Logistic Distribution

Logistic distribution is utilized to model growth and is widely applied in machine learning, particularly in logistic regression and neural networks.

It has three parameters:

loc: Mean, indicating the peak (default is 0).

scale: Standard deviation, representing the distribution’s flatness (default is 1).

size: Shape of the resulting array.

Example

Generate a 2×3 sample from a logistic distribution with a mean of 1 and a standard deviation of 2.0.

from numpy import random

x = random.logistic(loc=1, scale=2, size=(2, 3))

print(x)

Visualization of Logistic Distribution

Example

from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

sns.distplot(random.logistic(size=1000), hist=False)

plt.show()

Result

Difference Between Logistic and Normal Distribution

Both distributions are similar, but the logistic distribution has heavier tails, indicating a greater likelihood of events occurring farther from the mean. As the scale (standard deviation) increases, the normal and logistic distributions become nearly identical except for their peaks.

Example

from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns

sns.distplot(random.normal(scale=2, size=1000), hist=False, label=‘normal’)
sns.distplot(random.logistic(size=1000), hist=False, label=‘logistic’)

plt.show()