How to add 95% confidence interval for a line chart in Plotly?

As of Python 3.8 you can use NormalDist to calculate a confidence interval as explained in detail here. With a slight adjustment to that approach you can include it in your setup with fig.add_traces() using two go.Scatter() traces, and then set fill='tonexty', fillcolor = 'rgba(255, 0, 0, 0.2)') for the last one like this:

CI = confidence_interval(df.Expected, 0.95)
fig.add_traces([go.Scatter(x = df.index, y = df['Expected']+CI,
                           mode = 'lines', line_color = 'rgba(0,0,0,0)',
                           showlegend = False),
                go.Scatter(x = df.index, y = df['Expected']-CI,
                           mode = 'lines', line_color = 'rgba(0,0,0,0)',
                           name = '95% confidence interval',
                           fill='tonexty', fillcolor = 'rgba(255, 0, 0, 0.2)')])

Please not that this approach calculates a confidence interval from the very limited df.Expected series. And that might not be what you're looking to do here. So let me know how this initial suggestion works out for you and then we can take it from there.

Plot

Complete code:

import plotly.graph_objects as go
import pandas as pd
from statistics import NormalDist

def confidence_interval(data, confidence=0.95):
  dist = NormalDist.from_samples(data)
  z = NormalDist().inv_cdf((1 + confidence) / 2.)
  h = dist.stdev * z / ((len(data) - 1) ** .5)
  return h


df = pd.DataFrame({'Expected': {0: 0.119679,
                      1: 0.11389,
                      2: 0.108821,
                      3: 0.10432999999999999,
                      4: 0.10030800000000001,
                      5: 0.096677,
                      6: 0.093375,
                      7: 0.090352,
                      8: 0.08757000000000001,
                      9: 0.084997},
                     'Counts': {0: 4318,
                      1: 2323,
                      2: 1348,
                      3: 1298,
                      4: 3060,
                      5: 6580,
                      6: 10092,
                      7: 9847,
                      8: 8439,
                      9: 6635},
                     'Found': {0: 0.080052,
                      1: 0.043066,
                      2: 0.024991,
                      3: 0.024064,
                      4: 0.056729999999999996,
                      5: 0.12198699999999998,
                      6: 0.187097,
                      7: 0.182555,
                      8: 0.156452,
                      9: 0.12300699999999999},
                     'Dif': {0: -0.039626999999999996,
                      1: -0.070824,
                      2: -0.08383099999999999,
                      3: -0.08026599999999999,
                      4: -0.043579,
                      5: 0.02531,
                      6: 0.093722,
                      7: 0.092203,
                      8: 0.068882,
                      9: 0.03801},
                     'AbsDif': {0: 0.039626999999999996,
                      1: 0.070824,
                      2: 0.08383099999999999,
                      3: 0.08026599999999999,
                      4: 0.043579,
                      5: 0.02531,
                      6: 0.093722,
                      7: 0.092203,
                      8: 0.068882,
                      9: 0.03801},
                     'Z_scoreSec_Dig': {0: 28.347781,
                      1: 51.771489,
                      2: 62.513121999999996,
                      3: 60.975864,
                      4: 33.683738,
                      5: 19.884178,
                      6: 74.804141,
                      7: 74.687841,
                      8: 56.587749,
                      9: 31.646817}})

test_show = df
fig = go.Figure()
fig.add_trace(go.Bar(x=test_show.index,
                y=test_show.Found,
                name='Found',
                marker_color='rgb(55, 83, 109)',
                # color="color"
                ))
fig.add_trace(go.Scatter(x=test_show.index,
                y=test_show.Expected,
                mode='lines+markers',
                name='Expected'
                ))

fig.update_layout(
    title='Benfords Law',
    xaxis=dict(
        title='Digits',
        tickmode='linear',
        titlefont_size=16,
        tickfont_size=14),
    yaxis=dict(
        title='% Percentage',
        titlefont_size=16,
        tickfont_size=14,
    ),
    legend=dict(
        x=0,
        y=1.0,
        bgcolor='rgba(255, 255, 255, 0)',
        bordercolor='rgba(255, 255, 255, 0)'
    ))

CI = confidence_interval(df.Expected, 0.95)

fig.add_traces([go.Scatter(x = df.index, y = df['Expected']+CI,
                           mode = 'lines', line_color = 'rgba(0,0,0,0)',
                           showlegend = False),
                go.Scatter(x = df.index, y = df['Expected']-CI,
                           mode = 'lines', line_color = 'rgba(0,0,0,0)',
                           name = '95% confidence interval',
                           fill='tonexty', fillcolor = 'rgba(255, 0, 0, 0.2)')])

fig.show()