The dynamics of online word-of-mouth and product sales—An empirical investigation of the movie industry

There are growing interests in understanding how word-of-mouth (WOM) on the Internet is generated and how it influences consumers’ purchase decisions at retail outlets. A unique aspect of the WOM effect is the presence of a positive feedback mechanism between WOM and retail sales. We characterize the process through a dynamic simultaneous equation system, in which we separate the effect of online WOM as both a precursor to and an outcome of retail sales. We apply our approach to the movie industry, showing that both a movie's box office revenue and WOM valence significantly influence WOM volume. WOM volume in turn leads to higher box office performance. This positive feedback mechanism highlights the importance of WOM in generating and sustaining retail revenue.     

Approximate inference in multivariate nonlinear functional relationships

An estimation procedure based on estimating equations is presented for the parameters in a multivariate functional relationship model, where all observations are subject to error. The covariance matrix of the observational errors may be parametrized and is allowed to be different for different sets of observations. Estimators are defined for the unknown relation parameters and error parameters.
For linear models (i.e. where the model function is linear in the incidental parameters) the estimators are consistent and asymptotically normal. A consistent expression for the covariance matrix of the estimators is derived. The results are valid for general error distributions.
For nonlinear models the estimators are based on locally linear approximations to the model function. The afore mentioned properties of the estimators are now only approximately valid. The adequacy of the approximate inference, based on asymptotic theory for the linearized model, needs at least informal check. Some examples are given to illustrate the estimation procedure.     

About an interactive model for sexual populations

In this paper the continuous random mating two-sex model with «harmonic mean» fertility function, partially investigated by Schoen (1983), is studied. Its closed form solution in the phase space is obtained in virtue of the homogeneity of the vector field considered. By introducing the notion of survival ability it has been clarified the balancing role played by the «marriage market».

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Riassunto Questo lavoro tratta il modello a «media armonica» per popolazioni sessuate parzialmente studiato da Schoen (1983). Si ricavano e si studiano dettagliatamente le soluzioni corrispondenti a quei valori dei parametri che individuano i casi più rilevanti dal punto di vista demografico. Per completezza, si presentano cornunque i diagrammi di fase in relazione a tutti i possibili valori delle «capacità di sopravvivenza». È stato così possibile definire chiaramente le situazioni che danno luogo, nel lungo periodo, a comportamenti di tipo stabile secondo la definizione di Lotka, facendo, in particolare, luce sul ruolo giocato dal «mercato matrimoniale».

     

Legendre小波求解Fredholm-Volterra方程

本文运用Legendre小波求解Fredholm-Volterra方程,建立了Legendre小波的算子矩阵,利用Legendre小波方法求解积分方程的基本思想是将求解积分方程的问题转化为求解一组代数方程组的问题。     

Three dual regression schemes for the Lukacs theorem

In the paper we study regressional versions of Lukacs' characterization of the gamma law. We consider constancy of regression instead of Lukacs' independence condition in three new schemes. Up to now the constancy of regressions of U=X/(X + Y) given V=X + Y for independent X and Y has been considered in the literature. Here we are concerned with constancy of regressions for X and Y while independence of U and V is assumed instead.     

Actuarial validity of the binomial distribution for large numbers of lives with small mortality probabilities

Abstract

In a previous paper (see reference [1]), the binomial distribution was shown to be valid under rather general conditions for the case of a large number of statistically independent lives with possibly unequal mortality probabilities. This note extends these results to some situations where the lives are not necessarily statistically independent. An analysis is presented which indicates that these situations include most actuarial applications involving a large number of lives.