Using random.Generator.standard_gamma() method in NumPy (5 examples)

Introduction

Random sampling is an integral part of data science, simulations, and statistical modeling. NumPy, a cornerstone library for numerical computations in Python, offers a vast array of functions for generating random data. Among these, the random.Generator.standard_gamma() method is particularly noteworthy for generating gamma distributed numbers, a common necessity in various statistical analyses and simulations. This tutorial dives deep into the usage of standard_gamma() with five comprehensive examples ranging from basic to advanced.

Prerequisites: Understanding of Python basics, familiarity with NumPy, and basic knowledge of gamma distribution are recommended to get the most out of this tutorial. If you’re not up to speed with these concepts, consider reviewing them before continuing.

Syntax & Parameters

The syntax for random.Generator.standard_gamma() is as follows:

Generator.standard_gamma(shape, size=None, dtype=np.float64, out=None)

Parameters:

• shape: The shape parameter k of the Gamma distribution. It must be a positive float.
• size: This optional parameter defines the output shape. If the size is None (default), a single value is returned if shape is a scalar. Otherwise, np.array(shape).size samples are drawn.
• dtype: The desired data-type for the samples. For integer arguments, the default is float64; for floating point arguments, it is the same as the input type.
• out: An alternative output array in which to place the result. It must have a shape that the inputs broadcast to.

Returns:

• out: Samples from the standard Gamma distribution.

Example 1: Basic Usage of standard_gamma()

First, let’s dive into the basic usage of standard_gamma(). The gamma distribution is characterized by its shape parameter, and this method generates samples based on this parameter.

import numpy as np
np.random.seed(0)  # For reproducibility

# Generate five random numbers from a standard gamma distribution
shape = 2.0  # Shape parameter
samples = np.random.default_rng().standard_gamma(shape, 5)
print(samples)

Output:

[1.49953915, 2.92489411, 1.99222303, 1.15113876, 2.38102743]

This code snippet demonstrates how to generate a simple array of random numbers from a standard gamma distribution with a specific shape parameter. Notice how we utilize np.random.default_rng() to create a new instance of the random number generator for improved randomness and repeatability.

Example 2: Generating a Multidimensional Array

Expanding on the basics, you can generate multidimensional arrays filled with gamma distributed numbers. This is particularly useful for simulations or models that require a more complex data structure.

import numpy as np
np.random.seed(0)

# Generate a 3x3 array
shape = 3.0
array = np.random.default_rng().standard_gamma(shape, (3, 3))
print(array)

Output:

[[2.24431407, 4.38923415, 3.98513599],
 [1.52610424, 3.76079103, 3.57383794],
 [2.11976753, 4.66262195, 7.21450119]]

This example demonstrates generating a 3×3 array of numbers distributed according to a gamma distribution, showcasing how to work with multidimensional data structures in NumPy.

Example 3: Generating Random Samples for a Given Shape Parameter Array

Moving into more advanced usage, suppose you have an array of shape parameters and wish to generate gamma distributed samples for each. This scenario is quite common in statistical modeling where parameters vary across observations.

import numpy as np

# Array of shape parameters
shapes = np.array([2.0, 3.0, 4.0, 5.0])

# Generate samples for each shape parameter
samples = [np.random.default_rng().standard_gamma(shape) for shape in shapes]
print(samples)

Output:

[2.4873357717684503, 0.9617769764063332, 3.84232746239004, 5.836652045320263]

This sophisticated example illustrates how to generate a set of gamma distributed numbers where each number corresponds to a different shape parameter, emphasizing the flexibility of standard_gamma() in statistical modeling applications.

Example 4: Using standard_gamma() for Simulation Studies

In simulation studies, you might need to generate large datasets of gamma distributed numbers to represent various scenarios or conditions. Here’s how you can do that proficiently.

import numpy as np

# Simulation of 1000 samples with shape 2.5
shape = 2.5
samples = np.random.default_rng().standard_gamma(shape, 1000)

# Calculate and print descriptive statistics
mean = np.mean(samples)
std = np.std(samples)
print(f'Mean: {mean}, Standard Deviation: {std}')

Output:

Mean: 2.489258861426215, Standard Deviation: 1.580138847506916

This example goes beyond basic sampling by showcasing how standard_gamma() can be utilized for generating large datasets for simulation studies, complete with demonstration of how to compute and interpret descriptive statistics of the generated data.

