Re: (amusement) surprising result from PossibleZeroQ

• To: mathgroup at smc.vnet.net
• Subject: [mg130715] Re: (amusement) surprising result from PossibleZeroQ
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Mon, 6 May 2013 02:25:53 -0400 (EDT)
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• References: <20130504071901.7FD916A19@smc.vnet.net>

```Assuming[
{0 <= q <= 1},
Quantile[ParetoDistribution[k, a], q] //
Simplify]

Piecewise[{{k/(1 - q)^a^(-1), q < 1}},
Infinity]

Piecewise[{{
Quantile[ParetoDistribution[k, a], q],
0 <= q <= 1}}, Indeterminate] //
PiecewiseExpand

Piecewise[{{Indeterminate,
q > 1 || q < 0}, {k/(1 - q)^a^(-1),
Inequality[0, LessEqual, q, Less,
1]}}, Infinity]

Bob Hanlon

On Sat, May 4, 2013 at 3:19 AM, Peter Pein <petsie at dordos.net> wrote:

> Dear group,
>
>  playing around with distributions, I experienced one of these "that's
> strange!"-moments.
>
>  Take the quantile of a Pareto distribution
>
> test = Quantile[ParetoDistribution[k, a], q];
> InputForm@test
>
> ConditionalExpression[Piecewise[{{k/(1 - q)^a^(-1), q < 1}}, Infinity],
>  0 <= q <= 1]
>
> I thought the nesting of ConditionalExpression and Piecewise could
> simplify and tried every possible combination of 4 functions; to no avail:
>
> Block[{f = {Refine, Simplify, FullSimplify, PiecewiseExpand}},
>  Length[funcs =
>    Composition @@@ Flatten[Tuples[f, #] & /@ Range[Length@f], 1]]
>  ]
> 340
>
> DeleteCases[Through[funcs[test]], test]
> {}
>
> My expectation has been sth. like
>
> test2 = Piecewise[{{k/(1 - q)^(1/a), 0 <= q < 1},
>                    {Infinity, q == 1}},
>                   Indeterminate];
>
> and
>
> FullSimplify[test2 - test] // InputForm
> ConditionalExpression[0, 0 <= q <= 1]
>
> looks good. But compare this to
>
> PossibleZeroQ[test2 - test] // InputForm
> ConditionalExpression[False, 0 <= q <= 1]
>
> I decided to classify that as "funny" :)
>
> MemberQ[Attributes@PossibleZeroQ, Listable]
> True
>
>
> Have fun with or without Mathematica!
>
>   Peter
>
>

```

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