Goulib.stats module

very basic statistics functions

Goulib.stats.mean_var(data)

mean and variance by stable algorithm :param :return: float (mean, variance) of data uses a stable algo by Knuth

Goulib.stats.mean(data)

Returns:mean of data

Goulib.stats.avg(data)

Returns:mean of data

Goulib.stats.variance(data)

Returns:variance of data, faster (?) if mean is already available

Goulib.stats.var(data)

Returns:variance of data, faster (?) if mean is already available

Goulib.stats.stddev(data)

Returns:standard deviation of data

Goulib.stats.confidence_interval(data, conf=0.95)

Returns:(low,high) bounds of 95% confidence interval of data

Goulib.stats.median(data, is_sorted=False)

Returns:median of data

Goulib.stats.mode(data, is_sorted=False)

Returns:mode (most frequent value) of data

Goulib.stats.kurtosis(data)

Goulib.stats.covariance(data1, data2)

Goulib.stats.stats(l)

Returns:min,max,sum,sum2,avg,var of a list

class Goulib.stats.Stats(data=[], mean=None, var=None)

Bases: object

an object that computes mean, variance and modes of data that is appended to it as in a list (but actual values are not stored)

__init__(data=[], mean=None, var=None)

Initialize self. See help(type(self)) for accurate signature.

__repr__()

Return repr(self).

append(x)

add data x to Stats

extend(data)

remove(data)

remove data from Stats :param data: value or iterable of values

sum

sum1

sum2

mean

avg

average

mu

variance

var

stddev

sigma

__add__(other)

__sub__(other)

__mul__(other)

__neg__()

__pow__(n)

covariance(other)

__class__

alias of builtins.type

__delattr__

Implement delattr(self, name).

__dir__()

Default dir() implementation.

__eq__

Return self==value.

__format__()

Default object formatter.

__ge__

Return self>=value.

__getattribute__

Return getattr(self, name).

__gt__

Return self>value.

__hash__

Return hash(self).

__init_subclass__()

This method is called when a class is subclassed.

The default implementation does nothing. It may be overridden to extend subclasses.

__le__

Return self<=value.

__lt__

Return self<value.

__ne__

Return self!=value.

__new__()

Create and return a new object. See help(type) for accurate signature.

__reduce__()

Helper for pickle.

__reduce_ex__()

Helper for pickle.

__setattr__

Implement setattr(self, name, value).

__sizeof__()

Size of object in memory, in bytes.

__str__

Return str(self).

class Goulib.stats.Discrete(data)

Bases: Goulib.stats.Stats

discrete probability density function

Parameters:data – can be:

• list of equiprobable values (uniform distribution)
• dict of x:p values:probability pairs

__init__(data)

Parameters:data – can be:

• list of equiprobable values (uniform distribution)
• dict of x:p values:probability pairs

__call__(x)

Call self as a function.

__add__(other)

__class__

alias of builtins.type

__delattr__

Implement delattr(self, name).

__dir__()

Default dir() implementation.

__eq__

Return self==value.

__format__()

Default object formatter.

__ge__

Return self>=value.

__getattribute__

Return getattr(self, name).

__gt__

Return self>value.

__hash__

Return hash(self).

__init_subclass__()

This method is called when a class is subclassed.

The default implementation does nothing. It may be overridden to extend subclasses.

__le__

Return self<=value.

__lt__

Return self<value.

__mul__(other)

__ne__

Return self!=value.

__neg__()

__new__()

Create and return a new object. See help(type) for accurate signature.

__pow__(n)

__reduce__()

Helper for pickle.

__reduce_ex__()

Helper for pickle.

__repr__()

Return repr(self).

__setattr__

Implement setattr(self, name, value).

__sizeof__()

Size of object in memory, in bytes.

__str__

Return str(self).

__sub__(other)

append(x)

add data x to Stats

average

avg

covariance(other)

extend(data)

mean

mu

remove(data)

remove data from Stats :param data: value or iterable of values

sigma

stddev

sum

sum1

sum2

var

variance

class Goulib.stats.PDF(pdf, data=[])

Bases: Goulib.expr.Expr, Goulib.stats.Stats

probability density function

__init__(pdf, data=[])

Parameters:f – function or operator, Expr to copy construct, or formula string

__call__(x=None, **kwargs)

evaluate the Expr at x OR compose self(x())

__add__(right)

__and__(right)

__class__

alias of builtins.type

__delattr__

Implement delattr(self, name).

__dir__()

Default dir() implementation.

__div__(right)

__eq__(other)

Return self==value.

__float__()

__format__()

Default object formatter.

__ge__(other)

Return self>=value.

__getattribute__

Return getattr(self, name).

__gt__(other)

Return self>value.

