# Talk:Singular distribution

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Field: Probability and statistics

"A singular distribution is not a discrete probability distribution because each discrete point has a zero probability" Is this correct?I think each discrete point has nonzero probability. —The preceding unsigned comment was added by Srgvie (talkcontribs).

Well, taking the Cantor distribution as an example, each point indeed has a zero probability. Indeed the definition "a singular distribution is a probability distribution concentrated on a measure zero set where the probability of each point in that set is zero" makes this clear: every point where the distribution is concentrated has zero probability. --Henrygb 21:02, 4 February 2007 (UTC)

Actually, there is a little confusion here, at least for me. So let's make the things clear: Discrete probability distribution: each point has a nonzero probability. Singular distribution:each point has a zero probability. Ok? —Preceding unsigned comment added by Srgvie (talkcontribs) 21:00, 6 April 2008 (UTC)

## Measure zero !?!?

I am not convinced that the requirement that the distribution be non-vanishing only on a set of measure zero is germane/important/correct. One example is the CDF built from the fat Cantor set, which I think qualifies as a singular distribution w.r.t. the Lebesgue measure, but clearly is singular on a set of measure greater than zero. I give two more examples on the talk page for singular function, which appears to have the same 'measure-zero' problem ... linas (talk) 05:40, 11 February 2010 (UTC)