A comparison of sales response predictions from demand models applied to store-level versus panel data

In order to generate sales promotion response predictions, marketing analysts estimate demand models using either disaggregated (consumer-level) or aggregated (store-level) scanner data. Comparison of predictions from these demand models is complicated by the fact that models may accommodate different forms of consumer heterogeneity depending on the level of data aggregation. This study shows via simulation that demand models with various heterogeneity specifications do not produce more accurate sales response predictions than a homogeneous demand model applied to store-level data, with one major exception: a random coefficients model designed to capture within-store heterogeneity using store-level data produced significantly more accurate sales response predictions (as well as better fit) compared to other model specifications. An empirical application to the paper towel product category adds additional insights. This article has supplementary material online.

Fokker-Planck equation approach to the description of soliton statistics in optical fiber transmission systems

We derive rigorously the Fokker-Planck equation that governs the statistics of soliton parameters in optical transmission lines in the presence of additive amplifier spontaneous emission. We demonstrate that these statistics are generally non-Gaussian. We present exact marginal probability-density functions for soliton parameters for some cases. A WKB approach is applied to describe the tails of the probability-density functions. © 2005 Optical Society of America.

Statistics of noise-driven coupled nonlinear oscillators:applications to systems with Kerr nonlinearity

We present exact analytical results for the statistics of nonlinear coupled oscillators under the influence of additive white noise. We suggest a perturbative approach for analysing the statistics of such systems under the action of a deterministic perturbation, based on the exact expressions for probability density functions for noise-driven oscillators. Using our perturbation technique we show that our results can be applied to studying the optical signal propagation in noisy fibres at (nearly) zero dispersion as well as to weakly nonlinear lattice models with additive noise. The approach proposed can account for a wide spectrum of physically meaningful perturbations and is applicable to the case of large noise strength. © 2005 Elsevier B.V. All rights reserved.

Non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission

A study was performed on non-Gaussian statistics of an optical soliton in the presence of amplified spontaneous emission. An approach based on the Fokker-Planck equation was applied to study the optical soliton parameters in the presence of additive noise. The rigorous method not only allowed to reproduce and justify the classical Gordon-Haus formula but also led to new exact results.