__hash__ = None

__init_subclass__()

This method is called when a class is subclassed.

The default implementation does nothing. It may be overridden to extend subclasses.

__invert__()

__le__(other)

Return self<=value.

__lshift__(dx)

__lt__(other)

Return self<value.

__mul__(right)

__ne__(other)

Return self!=value.

__neg__()

__new__()

Create and return a new object. See help(type) for accurate signature.

__or__(right)

__pow__(right)

__reduce__()

Helper for pickle.

__reduce_ex__()

Helper for pickle.

__repr__()

Return repr(self).

__rmul__(right)

__rshift__(dx)

__setattr__

Implement setattr(self, name, value).

__sizeof__()

Size of object in memory, in bytes.

__str__()

Return str(self).

__sub__(right)

__truediv__(right)

__xor__(right)

append(x)

add data x to Stats

applx(f, var='x')

function composition f o self = self(f(x))

apply(f, right=None)

function composition self o f = f(self(x))

average

avg

complexity()

measures the complexity of Expr :return: int, sum of the precedence of used ops

covariance(other)

extend(data)

html(**kwargs)

isNum

isconstant

Returns:True if Expr evaluates to a constant number or bool

latex()

Returns:string LaTex formula

mean

mu

plot(**kwargs)

renders on IPython Notebook (alias to make usage more straightforward)

png(**kwargs)

points(xmin=-1, xmax=1, step=0.1)

Returns:x,y lists of float : points for a line plot

remove(data)

remove data from Stats :param data: value or iterable of values

render(fmt='svg', **kwargs)

save(filename, **kwargs)

sigma

stddev

sum

sum1

sum2

svg(**kwargs)

var

variance

Goulib.stats.normal_pdf(x, mu, sigma)

Return the probability density function at x

class Goulib.stats.Normal(data=[], mean=0, var=1)

Bases: Goulib.stats.PDF

represents a normal distributed variable the base class (list) optionally contains data

if data is specified, it it used to fit a normal law

__init__(data=[], mean=0, var=1)

if data is specified, it it used to fit a normal law

__str__()

Return str(self).

latex()

Returns:string LaTex formula

linear(a, b=0)

Returns:a*self+b

__mul__(a)

__div__(a)

__truediv__(a)

__add__(other)

__radd__(other)

__neg__()

__sub__(other)

__rsub__(other)

covariance(other)

cov(other)

pearson(other)

correlation(other)

corr(other)

__and__(right)

__call__(x=None, **kwargs)

evaluate the Expr at x OR compose self(x())

__class__

alias of builtins.type

__delattr__

Implement delattr(self, name).

__dir__()

Default dir() implementation.

__eq__(other)

Return self==value.

__float__()

__format__()

Default object formatter.

__ge__(other)

Return self>=value.

__getattribute__

Return getattr(self, name).

__gt__(other)

Return self>value.

__hash__ = None

__init_subclass__()

This method is called when a class is subclassed.

The default implementation does nothing. It may be overridden to extend subclasses.

__invert__()

__le__(other)

Return self<=value.

__lshift__(dx)

__lt__(other)

Return self<value.

__ne__(other)

Return self!=value.

__new__()

Create and return a new object. See help(type) for accurate signature.

__or__(right)

__pow__(right)

__reduce__()

Helper for pickle.

__reduce_ex__()

Helper for pickle.

__repr__()

Return repr(self).

__rmul__(right)

__rshift__(dx)

__setattr__

Implement setattr(self, name, value).

__sizeof__()

Size of object in memory, in bytes.

__xor__(right)

append(x)

add data x to Stats

applx(f, var='x')

function composition f o self = self(f(x))

apply(f, right=None)

function composition self o f = f(self(x))

average

avg

complexity()

measures the complexity of Expr :return: int, sum of the precedence of used ops

extend(data)

html(**kwargs)

isNum

isconstant

Returns:True if Expr evaluates to a constant number or bool

mean

mu

plot(**kwargs)

renders on IPython Notebook (alias to make usage more straightforward)

png(**kwargs)

points(xmin=-1, xmax=1, step=0.1)

Returns:x,y lists of float : points for a line plot

remove(data)

remove data from Stats :param data: value or iterable of values

render(fmt='svg', **kwargs)

save(filename, **kwargs)

sigma

stddev

sum

sum1

sum2

svg(**kwargs)

var

variance

Goulib.stats.linear_regression(x, y, conf=None)

Parameters:

• x,y – iterable data
• conf – float confidence level [0..1]. If None, confidence intervals are not returned

Returns:

b0,b1,b2, (b0

Return the linear regression parameters and their <prob> confidence intervals.

ex: >>> linear_regression([.1,.2,.3],[10,11,11.5],0.95)