New Term Entry: NumPy Random Module: .power()

content/numpy/concepts/random-module/terms/power/power.md

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+---
+Title: '.power()'
+Description: 'Returns a NumPy array of random samples drawn from the power distribution.'
+Subjects: 
+    - 'AI'
+    - 'Computer Science'
+    - 'Data Science'
+Tags:
+    - 'Arrays'
+    - 'Functions'
+    - 'Math'
+    - 'Numpy'
+CatalogContent:
+    - 'learn-python'
+    - 'paths/data-science'
+---
+
+The **`.power()`** function, also known as the *power function distribution*, is part of the NumPy random module. It draws random samples from the distribution $\( x^{a-1} \), where \( a > 0 \)$, returning values in the range [0, 1] as a NumPy array. This function is often used in statistical simulations, hypothesis testing, and generating synthetic data for machine learning.
+
+## Syntax
+
+```pseudo
+random.power(a, size=None)
+```
+
+**Parameters:**
+
+- `a` (float or array_like of floats): The shape parameter of the distribution. Must be positive.
+- `size` (int or tuple of ints, optional): Output shape. If specified as `(m, n, k)`, then `m * n * k` samples are drawn. If `None` (default), a single value is returned if `a` is a scalar; otherwise, `np.array(a).size` samples are drawn.
+
+**Return value:**
+
+An [`ndarray`](https://www.codecademy.com/resources/docs/numpy/ndarray) of random floats drawn from a power distribution over the interval [0, 1), with shape determined by `size`.
+
+## Example 1: Drawing a Single Value (`size=None`)
+
+When `size=None` (default), `np.random.power(a)` returns a single float from the power distribution over the range [0, 1):
+
+```py
+import numpy as np
+
+# Single sample with shape parameter a = 2
+print(np.random.power(2))
+
+# Single sample with a = 7
+print(np.random.power(7))
+```
+
+A possible output of this code is:
+
+```shell
+0.3279803284599577
+0.9487782510180921
+```
+
+When no size is specified, a single float is returned.
+
+## Example 2: Drawing Multiple Values Using an Integer `size`
+
+When `size` is an integer, it specifies how many random values to draw from the power distribution:
+
+```py
+import numpy as np
+
+# 3 values with a = 2
+print(np.random.power(2, 3))
+
+# 10 values with a = 10
+print(np.random.power(10, 10))
+
+# 3 values with a very large shape parameter
+print(np.random.power(1000, 3))
+```
+
+The possible output of this code is:
+
+```shell
+[0.71399645 0.67523938 0.59913375]
+[0.89043235 0.94651471 0.74650338 0.97812045 0.73832165 0.98408732
+ 0.94639479 0.89403161 0.95649183 0.91259268]
+[0.99993867 0.99989337 0.99973659]
+```
+
+## Codebyte Example
+
+The following example generates multi-dimensional arrays by passing a [tuple](https://www.codecademy.com/resources/docs/python/tuples) as the `size` argument:
+
+```codebyte/python
+import numpy as np
+
+# Generate a 5x5 matrix of power-distributed values with a large shape parameter
+samples = np.random.power(1000, (5, 5))
+print(samples)
+```