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 : string, 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’) ncf.rvs(dfn,dfd,nc,loc=0,scale=1,size=1) : random variates ncf.pdf(x,dfn,dfd,nc,loc=0,scale=1) : probability density function ncf.cdf(x,dfn,dfd,nc,loc=0,scale=1) : cumulative density function ncf.sf(x,dfn,dfd,nc,loc=0,scale=1) : survival function (1-cdf — sometimes more accurate) ncf.ppf(q,dfn,dfd,nc,loc=0,scale=1) : percent point function (inverse of cdf — percentiles) ncf.isf(q,dfn,dfd,nc,loc=0,scale=1) : inverse survival function (inverse of sf) ncf.stats(dfn,dfd,nc,loc=0,scale=1,moments=’mv’) : mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’) ncf.entropy(dfn,dfd,nc,loc=0,scale=1) : (differential) entropy of the RV. ncf.fit(data,dfn,dfd,nc,loc=0,scale=1) : Parameter estimates for ncf data 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

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,c))+1e-20)
```

Random number generation

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

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.

scipy.stats.ncx2

scipy.stats.t