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Uniform

How to sample numbers from any uniform distribution on the real line.

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Imports

This tutorial imports Plotly and Numpy.

In [1]:
import plotly.plotly as py
import plotly.graph_objs as go

import numpy as np

Uniform

Unlike np.random.random() where you can sample a number between a fixed interval of [0, 1), np.random.uniform() allows you to set your own low and high bounds to your interval and draw uniformly from that. Also like np.random.random(), there is a size parameter for sampling several times from the uniform distribution.

In [2]:
import plotly.plotly as py
import plotly.graph_objs as go

num_of_points = 150
uniform_array_1 = np.random.uniform(0, 1, num_of_points)
uniform_array_2 = np.random.uniform(2, 4, num_of_points)
uniform_array_3 = np.random.uniform(6, 10, num_of_points)

trace1 = go.Scatter(
    x=[j for j in range(num_of_points)],
    y=uniform_array_1,
    mode='markers',
    marker = dict(
        size=14,
        color=uniform_array_1,
        colorscale='Reds'
    ),
    name='[0, 1]'
)

trace2 = go.Scatter(
    x=[j for j in range(num_of_points)],
    y=uniform_array_2,
    mode='markers',
    marker = dict(
        size=13,
        color=uniform_array_2,
        colorscale='Blues'
    ),
    name='[2, 4]'
)

trace3 = go.Scatter(
    x=[j for j in range(num_of_points)],
    y=uniform_array_3,
    mode='markers',
    marker = dict(
        size=12,
        color=uniform_array_3,
        colorscale='Greens'
    ),
    name='[6, 10]'
)

py.iplot([trace1, trace2, trace3], filename='numpy-uniform')
Out[2]:
In [4]:
help(np.random.uniform)
Help on built-in function uniform:

uniform(...)
    uniform(low=0.0, high=1.0, size=None)
    
    Draw samples from a uniform distribution.
    
    Samples are uniformly distributed over the half-open interval
    ``[low, high)`` (includes low, but excludes high).  In other words,
    any value within the given interval is equally likely to be drawn
    by `uniform`.
    
    Parameters
    ----------
    low : float, optional
        Lower boundary of the output interval.  All values generated will be
        greater than or equal to low.  The default value is 0.
    high : float
        Upper boundary of the output interval.  All values generated will be
        less than high.  The default value is 1.0.
    size : int or tuple of ints, optional
        Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
        ``m * n * k`` samples are drawn.  Default is None, in which case a
        single value is returned.
    
    Returns
    -------
    out : ndarray
        Drawn samples, with shape `size`.
    
    See Also
    --------
    randint : Discrete uniform distribution, yielding integers.
    random_integers : Discrete uniform distribution over the closed
                      interval ``[low, high]``.
    random_sample : Floats uniformly distributed over ``[0, 1)``.
    random : Alias for `random_sample`.
    rand : Convenience function that accepts dimensions as input, e.g.,
           ``rand(2,2)`` would generate a 2-by-2 array of floats,
           uniformly distributed over ``[0, 1)``.
    
    Notes
    -----
    The probability density function of the uniform distribution is
    
    .. math:: p(x) = \frac{1}{b - a}
    
    anywhere within the interval ``[a, b)``, and zero elsewhere.
    
    Examples
    --------
    Draw samples from the distribution:
    
    >>> s = np.random.uniform(-1,0,1000)
    
    All values are within the given interval:
    
    >>> np.all(s >= -1)
    True
    >>> np.all(s < 0)
    True
    
    Display the histogram of the samples, along with the
    probability density function:
    
    >>> import matplotlib.pyplot as plt
    >>> count, bins, ignored = plt.hist(s, 15, normed=True)
    >>> plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')
    >>> plt.show()

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