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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*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 > >

**References**:**(amusement) surprising result from PossibleZeroQ***From:*Peter Pein <petsie@dordos.net>