Why does my probability plot not agree with my histogram? I am trying to determine the best distribution to characterize a dataset. My dataset visually looks like Cauchy distribution would be a good fit, so I used python to fit a Cauchy distribution to my dataset. Visually, with the fitted Cauchy distribution plotted over the histogram of my data, it looks to fit well. However, the probability plot says otherwise. How could these two plots disagree so much? My coefficient of determination is 0.04. The top plot is sample data (y-axis) against the quantiles of the Cauchy distribution (x-axis), and the bottom plot is the probability density histogram with the x-axis being the values in my dataset.

My "data" is a NumPy array of ~2 million data points imported from a txt file.
out = stats.cauchy.fit(data)
tmp = np.linspace(-3, 3, 1000)
y = stats.cauchy.pdf(tmp, *out)
plt.figure()
ax = plt.subplot(2,1,1);
(_, o2) = stats.probplot(data, dist='cauchy', fit=True, plot=ax);
plt.subplot(2,1,2)
plt.hist(data, 100, density=True)
plt.plot(tmp, y)
print(f"slope: {o2[0]}")
print(f"intercept: {o2[1]}")
print(f"r2: {o2[2]}")


Various reasons. Perhaps most directly, consider that the horizontal scales of your two graphs are vastly different so that the density and the CDF cannot be fairly compared. The standard Cauchy distribution ($\mathsf{T}(\nu=1))$ puts only about half of its probability in $(-3,3),$ whereas standard normal puts nearly all of its probability in that interval.
[R code:]
diff(pt(c(-3,.3), 1))
[1] 0.4903572
diff(pnorm(c(-3,3)))
[1] 0.9973002

