A uniform discrete random variable.
Discrete random variables are defined from a standard form and may require some shape parameters to complete its specification. Any optional keyword parameters can be passed to the methods of the RV object as given below:
Parameters: | x : array_like
q : array_like
low, high : array_like
loc : array_like, optional
size : int or tuple of ints, optional
moments : str, optional
Alternatively, the object may be called (as a function) to fix the shape and location parameters returning a “frozen” discrete RV object: rv = randint(low, high, loc=0)
|
---|
Notes
The probability mass function for randint is:
randint.pmf(k) = 1./(high - low)
for k = low, ..., high - 1.
randint takes low and high as shape parameters.
Note the difference to the numpy random_integers which returns integers on a closed interval [low, high].
Examples
>>> from scipy.stats import randint
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> low, high = 7, 31
>>> mean, var, skew, kurt = randint.stats(low, high, moments='mvsk')
Display the probability mass function (pmf):
>>> x = np.arange(randint.ppf(0.01, low, high),
... randint.ppf(0.99, low, high))
>>> ax.plot(x, randint.pmf(x, low, high), 'bo', ms=8, label='randint pmf')
>>> ax.vlines(x, 0, randint.pmf(x, low, high), colors='b', lw=5, alpha=0.5)
Alternatively, freeze the distribution and display the frozen pmf:
>>> rv = randint(low, high)
>>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
... label='frozen pmf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
Check accuracy of cdf and ppf:
>>> prob = randint.cdf(x, low, high)
>>> np.allclose(x, randint.ppf(prob, low, high))
True
Generate random numbers:
>>> r = randint.rvs(low, high, size=1000)
Methods
rvs(low, high, loc=0, size=1) | Random variates. |
pmf(x, low, high, loc=0) | Probability mass function. |
logpmf(x, low, high, loc=0) | Log of the probability mass function. |
cdf(x, low, high, loc=0) | Cumulative density function. |
logcdf(x, low, high, loc=0) | Log of the cumulative density function. |
sf(x, low, high, loc=0) | Survival function (1-cdf — sometimes more accurate). |
logsf(x, low, high, loc=0) | Log of the survival function. |
ppf(q, low, high, loc=0) | Percent point function (inverse of cdf — percentiles). |
isf(q, low, high, loc=0) | Inverse survival function (inverse of sf). |
stats(low, high, loc=0, moments=’mv’) | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). |
entropy(low, high, loc=0) | (Differential) entropy of the RV. |
expect(func, low, high, loc=0, lb=None, ub=None, conditional=False) | Expected value of a function (of one argument) with respect to the distribution. |
median(low, high, loc=0) | Median of the distribution. |
mean(low, high, loc=0) | Mean of the distribution. |
var(low, high, loc=0) | Variance of the distribution. |
std(low, high, loc=0) | Standard deviation of the distribution. |
interval(alpha, low, high, loc=0) | Endpoints of the range that contains alpha percent of the distribution |