Dist_cubicSpline

class stats.Dist_cubicSpline(x, y, N_cs=1000)

Bases: stats.Dist_qilum

Distribution for (x,y): cubic splaine approximation for both cumulative ans values

Parameters

• x (array like) –

• y (array like) –

• N_cs (int) – number of point to set up the cubic spline

Examples

>>> import qilum.stats as qs
>>> # test function: truncated gaussian
>>> def f_f(xs):
...     return 3.*np.exp(-np.square(xs)/10.)
>>>
>>> # initialize class
>>> x = np.linspace(-12, 12, 51)
>>> y = f_f(x)
>>> dist = qs.Dist_cubicSpline(x, y, N_cs=1000)

Methods Summary

F_tot()	Cumulative of the function f() on the whole valid range x
cdf(x)	Cumulative distribution function.
f(x)	Cubic spline of (x,y) Approximation: should be 1/F’(F_inverse(x)), but very small error
name()	Name of the class
pdf(x)	Probability density function.
ppf(q)	Percent point function (inverse of cdf) at q
rvs(size)	random numbers in ndarray of lenght size
rvs_xy(size)	random numbers rans in ndarray of lenght size and function(rans)

Methods Documentation

F_tot()

Cumulative of the function f() on the whole valid range x

Returns

Return type

int

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> print(dist.F_tot())
16.81497238763992

cdf(x)

Cumulative distribution function.

Parameters

x (array_like of type(values)) –

Returns

Cumulative distribution function evaluated at x

Return type

ndarray

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> x = [-3,1,2,3]
>>> print('cdf(x)=',dist.cdf(x))
cdf(x)= [0.09161441 0.67650553 0.81730869 0.91187099]

f(x)

Cubic spline of (x,y) Approximation: should be 1/F’(F_inverse(x)), but very small error

Parameters

x (array_like of type(values)) –

Returns

f(x)

Return type

ndarray

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> x = [-3,1,2,3]
>>> print('f(x)=',dist.f(x))
f(x)= [1.21972729 2.71451285 2.01096922 1.21972729]

name()

Name of the class

Returns

‘Dist_reject’

Return type

string

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> dist.name()
'Dist_cubicSpline'

pdf(x)

Probability density function. Cubic spline of (x,y)

Parameters

x (array_like of type(values)) –

Returns

f(x)/F_tot()

Return type

ndarray

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> x = [-3,1,2,3]
>>> print('pdf(x)=',dist.pdf(x))
pdf(x)= [0.07253817 0.16143427 0.11959396 0.07253817]

ppf(q)

Percent point function (inverse of cdf) at q

Parameters

q (array_like of double) – lower tail probability

Returns

quantile corresponding to the lower tail probability q

Return type

ndarray

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> q = [0, 0.3,0.5,0.7,1]
>>> print('ppf(q)=',dist.ppf(q))
ppf(q)= [-12.          -1.19663998  -0.02402402   1.14859193  11.97597598]

rvs(size)

random numbers in ndarray of lenght size

Parameters

size (int) – number of random number

Returns

random numbers

Return type

ndarray

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> print('rans=',dist.rvs(4))
rans= [ 3.1874446  -0.24592411 -2.9817858  -1.65194734]

rvs_xy(size)

random numbers rans in ndarray of lenght size and function(rans)

Parameters

size (int) – number of random number

Returns

• ndarray – random numbers

• ndarray – f(random numbers)

Examples

>>> x = np.linspace(-12, 12, 51)
>>> dist = qs.Dist_cubicSpline(x, y= 3.*np.exp(-np.square(x)/10.), N_cs=1000)
>>> print('rans=',dist.rvs_xy(2))
rans= (array([-0.17748735,  1.35683644]), array([2.9905203 , 2.49554626]))