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UniformDistribution

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

UniformDistribution[{lo, hi}]

represents a continuous uniform distribution; UniformDistribution[] is uniform on {0, 1}.

Examples (3)

Every input below was run against the current Mathilda build and its output recorded.

Applications (3)

An inert distribution object

In[1]:= Head[UniformDistribution[{0, 1}]]
Out[1]= UniformDistribution

Density 1/(hi - lo) inside the support

In[2]:= PDF[UniformDistribution[{0, 1}], 1/2]
Out[2]= 1.0

Zero strictly outside [lo, hi]

In[3]:= PDF[UniformDistribution[{2, 6}], 10]
Out[3]= 0.0

Implementation notes

Definition. UniformDistribution[{lo, hi}] is a distribution object representing the continuous uniform distribution on [lo, hi]; UniformDistribution[] is uniform on {0, 1}. It is an inert, Protected head, not a function: UniformDistribution[{0, 1}] evaluates to itself, and its meaning is supplied by the consumers in src/ml/dist.c (PDF, RandomVariate), which parse it into an internal MlDist record.

Representation. The object stays an EXPR_FUNCTION with head UniformDistribution, so Head[UniformDistribution[{0, 1}]] is UniformDistribution. When a consumer reads it, the parser (ml_parse_distribution in dist.c) sets the internal kind to ML_D_UNIFORM with endpoints a = lo, b = hi; the no-argument form defaults to a = 0, b = 1. A spec whose upper endpoint does not exceed the lower (b > a fails) is rejected, so the object never yields a degenerate density.

Usage & limits. PDF[UniformDistribution[{lo, hi}], x] returns 1/(hi - lo) for lo <= x <= hi (endpoints included, Wolfram's convention for a continuous uniform) and 0 strictly outside; RandomVariate[UniformDistribution[{lo, hi}]] draws a sample. These numeric consumers evaluate at machine precision, so PDF[...] comes back as a machine real. Symbolic moment functions such as Mean, Variance and CDF are not yet wired to this object and are left unevaluated. It sits beside NormalDistribution in the same module.

Attributes: Protected.

References

Notes & additional examples

Notes

UniformDistribution[{lo, hi}] represents the continuous uniform distribution on [lo, hi], and UniformDistribution[] the standard uniform on {0, 1}. It is an inert, Protected object ā€” it evaluates to itself, Head is UniformDistribution ā€” whose meaning is supplied by the consumers PDF and RandomVariate.

PDF[UniformDistribution[{lo, hi}], x] is 1/(hi - lo) for lo <= x <= hi (endpoints included) and 0 outside; these numeric consumers work at machine precision, so the density comes back as a machine real. Symbolic moment functions such as Mean, Variance and CDF are not yet wired to this object and are left unevaluated.