Smoother

smoother.Smoother

class smoother.Smoother(lb=0, ub=1, num=50) [source]

The smoother computes a distribution by maximizing an objective function (i.e. a smoothness function) given constraints.

Attributes:

x : np.array

A linearly spaced (self.num,) array of points between the lower and upper bounds of the distribution.

f_x : np.array

The probability density function of self.x.

F_x : np.array

The cumulative distribution function of self.x.

Methods

mean(self) [source]

Returns:	mean : float

var(self) [source]

Returns:	variance : float

std(self) [source]

Returns:	standard deviation : float

median(self) [source]

Returns:	median : float

entropy(self) [source]

Returns:	entropy : float

pdf(self, x) [source]

Parameters:	x : float
Returns:	pdf(x) : float Probability density function of `x`.

cdf(self, x) [source]

Parameters:	x : float
Returns:	cdf(x) : float between 0. and 1. Cumulative distribution function of `x`.

ppf(self, q) [source]

Parameters:	q : float between 0. and 1. Quantile.
Returns:	ppf(q) : float Percent point function; inverse of `self.cdf`.

sf(self, x) [source]

Parameters:	x : float
Returns:	sf(x) : float between 0. and 1. Survival function; `1-self.cdf`.

isf(self, q) [source]

Parameters:	q : float between 0. and 1.
Returns:	isf(x) : float Inverse survival function.

moment(self, degree=1, type_='raw', norm=False) [source]

Parameters:	degree : int, default=1 The degree of the moment, e.g. first (mean), second (var). type_ : str, default='raw' Type of moment; `'raw'`, `'central'`, or `'standardized'`. norm : bool, default=False Indicates whether to return the norm of the moment. If `True`, return `moment**(1/degree)`.
Returns:	moment : float

fit(self, lb, ub, constraints, objective=lambda self: self.entropy(), num=50) [source]

Parameters:

lb : scalar

Lower bound of the distribution.

ub : scalar

Upper bound of the distribution.

constraints : list of callables

Constraints take in a Smoother and return a float. Lower values indicate that the constraints are satisfied.

objective :

The objective or smoothing function. The objective function takes a Smoother and returns a float. This objective function is maximized subject to constraints. By default, it maximizes entropy.

num : int, default=50

Number of points on the distribution used for approximation.

Returns:

self :

dump(self) [source]

Returns:	state_dict : dict JSON dump of the state dictionary.

load(state_dict) [source]

Parameters:	state_dict : dict Output of `Smoother.dump`.
Returns:	smoother : Smoother Smoother with the specified state dictionary.