On 17/01/2020 17:21, Alex Herbert wrote:
A uniform sampler of the IEEE 754 finite doubles would sample from a
log-uniform distribution as the limiting distribution and I don't
think that is actually what people require when creating random double
data. So either it: (a) is discarded as an idea; (b) is well
documented and put in examples; (c) is actually formalised to
correctly sample from the log-uniform distribution using the PDF:
1 / (x (log(b) - log(a)))
for x in the interval [a, b] from a uniform deviate (U) in the range
of the natural logarithm of the interval:
X = exp(U(log(a), log(b)))
I think that adding a LogUniformSampler may be of use.
It would allow creation of data approximately uniform in the
distribution of exponents. The numbers would be uniform on a log scale.
The implementation is simple and I don't see the harm in adding it since
it is a valid distribution with known PDF and CDF.
Likewise the LogUniformDistribution can be added to commons-statistics
distribution. There already is a vaguely related
LogNormalDistribution/NormalDistribution pair so this would be and the
LogUniformDistribution/UniformContinuousDistribution pair. I don't see
the need to name it LogUniformContinuousDistribution as there is no
discrete version that I could find documented.
Alex
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