An F continuous random variable.
Continuous 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
dfn, dfd : array_like
loc : array_like, optional
scale : 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, location, and scale parameters returning a “frozen” continuous RV object: rv = f(dfn, dfd, loc=0, scale=1)
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Notes
The probability density function for f is:
df2**(df2/2) * df1**(df1/2) * x**(df1/2-1)
F.pdf(x, df1, df2) = --------------------------------------------
(df2+df1*x)**((df1+df2)/2) * B(df1/2, df2/2)
for x > 0.
Examples
>>> from scipy.stats import f
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)
Calculate a few first moments:
>>> dfn, dfd = 29, 18
>>> mean, var, skew, kurt = f.stats(dfn, dfd, moments='mvsk')
Display the probability density function (pdf):
>>> x = np.linspace(f.ppf(0.01, dfn, dfd),
... f.ppf(0.99, dfn, dfd), 100)
>>> ax.plot(x, f.pdf(x, dfn, dfd),
... 'r-', lw=5, alpha=0.6, label='f pdf')
Alternatively, freeze the distribution and display the frozen pdf:
>>> rv = f(dfn, dfd)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
Check accuracy of cdf and ppf:
>>> vals = f.ppf([0.001, 0.5, 0.999], dfn, dfd)
>>> np.allclose([0.001, 0.5, 0.999], f.cdf(vals, dfn, dfd))
True
Generate random numbers:
>>> r = f.rvs(dfn, dfd, size=1000)
And compare the histogram:
>>> ax.hist(r, normed=True, histtype='stepfilled', alpha=0.2)
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()
Methods
rvs(dfn, dfd, loc=0, scale=1, size=1) | Random variates. |
pdf(x, dfn, dfd, loc=0, scale=1) | Probability density function. |
logpdf(x, dfn, dfd, loc=0, scale=1) | Log of the probability density function. |
cdf(x, dfn, dfd, loc=0, scale=1) | Cumulative density function. |
logcdf(x, dfn, dfd, loc=0, scale=1) | Log of the cumulative density function. |
sf(x, dfn, dfd, loc=0, scale=1) | Survival function (1-cdf — sometimes more accurate). |
logsf(x, dfn, dfd, loc=0, scale=1) | Log of the survival function. |
ppf(q, dfn, dfd, loc=0, scale=1) | Percent point function (inverse of cdf — percentiles). |
isf(q, dfn, dfd, loc=0, scale=1) | Inverse survival function (inverse of sf). |
moment(n, dfn, dfd, loc=0, scale=1) | Non-central moment of order n |
stats(dfn, dfd, loc=0, scale=1, moments=’mv’) | Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). |
entropy(dfn, dfd, loc=0, scale=1) | (Differential) entropy of the RV. |
fit(data, dfn, dfd, loc=0, scale=1) | Parameter estimates for generic data. |
expect(func, dfn, dfd, loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) | Expected value of a function (of one argument) with respect to the distribution. |
median(dfn, dfd, loc=0, scale=1) | Median of the distribution. |
mean(dfn, dfd, loc=0, scale=1) | Mean of the distribution. |
var(dfn, dfd, loc=0, scale=1) | Variance of the distribution. |
std(dfn, dfd, loc=0, scale=1) | Standard deviation of the distribution. |
interval(alpha, dfn, dfd, loc=0, scale=1) | Endpoints of the range that contains alpha percent of the distribution |