I bootstrapped a few hundred scenarios, and I’d like to assess the convergence of Mean and Standard Deviation over the runtime of the scenarios, if that makes sense.

Basically, I have a dataframe ordered by Scenario, with a column Value. I’d like to take the mean and std for each cell of the dataframe starting from scenario 0 and running up to the current scenario.

Here is sample code:

import pandas as pd
from io import StringIO

scenario_data = u"""
    Value, Scenario
    10, 000
    15, 001
    12, 002
    9, 003
    13, 004
    8, 005
    3, 006
    11, 007
    10, 008
    9, 009
"""

df = pd.read_csv(StringIO(scenario_data))

And these are the results I want (rounded for this post):

Value, Scenario, Running Mean, Running StD
10, 000, 10, 0
15, 001, 12.5, 3.54 # Running Mean = (10+15)/2, similar formula for StD
12, 002, 12.33, 2.52  # Running Mean = (10+15+12)/3, etc
9, 003, 11.5, 2.65
13, 004, 11.8, 2.40
8, 005, 11.17, 2.64
3, 006, 10, 3.92
11, 007, 10.13, 3.64
10, 008, 10.11, 3.41
9, 009, 10, 3.23

Ideally, I would like to plot the mean and std as line graphs, as well, but that’s the easy part.