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Forecasting product sales with a stochastic Bass model
Journal of Mathematics in Industry Pub Date : 2019-02-07 , DOI: 10.1186/s13362-019-0059-6
Johan Grasman , Marcel Kornelis

With the Bass model and data of previous sales a point estimate of future sales can be made for the purpose of stock management. In order to obtain information about the accuracy of that estimate a confidence interval can be of use. In this study such an interval is constructed from a Bass model extended with a noise term. The size of the noise is assumed to be proportional with the yearly sales. It is also assumed that the deviation from the deterministic solution is sufficiently small to make a small noise approximation. This perturbation takes the form of a time dependent Ornstein–Uhlenbeck process. For the variance of the perturbation an exact expression can be given which is needed in order to obtain confidence intervals.

中文翻译:

使用随机巴斯模型预测产品销售

利用Bass模型和以前的销售数据,可以对未来的销售进行点估计,以进行库存管理。为了获得有关该估计的准确性的信息,可以使用置信区间。在这项研究中,这样的间隔是根据带有噪声项的Bass模型构造的。假定噪声的大小与年销售额成正比。还假定与确定性解决方案的偏差足够小,可以使噪声近似较小。这种扰动采取时间依赖的Ornstein–Uhlenbeck过程的形式。对于扰动的变化,可以给出精确的表达式,该表达式需要获得置信区间。
更新日期:2019-02-07
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