Histogram Keywords¶

The ax.hist() method accepts various keyword arguments to customize histogram appearance and behavior.

bins¶

The bins parameter controls how data is grouped. It accepts either an integer (number of bins) or a sequence (explicit bin edges).

bins as int¶

When bins is an integer, matplotlib automatically calculates bin edges spanning the data range.

```python import matplotlib.pyplot as plt import numpy as np

def main(): # data generation n_samples = 10_000 data = np.random.randn(n_samples)

# plot histogram with integer bins
fig, ax = plt.subplots(figsize=(12, 4))
ax.hist(data, bins=100, alpha=0.2)  # <--- int used
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.tight_layout()
plt.show()

if name == "main": main() ```

bins as sequence¶

When bins is a sequence, it defines the exact positions of bin edges, providing precise control over binning.

```python import matplotlib.pyplot as plt import numpy as np

def main(): # data generation n_samples = 10_000 data = np.random.randn(n_samples)

# plot histogram with sequence bins
fig, ax = plt.subplots(figsize=(12, 4))
ax.hist(data, bins=np.linspace(-4, 4, 100), alpha=0.2)  # <--- sequence used
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.tight_layout()
plt.show()

if name == "main": main() ```

density¶

The density parameter controls whether the histogram shows counts or probability density.

• density=False (default): y-axis shows raw counts
• density=True: y-axis shows probability density (area under histogram equals 1)

```python import matplotlib.pyplot as plt import numpy as np

def main(): # data generation n_samples = 10_000 data = np.random.randn(n_samples)

# plot histogram in density scale
fig, ax = plt.subplots()
ax.hist(data, bins=100, density=True, alpha=0.2)  # <--- density=True
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.show()

if name == "main": main() ```

histtype¶

The histtype parameter controls the visual style of the histogram.

Example: step histogram with PMF overlay¶

```python import matplotlib.pyplot as plt import numpy as np from scipy import stats

Set the seed for reproducibility¶

np.random.seed(42)

Parameters for the binomial distribution¶

num_trials = 10 success_probability = 0.6

Number of random samples to generate¶

num_samples = 100

Generate random samples from the binomial distribution¶

samples = stats.binom(num_trials, success_probability).rvs(num_samples)

Possible outcomes from 0 successes to 'num_trials' successes¶

outcomes = np.arange(num_trials + 1)

Probability mass function values for each outcome¶

pmf_values = stats.binom(num_trials, success_probability).pmf(outcomes)

Set up the plot¶

fig, ax = plt.subplots(figsize=(12, 3))

Bar plot to show the probability mass function¶

ax.bar(outcomes, pmf_values, alpha=0.2, color='red', label='Binomial PMF')

Histogram of the sampled data with step style¶

ax.hist(samples, bins=np.arange(num_trials + 2) - 0.5, density=True, histtype='step', label='Sampled Data Histogram')

Adding labels and legend¶

ax.set_xlabel('Number of Successes') ax.set_ylabel('Probability') ax.legend()

plt.show() ```

Documentation¶

• matplotlib.axes.Axes.hist

Exercises¶

Exercise 1. Write code demonstrating the histtype parameter by creating a 2x2 subplot grid showing the same data with histtype='bar', 'barstacked', 'step', and 'stepfilled'.

Exercise 2. Explain the difference between bins=30 (integer) and bins='auto' in ax.hist(). What algorithm does 'auto' use?

Exercise 3. Create a histogram with custom bin edges using bins=[0, 1, 2, 5, 10, 20] (non-uniform spacing). Explain when non-uniform bins are useful.

Exercise 4. Write code that creates a cumulative histogram using cumulative=True and overlays the theoretical CDF for the same distribution.