Modeling Session Length

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Revision as of 22:27, 4 November 2009

Contents 1 Exponential and Mixture of Exponentials 1.1 Single Exponential 1.1.1 Entire data 1.1.2 Truncated Data 1.2 Two Exponentials 1.2.1 Entire data 1.2.2 Truncated data 1.3 Three Exponentials 1.4 Skewed Normal 1.5 Pareto Distribution 1.6 Weibull Dist. 1.6.1 Entire Data 1.6.2 All User 1.7 Mixture of two Weibull distributions

Exponential and Mixture of Exponentials

In this section, I try to fit the session length of each user to several exponential models.

Single Exponential

Entire data

User 27
rate: 1.019121e-05

Two-sample Kolmogorov-Smirnov test: D = 0.1308, p-value < 2.2e-16

Truncated Data

User 27: values less than session length mean
rate:  2.647844e-05

Two-sample Kolmogorov-Smirnov test: D = 0.1441, p-value < 2.2e-16

Two Exponentials

Entire data

user 27:
lambda1 = 0.8352734
lambda2 = 0.1647266 (1-lambda1)

theta1 = 115838.0
theta2 = 8301.25

Two-sample Kolmogorov-Smirnov test: D = 0.0842, p-value < 2.2e-16

Truncated data

All values larger than the mean of session length was filtered.

user 27:
lambda1 = 9.999998e-01
lambda2 = 2.184364e-07 (1-lambda1)

theta1 = 3.776658e+04
theta2 = 5.883020e+03

Two-sample Kolmogorov-Smirnov test: D = D = 0.1569, p-value < 2.2e-16

Three Exponentials

Skewed Normal

Does not seem to fit well.

Pareto Distribution

Does not seem to fit well

Weibull Dist.

Entire Data

User 27

      shape          scale    
  8.031812e-01   8.545603e+04

Two-sample Kolmogorov-Smirnov test: D = 0.0862, p-value < 2.2e-16

All User

zoomed in versions:

Mixture of two Weibull distributions

Zoomed-in