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The K-S test for Exponentiality

Test the null hypothesis that the interearthquake times of the Parkfield sequence are Exponentially distributed. That is, earthquakes happen at random with no memory of when the last one was. Note: This calculation is computationally intensive (you will draw more than 108 random numbers), so it will take about 10 seconds to complete.

Diese Übung ist Teil des Kurses

Case Studies in Statistical Thinking

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Anleitung zur Übung

  • Draw 10,000 replicates from the Exponential distribution using np.random.exponential(). The mean time gap between earthquakes is stored as mean_time_gap, which you computed in a previous exercise. Store the result in x_f.
  • Use these samples, x_f, along with the actual time gaps, stored in time_gap, to compute the Kolmogorov-Smirnov statistic using dcst.ks_stat().
  • Use the function you wrote in the last exercise, now conveniently stored as dcst.draw_ks_reps() to draw 10,000 K-S replicates from the Exponential distribution. Use the size=10000 keyword argument for drawing out of the target Exponential distribution. Store the replicates as reps.
  • Compute and print the p-value. Remember that "at least as extreme as" is defined in this case as the test statistic under the null hypothesis being greater than or equal to what was observed.

Interaktive Übung

Versuche dich an dieser Übung, indem du diesen Beispielcode vervollständigst.

# Draw target distribution: x_f
x_f = ____

# Compute K-S stat: d
d = ____

# Draw K-S replicates: reps
reps = ____(len(____), ____, 
                         args=(mean_time_gap,), size=____, n_reps=____)

# Compute and print p-value
p_val = ____(____ >= ____) / 10000
print('p =', p_val)
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