# scipy.stats.ncf¶

scipy.stats.ncf

A non-central F distribution 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 dfn, dfd, nc : 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 = ncf(dfn, dfd, nc, loc=0, scale=1) : Frozen RV object with the same methods but holding the given shape, location, and scale fixed.

Notes

Non-central F distribution

ncf.pdf(x,df1,df2,nc) = exp(nc/2 + nc*df1*x/(2*(df1*x+df2)))
• df1**(df1/2) * df2**(df2/2) * x**(df1/2-1)
• (df2+df1*x)**(-(df1+df2)/2)
• gamma(df1/2)*gamma(1+df2/2)
• L^{v1/2-1}^{v2/2}(-nc*v1*x/(2*(v1*x+v2)))

/ (B(v1/2, v2/2) * gamma((v1+v2)/2))

for df1, df2, nc > 0.

Examples

```>>> import matplotlib.pyplot as plt
>>> numargs = ncf.numargs
>>> [ dfn, dfd, nc ] = [0.9,] * numargs
>>> rv = ncf(dfn, dfd, nc)
```

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 = ncf.cdf(x, dfn, dfd, nc)
>>> h = plt.semilogy(np.abs(x - ncf.ppf(prb, dfn, dfd, nc)) + 1e-20)
```

Random number generation

```>>> R = ncf.rvs(dfn, dfd, nc, size=100)
```

Methods

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

scipy.stats.ncx2

scipy.stats.t