, and Levy and Litsyn
A comparison between the order and the volume fill rates for a base-stock inventory control system under a compound renewal demand process
The order fill rate is less commonly used than the volume fill rate (most often just denoted fill rate) as a performance measure for inventory control systems. However, in settings where the focus is on filling customer orders rather than total quantities, the order fill rate should be the preferred measure. In this paper we consider a continuous review, base-stock policy, where all replenishment orders have the same constant lead time and all unfilled demands are backordered. We develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the order fill rate can be interpreted as the (extended) ready rate. Furthermore, for the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the order fill rate and the volume fill rate are equal (though not equivalent when considering sample paths). For the case when customer inter-arrival times follow an Erlang distribution, we show how to compute the two fill rates.Backordering; continuous review; compound renewal process; inventory control; negative binomial distribution; service levels
A multispecies birth-death-immigration process and its diffusion approximation
We consider an extended birth-death-immigration process defined on a lattice
formed by the integers of semiaxes joined at the origin. When the process
reaches the origin, then it may jumps toward any semiaxis with the same rate.
The dynamics on each ray evolves according to a one-dimensional linear
birth-death process with immigration. We investigate the transient and
asymptotic behavior of the process via its probability generating function. The
stationary distribution, when existing, is a zero-modified negative binomial
distribution. We also study a diffusive approximation of the process, which
involves a diffusion process with linear drift and infinitesimal variance on
each ray. It possesses a gamma-type transient density admitting a stationary
limit.
As a byproduct of our study, we obtain a closed form of the number of
permutations with a fixed number of components, and a new series form of the
polylogarithm function expressed in terms of the Gauss hypergeometric function.Comment: 26 pages, 7 figure
Modelling overdispersion with integer-valued moving average processes
A new first-order integer-valued moving average, INMA(1), model based
on the negative binomial thinning operation defined by Risti´c et al. [21] is proposed
and characterized. It is shown that this model has negative binomial (NB) marginal
distribution when the innovations follow a NB distribution and therefore it can be
used in situations where the data present overdispersion. Additionally, this model is
extended to the bivariate context. The Generalized Method of Moments (GMM) is
used to estimate the unknown parameters of the proposed models and the results of
a simulation study that intends to investigate the performance of the method show
that, in general, the estimates are consistent and symmetric. Finally, the proposed
model is fitted to a real dataset and the quality of the adjustment is evaluated.publishe
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