The Exponential distribution

Statistical Thinking in Python (Part 1)

Justin Bois

Teaching Professor at the California Institute of Technology

The Exponential distribution

The waiting time between arrivals of a Poisson process is Exponentially distributed

The Exponential PDF

ch4-4.004.png

Possible Poisson process

Nuclear incidents:
- Timing of one is independent of all others

Exponential inter-incident times

mean = np.mean(inter_times)
samples = rng.exponential(mean, size=10000)
x, y = ecdf(inter_times)
x_theor, y_theor = ecdf(samples)
_ = plt.plot(x_theor, y_theor)
_ = plt.plot(x, y, marker='.', linestyle='none')
_ = plt.xlabel('time (days)')
_ = plt.ylabel('CDF')
plt.show()

Exponential inter-incident times

ch4-4.011.png

Let's practice!

Statistical Thinking in Python (Part 1)