Understanding Logistic Distribution
The Logistic Distribution is widely used to model growth and has significant applications in machine learning—especially in algorithms such as logistic regression and neural networks.
Key Parameters:
The logistic distribution has three key parameters:
- loc (location): Represents the mean, indicating the center or peak of the distribution. (Default: 0)
- scale: Defines the standard deviation, controlling the spread or flatness of the distribution. (Default: 1)
- size: Specifies the shape of the output array containing random samples.
Program:
Let’s generate a 2x3 sample from a logistic distribution with:
Mean (loc) = 1
Standard Deviation (scale) = 1
from numpy import random
x = random.logistic(loc=1, scale=2, size=(2, 3))
print(x)
Output:
[[ 1.65247251 -4.2787476 1.30817934]
[ 1.85770462 2.10677579 2.45309228]]
Visualizing the Logistic Distribution:
You can easily visualize the logistic distribution using Matplotlib and Seaborn:
Program:
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
sns.displot(random.logistic(size=1000), kind="kde")
plt.show()
Logistic vs. Normal Distribution:
At first glance, the Logistic Distribution and the Normal (Gaussian) Distribution appear quite similar. However, there’s a key difference:
- The logistic distribution has heavier tails, meaning it accounts for a higher probability of extreme values far from the mean.
- For larger scale values, both distributions become increasingly similar, with the logistic distribution showing a sharper peak.
Program:
from numpy import random
import matplotlib.pyplot as plt
import seaborn as sns
data = {
"normal": random.normal(scale=2, size=1000),
"logistic": random.logistic(size=1000)
}
sns.displot(data, kind="kde")
plt.show()
