Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Analysis of Theoretical Physics SE statistics


Published on

Analysis of Theoretical Physics SE statistics - model for estimation of Q&A site traffic trend (v1 May 26 replaced by v2 May 31)

Published in: Technology, Education
  • Be the first to comment

  • Be the first to like this

Analysis of Theoretical Physics SE statistics

  1. 1. Analysis of Theoretical Physics SE statistics Alexander Yu. Vlasov May 31, 2012 Number of questions in Q&A StackExchange site Theoretical Physics (un-til the closure) is presented on the plot below: 400 300 200 Q 100 0 0 50 100 150 200 T The plot may be approximated with a simple model. Let’s suggest: 1. Before opening of the Q&A site some number of old questions already existed. 2. After opening of the Q&A site the rate of incoming questions is the sum of two terms: it may be either an old or a new question. 3. The rate of incoming new questions is proportional to the total number of already asked questions. 1
  2. 2. Let us denote number of old questions as Q0 = Q0 (0) and number ofquestions in Q&A site as Q(T ). We may write system of two equations dQ0 (T ) = −λ0 Q0 (T ) (1a) dT dQ(T ) = λ0 Q0 (T ) + λQ(T ) (1b) dT Due to condition Q(0) = 0 a solution of Eqs. (1) may be written as λ0 + λ −λ0 T Q0 (T ) = C e (2a) λ0 Q(T ) = C (eλT − e−λ0 T ) (2b) Using nonlinear least square estimation (nls function from R packagewas used) it was found C = 248.1, λ = 0.002335, λ0 = 0.01322 (also, due toEq. (2a), Q0 = C λ0 +λ ≈ 292). Plot of the function Q(T ) for given model λ0together with data is represented below: Parameters Std. Error t value Pr(> |t|) C = 248.1 4.016 61.79 <2E-16 λ = 0.002335 6.817E-05 34.25 <2E-16 λ0 = 0.01322 2.61E-04 50.64 <2E-16 Residual standard error: 3.928 on 406 degrees of freedom 2
  3. 3. The function Q(T ) may be used for an extrapolation for the imaginaryscenario if Theoretical Physics SE site were not be closed. Derivative of the function Q(T ) dQ = C (λeλT + λ0 e−λ0 T ) (3) dTrepresents rate of the questions per unit of time (day). 3