[Scipy-tickets] [SciPy] #1547: stats problem sampling heavy tailed distributions ?

SciPy Trac scipy-tickets@scipy....
Mon Oct 31 11:22:43 CDT 2011


#1547: stats problem sampling heavy tailed distributions ?
-------------------------+--------------------------------------------------
 Reporter:  josefpktd    |       Owner:  somebody   
     Type:  defect       |      Status:  new        
 Priority:  normal       |   Milestone:  Unscheduled
Component:  scipy.stats  |     Version:  0.9.0      
 Keywords:               |  
-------------------------+--------------------------------------------------
 looking at a test failure for the variance of inverse gamma, I don't see
 where a problem could be

 variance of a sample is too small with an alpha close to the boundary
 where variance goes to infinite (alpha was initially randomly chosen for
 the test suite)

 {{{
 >>> rvsg2 = stats.invgamma.rvs(2.0668996136993067, size=100000)
 >>> rvsg2.mean()
 0.93872480525513002
 >>> rvsg2.var()
 4.2851923812716173
 >>> stats.invgamma.stats(2.0668996136993067, moments='mvsk')
 (array(0.9372953060997531), array(13.131951625091878),
 array(-0.4777296893768406
 ), array(-2.8665735140043456))
 }}}

 for larger values of alpha there are no problems
 {{{
 >>> rvsg8 = stats.invgamma.rvs(8., size=100000)
 >>> rvsg8.mean()
 0.14308306360000753
 >>> rvsg8.var()
 0.0034688970075502771
 >>> stats.invgamma.stats(8, moments='mvsk')
 (array(0.14285714285714285), array(0.003401360544217677),
 array(1.95959179422656
 13), array(8.700000000000012))
 }}}

 I checked a few values for the frequency distribution in the tails
 compared to ppf, and it matches pretty well.

 I have no clue why there is the discrepancy in the variance. I checked the
 calculations for variance with Wikipedia. The rvs works generically with a
 specified ppf.

-- 
Ticket URL: <http://projects.scipy.org/scipy/ticket/1547>
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