Continuous interval modeling
Modeling a quantity with equal density across a bounded interval.
SciPy · Function
stats.uniform
scipy.stats.uniform represents a continuous uniform distribution. Its standard support is [0, 1]; loc shifts the lower endpoint and scale sets the interval width.
How it works
scipy.stats.uniform is a continuous distribution object with support from loc through loc + scale. Use its inherited distribution methods for density, probabilities, quantiles, moments, and random variates; calling it with parameters creates a frozen distribution that retains them.
Syntax
scipy.stats.uniform(loc=0, scale=1)Parameters
| Name | Type | Description |
|---|---|---|
loc | array_like, optional | Location parameter; the lower endpoint of the distribution's support. Defaults to 0. |
scale | array_like, optional | Scale parameter; the support width. The upper endpoint is loc + scale; defaults to 1. |
size | int or tuple of ints, optional | Number or shape of random variates returned by rvs; defaults based on input arguments. |
moments | str, optional | Requested moments for stats, selected using letters such as m, v, s, and k. |
Returns
A frozen continuous random-variable object when called with parameters; distribution methods return values appropriate to the selected operation.
Key points
scipy.stats.uniformmodels a continuous random variable whose density is constant over its interval.- With default parameters, the distribution covers the unit interval from zero through one.
- Its probability density is flat inside the support and zero outside it.
- The distribution provides the standard continuous-distribution API through inheritance.
- Parameterizing the distribution produces a reusable frozen object with fixed settings.
Common mistakes
scaleis the interval width, so the upper endpoint is computed asloc + scale, not supplied independently.- Calling
uniformreturns a frozen random-variable object; use that object when repeatedly evaluating the same parameterized distribution.
Example: Evaluate and sample a shifted uniform distribution
from scipy.stats import uniform
x = uniform(loc=2, scale=3)
print(x.pdf(3.5))
print(x.cdf(4.0))
print(x.rvs(random_state=0, size=3))This creates a frozen uniform distribution on [2, 5], evaluates its density and cumulative probability, and draws three reproducible samples.
When to use it
Randomized testing
Generating random test inputs within configurable bounds.
Distribution analysis
Computing densities, cumulative probabilities, quantiles, and moments for a uniform model.
Interview questions
QHow do loc and scale change the support of scipy.stats.uniform?
The standard distribution is uniform on [0, 1]. loc shifts the lower endpoint, while scale determines the interval width, producing support [loc, loc + scale].
Follow-up: How would you represent a uniform distribution on [a, b]? Use loc=a and scale=b-a, assuming b is greater than a.
QWhich kinds of operations can be performed with uniform?
The object inherits generic methods from rv_continuous, including methods for probabilities, density, moments, quantiles, and random variates. For example, pdf, cdf, ppf, stats, and rvs can be used on the distribution object.
Follow-up: Why use a frozen object? It stores the chosen parameters once, making repeated method calls less error-prone and easier to read.
QWhat is a frozen uniform random variable?
Calling the distribution with location and scale parameters creates a frozen continuous random-variable object. Its methods then use those fixed parameters automatically.
Follow-up: What must be checked when converting [a, b] into loc and scale? Ensure the width b-a is positive.
Related
scipy.stats.rv_continuousscipy.stats.uniform.pdfscipy.stats.uniform.cdfscipy.stats.uniform.ppfscipy.stats.uniform.rvsscipy.stats.uniform.stats