微信用户数发展趋势的理论分析与因素探讨

给出Logistic,Gompertz,Usher和Von Bertalanffy 4种增长曲线的拐点、最大加速点和最大减速点的表达式.利用R语言编写程序,结合拟牛顿算法与随机优化算法,对微信月活跃用户数(WMAUs)的发展趋势进行分析与拟合.结果表明,4条曲线的拟合值在最大加速点到最大减速点时间段内基本吻合,但在初期和后期有所差别.Logistic曲线在初期的预测值偏大,而后期偏小,偏差相对较大;Von Bertalanffy曲线的偏差最小,且在饱和值、拐点、最大加速点、最大减速点及拟合优度的估计值方面都优于另外3种曲线;Usher和Gompertz曲线居于Logistic与Von Bertalanffy曲线之间,对后期的预测值有些保守.最后,基于价值理念的观点分析了影响WMAUs变动的主要因素.

Theoretical Analysis and Factors Discussion on Trend of WeChat Users

The expression of the inflection point, the maximum acceleration point and the maximum deceleration point of Logistic, Gompertz, Usher and Von Bertalanffy growth curves were given.Using the R language program, combined with quasi-Newton algorithm and stochastic optimization algorithm, the development trend of WeChat monthly active users was analyzed and fitted. The results show that the fitting value of the four curves is basically consistent between the period of the maximum acceleration point to the maximum decelerationpoint, but it is different in the initial and later stages.The fitting value of Logistic curve is too large in the initial period and small in the later stage, and the deviation is relatively large. The Von Bertalanffy curve has the least deviation and is superior to the other three curves in terms of the estimated values of saturation value, inflection point, maximum acceleration point, maximum deceleration point and goodness of fit. Usher and Gompertz curves reside between the Logistic and Von Bertalanffy curves, and its predictions are somewhat conservative in the later period.Finally, the main factors influencing the WMAUs were analyzed based on the viewpoint of value idea.