Relationship To Other Functions
As long as the same conventions are followed at the transition points, the probability density function may also be expressed in terms of the Heaviside step function:
or in terms of the rectangle function
There is no ambiguity at the transition point of the sign function. Using the half-maximum convention at the transition points, the uniform distribution may be expressed in terms of the sign function as:
Read more about this topic: Uniform Distribution (continuous)
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