benford | Benford's Law

You can use purrr::map_dfr() to extract MAD.conformity on each iteration, row-bind the results, and add an .id column containing the names of each element of dat_list. Since dat_list was created by splitting on CITY, the names already correspond to the levels of CITY. (I'm not familiar with the structure of Benford objects, so you may have to tweak the $MAD.conformity index.)

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:

This answer is a follow-up to a comment by the OP

Why doesn't it cycle further by the prop_cycler?

The reason why is, even if the prop_cycle is loosely defined as a property of the axes (you retrieve it using plt.rcParams['axes.prop_cycle']), in reality the axes.bar method and the axes.plot method, during initialization, instantiate separate copies of the cycler so, by default (as Matplotlib 3.4), the bars and the lines both start from blue

I had installed the R plugin and did not restart the IDE. In the past Intellij-Idea had always required a restart. I had thought - given I was not required to restart before using the plugin - that maybe in the lastest 2021.2.X they had relaxed that requirement.

Well what happened is the plugin partially worked : syntax highlighting popped up and the R commands / menu items appeared. But apparently this "install plugins without restart" is not reliable - at least for the R plugin. After restarting IJ the problem desribed inthe question disappeared and R scripts appear to be working within Intellij now.

I think the low p-value is because you have a good number of measurements, and the data just doesn't fit the theoretical expectation well enough.

If you had fewer measurements there would be more uncertainty and you would get higher p-values.

The problem is that the values for the bars are stored as strings. Matplotlib plots these strings like any other strings, placing them side-by-side on the x-axis starting at location 0 up to the last string at position 4 (bar for digit 9). You can verify this by adding print(plt.xticks()) to your code just before plt.show().

To solve this, you must use an array of integers. In the following example, this is done by changing the data type of first. In addition, the ticks are edited to show a tick label for each integer in the range of values:

In your expression, you need use boolean expression instead of assignment, e.g. if (benfordArrayProcessed[i] == 1). The values in the error get overwritten with because of assignment int he first statement itself and that's the reason you see 1 for all the elements.

I would recommend checking out this link: https://github.com/nyoshimizu/benfordspy. It's not downloadable via Conda, but you can install it directly from GitHub.