# Riddler: Simulating a Branching Process

Simulation, Probability distributions (Exponential and Geometric)

Published

April 12, 2020

Notable topics: Simulation, Probability distributions (Exponential and Geometric)

Recorded on: 2020-04-12

Timestamps by: Alex Cookson

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## Timestamps

Explanation of a Poisson process

Asking "How long do you have to wait for X to happen?", which the Exponential distribution can answer

rexp

Using rexp function to generate numbers from the Exponential distribution

rexp

Using a vector of rates inside the rexp function (to explore consecutive waiting times)

Using cumsum function to calculate total waiting time until hitting a specific number in the Poisson process

which

Using which function to determine the first instance > 3 in a vector

replicate

Using replicate function to do a quick simulation of the function just written

Discussing methods of making the simulation function faster

crossing

Using crossing function to set up "tidy" simulation (gives you all possible combinations of values you provide it)

Noting how the consecutive waiting times seems to follow the Harmonic series

Noticing that we are missing trials with 0 comments and fixing

nls

Using nls function (non-linear least squares) to test how well the data fits with an exponential curve

Visualizing fit between data and the exponential curve calculated with nls in previous step

augment

Using augment function to added fitted values of the nls function

Exploring whether the data actually follows a Geometric distribution

Explanation of the Geometric distribution as it applies to this question

Generalizing the question to ask how long it takes to get to multiple comments (not just 3)

Explanation of why we subtract 1 when fitting an exponential curve

Summary of screencast