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.
Let us denote number of old questions as Q0 = Q0 (0) and number of
questions 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 package
was used) it was found C = 248.1, λ = 0.002335, λ0 = 0.01322 (also, due to
Eq. (2a), Q0 = C λ0 +λ ≈ 292). Plot of the function Q(T ) for given model
λ0
together 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.
The function Q(T ) may be used for an extrapolation for the imaginary
scenario if Theoretical Physics SE site were not be closed.
Derivative of the function Q(T )
dQ
= C (λeλT + λ0 e−λ0 T ) (3)
dT
represents rate of the questions per unit of time (day).
3