Example 5: Custom Random Generation for Parallel Computations

For applications that require parallel computations, ensuring that random number generation does not bottleneck the process is essential. Here’s how you can use standard_gamma() in such contexts:

import numpy as np
from multiprocessing import Pool

# Function to generate gamma distributed samples in parallel
def generate_samples(shape):
    # Each call creates a new random generator instance
    rng = np.random.default_rng()
    return rng.standard_gamma(shape, 100)

# Shape parameters
shapes = [2.0, 3.0, 4.0, 5.0]

# Generate samples in parallel
if __name__ == '__main__':  # Guard for multiprocessing to work properly on Windows
    with Pool(4) as p:
        results = p.map(generate_samples, shapes)

    print(results)

Note the addition of the if __name__ == '__main__': guard. This is necessary, especially on Windows, where the multiprocessing module requires that the code spawning new processes be under this guard to prevent unintended behavior when the script is run.

Output (vary, due to the randomness):

[array([1.03215648, 0.19820113, 1.81424245, 4.85714   , 1.77801427,
       2.96648589, 1.22172258, 1.07137073, 0.09265501, 2.30445097,
       5.06458131, 0.53288345, 4.83505199, 2.26228843, 5.3456901 ,
       2.50963277, 3.34792412, 0.74078586, 2.38912431, 3.70094032,
       1.08818886, 0.20581622, 3.01923297, 0.45590104, 1.83948848,
       3.54448234, 0.99553891, 1.84870773, 2.66600737, 0.74158068,
       3.4077227 , 0.86539404, 1.88816095, 1.00745997, 2.99213747,
       1.16922452, 0.99180187, 1.5748503 , 1.53149832, 2.05490344,
       1.9255714 , 0.95830758, 1.7849535 , 1.00478014, 1.22707778,
       0.94722799, 1.83682054, 4.80653628, 0.39451731, 1.18562844,
       0.67695911, 3.05766818, 1.58204203, 0.12953684, 0.98377307,
       1.45107267, 0.31595694, 5.87721361, 2.74665499, 1.93639048,
       2.17166081, 3.41485526, 2.14912927, 0.60265735, 0.52283887,
       1.07933269, 0.48432688, 0.7050529 , 3.69275189, 2.34569116,
       4.45227328, 2.34500396, 0.55065578, 1.05721137, 5.14028998,
       0.79181824, 0.6912421 , 0.27798349, 2.32897913, 5.7310411 ,
       0.6046941 , 2.64793667, 0.3556952 , 4.55182056, 2.00294139,
       1.35310091, 0.79701002, 1.39308509, 2.03077388, 1.87185943,
       1.4815736 , 0.6082856 , 1.5239448 , 4.3208234 , 0.53955845,
       2.5757316 , 1.22220494, 0.60094244, 3.45879575, 0.46287631]), array([1.77538868, 0.68440697, 2.45059241, 2.38191889, 2.39300634,
       2.75406166, 0.20873079, 1.04341527, 3.8856803 , 1.99110785,
       3.13236042, 0.63776397, 1.15187293, 6.20070852, 4.67621094,
       1.91421255, 3.58826726, 1.40378916, 2.50552795, 2.02405823,
       1.61769057, 4.69110904, 4.00017583, 4.86199535, 1.40478192,
       3.40218861, 2.27914079, 2.76271009, 2.69305211, 0.53728574,
       0.59911763, 4.14116918, 3.49074434, 4.18862845, 4.15505756,
       4.2486335 , 5.04601499, 5.12951341, 3.22818934, 1.30215021,
       3.46111393, 5.46789237, 3.35683718, 7.14117934, 3.68938277,
       1.54455841, 5.23089315, 1.20357937, 3.74006515, 3.72399435,
       0.67150224, 2.31204456, 1.45463135, 2.29655526, 4.23482386,
       1.04196745, 2.54214839, 1.87050623, 0.86069551, 1.7458431 ,
       3.22939672, 3.45658115, 2.35717679, 2.75604748, 1.32542078,
       5.3367374 , 5.09365234, 1.38709842, 2.38212061, 1.01524529,
       2.46481753, 2.41068638, 0.72916085, 3.94574688, 1.93986476,
       0.60453647, 0.9099644 , 1.5987728 , 0.78704179, 1.3563473 ,
       2.40091624, 2.40240219, 1.64429114, 2.96585323, 1.81038276,
       2.17227384, 2.55311256, 1.79161062, 6.26516347, 1.89654986,
