truncated.gaussian

Module: truncated.gaussian

Inheritance diagram for selectinf.truncated.gaussian:

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This module implements the class truncated_gaussian which performs (conditional) UMPU tests for Gaussians restricted to a set of intervals.

Classes

TruncatedGaussianError

class selectinf.truncated.gaussian.TruncatedGaussianError

Bases: ValueError

__init__($self, /, *args, **kwargs)

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

args

with_traceback()

Exception.with_traceback(tb) – set self.__traceback__ to tb and return self.

truncated_gaussian

class selectinf.truncated.gaussian.truncated_gaussian(I, mu=0, scale=1.0)

Bases: selectinf.truncated.base.truncated

>>> from selectinf.constraints.intervals import intervals
>>> I = intervals.intersection(intervals((-1, 6)),                                        intervals(( 0, 7)),                                        ~intervals((1, 4)))
>>> distr = truncated_gaussian(I, 3.1, 2.)

__init__(I, mu=0, scale=1.0)

Create a new object for a truncated_gaussian distribution

Parameters

I : intervals

The intervals the distribution is truncated to.

mu : int

Mean of Gaussian that is truncated.

scale : float

SD of Gaussian that is truncated.

cdf(z)

Compute the survival function of the truncated distribution

Parameters

z : float

Minimum bound of the interval

Returns

cdf : float

function The cumulative distribution function of the truncated distribution cdf(z) = P( X < z | X is in intervals )

WARNING : This method only use the sf method

more precise

pdf(z)

Compute the probability distribution funtion of the truncated distribution

Parameters

z : float

Returns

p : float

p(z) such that E[f(X)] = int f(z)p(z)dz

quantile(q, tol=1e-06)

rvs(size=1)

Sample a random variable from the truncated disribution

Parameters

size : int

Number of samples. Default : 1

Returns

X : np.array

array of sample

sf(z)

Compute the survival function of the truncated distribution

Parameters

z : float

Minimum bound of the interval

Returns

sf : float

The survival function of the truncated distribution sf(z) = P( X > z | X is in intervals )

truncated_gaussian_old

class selectinf.truncated.gaussian.truncated_gaussian_old(intervals, mu=0, scale=1)

Bases: object

A Gaussian distribution, truncated to

__init__(intervals, mu=0, scale=1)

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

property intervals

property negated

set_mu(mu)

get_mu()

property mu

set_scale(scale)

get_scale()

property scale

property delta

\[\begin{split}\begin{align} \delta_\mu(a,b) &\triangleq \int_a^b x\phi(x-\mu)\,dx \\ &= - \phi(b-\mu) + \phi(a-\mu) + \mu\left(\Phi(b-\mu)-\Phi(a-\mu)\right), \end{align}\end{split}\]

static twosided(thresh, mu=0, scale=1)

cdf(observed)

quantile(q)

right_endpoint(left_endpoint, alpha)

G(left_endpoint, alpha)

\(g_{\mu}\) from Will’s code

dG(left_endpoint, alpha)

\(gg_{\mu}\) from Will’s code

equal_tailed_interval(observed, alpha)

UMAU_interval(observed, alpha, mu_lo=None, mu_hi=None, tol=1e-08)

Functions

selectinf.truncated.gaussian.G(left_endpoints, mus, alpha, tg)

Compute the \(G\) function of tg(intervals) over zip(left_endpoints, mus).

A copy is made of tg and its \((\mu,\scale)\) are not modified.

selectinf.truncated.gaussian.dG(left_endpoints, mus, alpha, tg)

Compute the \(G\) function of tg(intervals) over zip(left_endpoints, mus).

A copy is made of tg and its \((\mu,\scale)\) are not modified.

selectinf.truncated.gaussian.find_root(f, y, lb, ub, tol=1e-06)

searches for solution to f(x) = y in (lb, ub), where f is a monotone decreasing function