張莉莉+郝新生
摘 要 給出Logistic,Gompertz,Usher和Von Bertalanffy 4種增長曲線的拐點、最大加速點和最大減速點的表達式.利用R語言編寫程序,結合擬牛頓算法與隨機優化算法,對微信月活躍用戶數(WMAUs)的發展趨勢進行分析與擬合.結果表明,4條曲線的擬合值在最大加速點到最大減速點時間段內基本吻合,但在初期和后期有所差別. Logistic曲線在初期的預測值偏大,而后期偏小,偏差相對較大;Von Bertalanffy曲線的偏差最小,且在飽和值、拐點、最大加速點、最大減速點及擬合優度的估計值方面都優于另外3種曲線;Usher和Gompertz曲線居于Logistic與Von Bertalanffy曲線之間,對后期的預測值有些保守.最后,基于價值理念的觀點分析了影響WMAUs變動的主要因素.
關鍵詞 增長曲線;WMAUs;R語言;價值理念
中圖分類號 O212文獻標識碼 A
Abstract 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.
Key words growth curve;WeChat monthly active users;R language;value idea
1 引 言
微信(WeChat)自從由騰訊于2011 年 1 月推出以來,已從單純的即時通訊服務APP發展為集社交、學習、購物、娛樂、理財、支付、廣告、小程序及云服務等于一體的綜合性服務APP,且其功能仍然在進一步發展和完善.根據騰訊按季度公布的業績來看,2014年年底,微信月活躍賬戶數突破5億,經過半年的時間,2015年第二季度就達6億,直到2017年6月底已達9.63億.[1]
經過6年多的飛速發展,微信已成為廣大網民們的一種生活方式,影響著人們的思想和行為.有關微信的理論研究已有好多成果,主要集中在有關微信的功能與特點、發展與傳播、應用與問題、統計與預測等方面,如文獻[2]利用擴散理論說明微信用戶數的發展呈“S型”增長曲線,文獻[3]采用Bass模型對微信用戶……