added script demonstrates the implementation of the Sigmoid function.

The sigmoid function is a logistic function, which describes growth as being initially
exponential, but then slowing down and barely growing at all when a limit is reached.
It's commonly used as an activation function in neural networks.

Author: Mathasuriya-infy

neural_network/activation_functions/sigmoid.py

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+"""
+This script demonstrates the implementation of the Sigmoid function.
+
+The sigmoid function is a logistic function, which describes growth as being initially
+exponential, but then slowing down and barely growing at all when a limit is reached.
+It's commonly used as an activation function in neural networks.
+
+For more detailed information, you can refer to the following link:
+https://en.wikipedia.org/wiki/Sigmoid_function
+"""
+
+import numpy as np
+
+
+def sigmoid(vector: np.ndarray) -> np.ndarray:
+    """
+    Implements the sigmoid activation function.
+
+    Parameters:
+        vector (np.ndarray): A vector that consists of numeric values
+
+    Returns:
+        np.ndarray: Input vector after applying sigmoid activation function
+
+    Formula: f(x) = 1 / (1 + e^(-x))
+
+    Examples:
+    >>> sigmoid(np.array([-1.0, 0.0, 1.0, 2.0]))
+    array([0.26894142, 0.5       , 0.73105858, 0.88079708])
+
+    >>> sigmoid(np.array([-5.0, -2.5, 2.5, 5.0]))
+    array([0.00669285, 0.07585818, 0.92414182, 0.99330715])
+    """
+    return 1 / (1 + np.exp(-vector))
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()