现有的网站往往向注册用户提供服务，而网站中的每日活跃用户量往往决定着网站建设的成败。为了描述网站中每日活跃用户的动态变化，将用户在网站上的交互行为分为响应、扩散和衰落三种类型，并提出了一种基于用户交互模型的每日活跃用户量模型。通过响应、扩散和衰落三种交互行为的定义，进一步推导出每日活跃用户随着时间的变化率。通过对每日活跃用户随着时间的变化率进行分析得到如下结论：当网站中用户的响应概率小于衰落概率时网站的活跃用户将趋向于0，反之活跃用户趋于某个固定的常数。大量的真实数据实验表明，不论网站自身的运营是否成功，

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Empirical Modeling and Data Analysis for Engineers and Applied Scientists English | 25 July 2016 | ISBN: 3319327674 | 264 Pages This textbook teaches advanced undergraduate and first-year graduate students in Engineering and Applied Sciences to gather and analyze empirical observations (data) in order to aid in making design decisions. While science is about discovery, the primary paradigm of engineering and “applied science” is design. Scientists are in the discovery business and want, in general, to understand the natural world rather than to alter it. In contrast, engineers and applied scientists design products, processes, and solutions to problems. That said, statistics, as a discipline, is mostly oriented toward the discovery paradigm. Young engineers come out of their degree programs having taken courses such as “Statistics for Engineers and Scientists” without any clear idea as to how they can use statistical methods to help them design products or processes. Many seem to think that statistics is only useful for demonstrating that a device or process actually does what it was designed to do. Statistics courses emphasize creating predictive or classification models – predicting nature or classifying individuals, and statistics is often used to prove or disprove phenomena as opposed to aiding in the design of a product or process. In industry however, Chemical Engineers use designed experiments to optimize petroleum extraction; Manufacturing Engineers use experimental data to optimize machine operation; Industrial Engineers might use data to determine the optimal number of operators required in a manual assembly process. This text teaches engineering and applied science students to incorporate empirical investigation into such design processes.

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