Uniform Distribution

Table of contents

Density Function

The density function of the Uniform distribution:

\[f(x; a, b) = \frac{1}{b-a} \times \mathbf{1}[ a \leq x \leq b]\]

Methods for scalar input, as well as for list input, are listed below.

Scalar Input

pystats.dunif(x: float, min: float = 0.0, max: float = 1.0, log: bool = False) → float

Density function of the Uniform distribution.

Example

>>> pystats.dunif(0.5, -1.0, 2.0)
0.3333333333333333
Parameters

  • x (float) – A real-valued input.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

  • log (bool) – Return the log-density or the true form.

Returns

The density function evaluated at x.

List Input

pystats.dunif(x: List[float], min: float = 0.0, max: float = 1.0, log: bool = False) → List[float]

Density function of the Uniform distribution.

Example

>>> pystats.dunif([-2.0, 0.0, 2.0], -1.0, 3.0)
[0.0, 0.25, 0.25]
Parameters

  • x (List[float]) – A standard list input.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

  • log (bool) – Return the log-density or the true form.

Returns

A list of density values corresponding to the elements of x.

Cumulative Distribution Function

The cumulative distribution function (CDF) of the Uniform distribution:

\[F(x; a, b) = \int_{a}^x f(z; a, b) dz = \frac{x - a}{b-a} \times \mathbf{1}[ a \leq x \leq b] + \times \mathbf{1}[x > b]\]

Methods for scalar input, as well as for list input, are listed below.

Scalar Input

pystats.punif(p: float, min: float = 0.0, max: float = 1.0, log: bool = False) → float

Distribution function of the Uniform distribution.

Example

>>> pystats.punif(0.5, -1.0, 2.0)
0.5
Parameters

  • p (float) – A real-valued input.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

  • log (bool) – Return the log-density or the true form.

Returns

The cumulative distribution function evaluated at p.

List Input

pystats.punif(p: List[float], min: float = 0.0, max: float = 1.0, log: bool = False) → List[float]

Distribution function of the Uniform distribution.

Example

>>> pystats.punif([-2.0, 0.0, 2.0], -1.0, 3.0)
[0.0, 0.25, 0.75]
Parameters

  • p (List[float]) – A standard list input.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

  • log (bool) – Return the log-density or the true form.

Returns

A list of CDF values corresponding to the elements of p.

Quantile Function

The quantile function of the Uniform distribution:

\[q(p; a, b) = a + p(b-a)\]

Methods for scalar input, as well as for list input, are listed below.

Scalar Input

pystats.qunif(q: float, min: float = 0.0, max: float = 1.0) → float

Quantile function of the Uniform distribution.

Example

>>> pystats.qunif(0.75, -1.0, 2.0)
1.25
Parameters

  • q (float) – A real-valued input.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

Returns

The quantile function evaluated at q.

List Input

pystats.qunif(q: List[float], min: float = 0.0, max: float = 1.0) → List[float]

Quantile function of the Uniform distribution.

Example

>>> pystats.qunif([0.3, 0.5, 0.9], -1.0, 3.0)
[0.2, 1.0, 2.6]
Parameters

  • q (List[float]) – A standard list input.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

Returns

A list of quantiles values corresponding to the elements of q.

Random Sampling

Random sampling for the Uniform distribution is achieved via the uniform_real_distribution class from the C++ standard library, imported from <random>.

Scalar Output

pystats.runif(min: float = 0.0, max: float = 1.0) → float

Random sampling function for the Uniform distribution.

Example

>>> pystats.runif(-1.0, 2.0)
1.0599044629461352
Parameters

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

Returns

A pseudo-random draw from the Uniform distribution.

List Output

pystats.runif(n: int, min: float = 0.0, max: float = 1.0) → List[float]

Random sampling function for the Uniform distribution.

Example

>>> pystats.runif(3, -1.0, 2.0)
[1.0552953561528309, 0.81837699091385, 0.17769962603787082]
Parameters

  • n (int) – The number of output values.

  • min (float) – The lower limit of the distribution, a real-valued input.

  • max (float) – The upper limit of the distribution, a real-valued input.

Returns

A list of pseudo-random draws from the Uniform distribution.