       4.10754811, 3.18699513, 4.17907868, 1.95235426, 0.32823287,
       1.72138785, 0.69220284, 2.95418008, 1.41800567, 1.44396346]), array([ 2.90991255,  2.3479888 ,  3.08088153,  2.6123674 ,  3.31251699,
        2.64243097,  4.44240819,  2.27946546,  1.3391295 ,  2.81257128,
        2.11003898,  4.85093964,  4.46974282,  8.32818876,  2.86303845,
        0.93571527,  0.83204113,  4.38660913,  3.86782967,  5.18101386,
        2.91355638,  4.10962785,  4.01898153,  4.49704157,  1.60969873,
        2.852206  ,  3.07794453,  2.16136238,  2.71703483,  3.99407383,
        5.02791451,  0.95171634,  4.63717189,  5.31828978,  5.94365347,
        1.02159937,  5.0564887 ,  7.58445294,  2.01157656,  6.04105805,
        3.60847596,  3.48869215,  1.98629559,  3.51019751,  2.56672931,
        4.1410473 ,  6.82324617,  5.11774268,  3.91694632,  9.37652685,
        3.13122644,  4.03998901,  2.32354754,  5.92768437,  4.31669804,
        3.76075514,  2.00300792, 10.16866683,  1.56640487,  1.67211328,
        7.98712143,  4.02822591,  7.84055174,  4.40263216,  4.47637386,
        2.16653474,  4.07713436,  3.13800045,  3.35637173,  7.18704908,
        2.70482386,  4.55115732,  6.74256392,  7.61725312,  3.132093  ,
        4.38061472,  1.89660605,  1.65186636,  4.72032542,  2.06317019,
        1.18922806,  4.68946689,  3.57229239,  1.95035215,  6.6465289 ,
        4.09525084,  3.05062237,  4.71373386,  4.36514359,  6.19922121,
        2.80802106,  3.86506017,  3.66474424,  1.06241258, 11.13898737,
        2.35583465,  4.34189367,  3.13098573,  5.91925453,  2.35049325]), array([ 4.95216005,  4.10489895,  2.1757513 ,  2.15934924,  3.54300004,
        4.58514434,  2.21419855,  1.93459086,  4.95946149,  4.71659572,
        8.696191  ,  6.17122206,  1.72171034, 13.22017942,  2.42441758,
        5.37011696,  5.2506531 ,  7.95256379,  3.66577956,  5.13559244,
        4.18569927,  7.20490656,  4.20936067,  8.13395933,  1.53815958,
        8.13650026,  8.22559075,  4.39225763,  4.28408697,  4.37867267,
        9.81315851,  9.67815025,  5.16419986,  6.49000279,  6.82645244,
        4.13174989,  5.0471945 ,  1.56723906,  3.04978393,  5.74534578,
        1.89210627,  3.7269689 ,  6.71040542,  3.66294815,  3.64230209,
        4.47183045,  4.20426715,  2.46453055,  3.23282696,  6.12270236,
        7.72950285,  4.52844638,  5.27103114,  5.16893768,  8.53224207,
        4.75352294,  3.93051508,  4.82207159,  4.41799663,  2.13069396,
        3.40372747,  3.30255154,  5.61506509,  6.90185422,  3.1554201 ,
        3.18926494,  7.5070901 ,  3.82707989,  5.25647247,  5.37317514,
        4.24434862,  7.02527599,  4.47850898,  8.40334225,  5.493274  ,
        4.61429355,  6.28078876,  5.17682327,  2.52392414,  5.04272182,
        4.97967034,  1.07329066,  4.9847681 ,  3.98480241,  3.70594701,
        1.54393133,  6.13026355,  5.45347691,  4.9206205 ,  7.50558065,
        7.6340099 ,  4.02256769,  5.13340491,  5.58727482,  8.00560707,
        6.08223163,  7.34391284,  2.48172951,  4.01150224,  3.81366499])]

This advanced example demonstrates how to incorporate standard_gamma() within parallel processing workflows, significantly boosting efficiency in scenarios that require heavy random data generation.

Conclusion

The random.Generator.standard_gamma() method in NumPy is a powerful tool for generating gamma distributed random numbers. Through the examples provided, we’ve explored its capability from basic usage to complex scenarios involving simulation studies and parallel processing. Harnessing the power of NumPy and standard_gamma(), you can elevate your statistical modeling and simulations to new heights.