discrete_rv

Filename: discrete_rv.py

Authors: Thomas Sargent, John Stachurski

Generates an array of draws from a discrete random variable with a specified vector of probabilities.

class quantecon.discrete_rv.DiscreteRV(q)[source]

Bases: object

Generates an array of draws from a discrete random variable with vector of probabilities given by q.

Parameters:

q : array_like(float)

Nonnegative numbers that sum to 1

Attributes

q Getter method for q.
Q (array_like(float)) The cumulative sum of q

Methods

draw([k]) Returns k draws from q.
draw(k=1)[source]

Returns k draws from q.

For each such draw, the value i is returned with probability q[i].

Parameters:

k : scalar(int), optional

Number of draws to be returned

Returns:

array_like(int)

An array of k independent draws from q

q

Getter method for q.

quantecon.discrete_rv.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 or array_like of floats, 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 or array_like of floats

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. If size is None (default), a single value is returned if low and high are both scalars. Otherwise, np.broadcast(low, high).size samples are drawn.

Returns:

out : ndarray or scalar

Drawn samples from the parameterized uniform distribution.

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

\[p(x) = \frac{1}{b - a}\]

anywhere within the interval [a, b), and zero elsewhere.

When high == low, values of low will be returned. If high < low, the results are officially undefined and may eventually raise an error, i.e. do not rely on this function to behave when passed arguments satisfying that inequality condition.

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()