# scipy.stats.t¶

scipy.stats.t

Student’s T 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 quantiles q : array-like lower or upper tail probability df : array-like shape parameters loc : array-like, optional location parameter (default=0) scale : array-like, optional scale parameter (default=1) size : int or tuple of ints, optional shape of random variates (default computed from input arguments ) moments : str, optional composed of letters [‘mvsk’] specifying which moments to compute where ‘m’ = mean, ‘v’ = variance, ‘s’ = (Fisher’s) skew and ‘k’ = (Fisher’s) kurtosis. (default=’mv’) Alternatively, the object may be called (as a function) to fix the shape, : location, and scale parameters returning a “frozen” continuous RV object: : rv = t(df, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Student’s T distribution

gamma((df+1)/2)
t.pdf(x,df) = ———————————————–
sqrt(pi*df)*gamma(df/2)*(1+x**2/df)**((df+1)/2)

for df > 0.

Examples

>>> import matplotlib.pyplot as plt
>>> numargs = t.numargs
>>> [ df ] = [0.9,] * numargs
>>> rv = t(df)

Display frozen pdf

>>> x = np.linspace(0, np.minimum(rv.dist.b, 3))
>>> h = plt.plot(x, rv.pdf(x))

Check accuracy of cdf and ppf

>>> prb = t.cdf(x, df)
>>> h = plt.semilogy(np.abs(x - t.ppf(prb, df)) + 1e-20)

Random number generation

>>> R = t.rvs(df, size=100)

Methods

 rvs(df, loc=0, scale=1, size=1) Random variates. pdf(x, df, loc=0, scale=1) Probability density function. cdf(x, df, loc=0, scale=1) Cumulative density function. sf(x, df, loc=0, scale=1) Survival function (1-cdf — sometimes more accurate). ppf(q, df, loc=0, scale=1) Percent point function (inverse of cdf — percentiles). isf(q, df, loc=0, scale=1) Inverse survival function (inverse of sf). stats(df, loc=0, scale=1, moments=’mv’) Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’). entropy(df, loc=0, scale=1) (Differential) entropy of the RV. fit(data, df, loc=0, scale=1) Parameter estimates for generic data.

scipy.stats.ncf

scipy.stats.nct