CODEWITHSUNDEEP
pythonrandomstatisticspoisson
user309575
user309575

Reputation: 41

Creating vector with intervals drawn from Poisson process

I'm looking for some advice on how to implement some statistical models in Python. I'm interested in constructing a sequence of z values (z_1,z_2,z_3,...,z_n) where the number of jumps in an interval (z_1,z_2] is distributed according to the Poisson distribution with parameter lambda(z_2-z_1) enter image description here

and the numbers of random jumps over disjoint intervals are independent random variables. I want my piecewise constant plot to look something like the two images below, where the y axis is Y(z), where Y(z) consists of N(0,1) random variables in each interval say.

To construct the z data, what would be the best way to tackle this? I have tried sampling values via np.random.poisson and then taking a cumulative sum, but the values drawn are repeated for small intensity values. Please any help or thoughts would be really helpful. Thanks.

enter image description here

Upvotes: 0

Views: 284

Answers (1)

Sam Mason
Sam Mason

Reputation: 16184

np.random.poisson is used to sample the count of events that occured in [z_i, z_j). if you want to sample the events as they occur, then you just want the exponential distribution. for example:

import numpy as np

n = 50
z = np.cumsum(np.random.exponential(1/n, size=n))
y = np.random.normal(size=n)

plotting these (using step in matplotlib) gives something similar to your plots:

plotting z vs y

note the 1/n sets a "lambda" so on average we expect n points within [0,1]. in this case we got slightly less so it overshoot. feel free to rescale if that's important to you

Upvotes: 1

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