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

I have Benford test results, test_show

    Expected    Counts  Found   Dif AbsDif  Z_score
Sec_Dig                     
0   0.119679    4318    0.080052    -0.039627   0.039627    28.347781
1   0.113890    2323    0.043066    -0.070824   0.070824    51.771489
2   0.108821    1348    0.024991    -0.083831   0.083831    62.513122
3   0.104330    1298    0.024064    -0.080266   0.080266    60.975864
4   0.100308    3060    0.056730    -0.043579   0.043579    33.683738
5   0.096677    6580    0.121987    0.025310    0.025310    19.884178
6   0.093375    10092   0.187097    0.093722    0.093722    74.804141
7   0.090352    9847    0.182555    0.092203    0.092203    74.687841
8   0.087570    8439    0.156452    0.068882    0.068882    56.587749
9   0.084997    6635    0.123007    0.038010    0.038010    31.646817

I'm trying to plot the Benford result using Plotly as below,

Here is the code that I tried so far

import plotly.graph_objects as go


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)'
    ))
fig.show()

How to add the confidence interval to the plot for test_show["Expected"]?

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()