Wikipedia:Reference desk/Archives/Mathematics/2014 October 23

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October 23

Continuous probability distribution, with finite support, and closed-form quantile function

For some computational experiments, I need a continuous probability distribution, with finite support, and closed-form quantile function. Kindly list any.

I'm already aware of probability distributions that satisfy my requirements except for finite support: Logistic distribution and Gumbel distribution. Thanks! --RM — Preceding unsigned comment added by 121.247.216.109 (talk) 10:45, 23 October 2014 (UTC)

How about the triangular distribution? Sławomir Biały (talk) 10:55, 23 October 2014 (UTC)

Thanks User:Sławomir Biały! I had missed this simple option. Other suggestions are welcome! --BR — Preceding unsigned comment added by 121.247.216.109 (talk) 11:40, 23 October 2014 (UTC)

It doesn't get simpler than the uniform distribution on [0,1]: Q(p) = p. --Mark viking (talk) 11:44, 23 October 2014 (UTC)

There's loads of probability distributions at List of probability distributions but yes having a closed-form quantile restricts the choices. I don't normally consider that as a problem with a computer though as given a function getting a good enough inverse should be easy enough even if only by tabulating values in a table and then doing a binary chop and interpolation for actual values.

I presume you mean on a finite interval rather than finite support which sounds more like on a finite set of points. Dmcq (talk) 13:40, 23 October 2014 (UTC)

Glancing through List of probability distributions#Supported on a bounded interval, the Irwin–Hall distribution, Kumaraswamy distribution, and raised cosine distribution look promising. -- BenRG (talk) 23:32, 23 October 2014 (UTC)