How to visualize an evolution of a distribution in time? Suppose you have a record of distribution for each day in some period. For example, some distribution which depends on a parameter which evolves over time. Suppose we have dozens or hundreds of days. How would you visualize the change of this distribution? I want the plot to contain as much info as possible. 
One way I could think of is: proxy the density function and plot these curves's evolution in 2D. It will be some form of homotopy: the initial distribution converging to the final with some smooth step. Of course here I assume smoothness.
Thanks for your help. 
The question is theoretical in nature but I am aiming for python realization so implementations or suggestions for libraries are also welcome.
 A: 
Ridge plots can be done with Python Seaborn.
I found this beautiful example in their documentation and will repost it here.
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
sns.set_theme(style="white", rc={"axes.facecolor": (0, 0, 0, 0)})

# Create random data
rs = np.random.RandomState(1979)
x = rs.randn(500)
g = np.tile(list("ABCDEFGHIJ"), 50)
df = pd.DataFrame(dict(x=x, g=g))
m = df.g.map(ord)
df["x"] += m

# Initialize the FacetGrid object
pal = sns.cubehelix_palette(10, rot=-.25, light=.7)
g = sns.FacetGrid(df, row="g", hue="g", aspect=15, height=.5, palette=pal)

# Draw the densities in a few steps
g.map(sns.kdeplot, "x",
      bw_adjust=.5, clip_on=False,
      fill=True, alpha=1, linewidth=1.5)
g.map(sns.kdeplot, "x", clip_on=False, color="w", lw=2, bw_adjust=.5)

# passing color=None to refline() uses the hue mapping
g.refline(y=0, linewidth=2, linestyle="-", color=None, clip_on=False)


# Define and use a simple function to label the plot in axes coordinates
def label(x, color, label):
    ax = plt.gca()
    ax.text(0, .2, label, fontweight="bold", color=color,
            ha="left", va="center", transform=ax.transAxes)


g.map(label, "x")

# Set the subplots to overlap
g.figure.subplots_adjust(hspace=-.25)

# Remove axes details that don't play well with overlap
g.set_titles("")
g.set(yticks=[], ylabel="")
g.despine(bottom=True, left=True)

A: EDIT
Didn't see it was a python question. I think the idea stands, but not sure if python implementation readily available. 

You might want to look into so called ridge-plots using R package ggridges (and gganimate for animation). 
Below is an example (obviously doesn't have to be an animation): 

Code is available in this gist. 
A: Assuming you have an empirical distribution for each day, as for example a store looking at total payment by each customer, per day. You can look upon this as a time series of histograms, and that could be plotted in various ways, maybe by a series of boxplots. If you have some example data we could try various options!
A similar question was asked&answered here:  https://stackoverflow.com/questions/11690194/time-series-histogram
