Re: Possible bug in InverseGammaRegularized?

*To*: mathgroup at smc.vnet.net*Subject*: [mg129943] Re: Possible bug in InverseGammaRegularized?*From*: Sseziwa Mukasa <mukasa at gmail.com>*Date*: Wed, 27 Feb 2013 03:07:38 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20130226061053.F0AAC68C0@smc.vnet.net>

On Feb 26, 2013, at 1:10 AM, psycho_dad <s.nesseris at gmail.com> wrote: > Hi, > The following code gives the \delta \chi^2 for the confidence intervals as a function of the number of parameters n and desired number of sigmas m: > \delta \chi^2=2 InverseGammaRegularized[n/2, 1 - Erf[m/Sqrt[2]]] > > The RHS can also be written as 2InverseGammaRegularized[n/2,0, Erf[m/Sqrt[2]]] > (notice the 0 in the arguments) > > For example, for 5 params, 1 sigma and 5 digit precision: > In[1]:= n = 5; m = 1; > In[2]:= > N[2 InverseGammaRegularized[n/2, 1 - Erf[m/Sqrt[2]]], 5] > N[2 InverseGammaRegularized[n/2, 0, Erf[m/Sqrt[2]]], 5] > > Out[2]= 5.8876 > Out[3]= 5.8876 > > but when I ask for only 3 digit precision, Mathematica 9 gives the following torrent of errors in the second case: > > In[4]:= > N[2 InverseGammaRegularized[n/2, 1 - Erf[m/Sqrt[2]]], 3] > N[2 InverseGammaRegularized[n/2, 0, Erf[m/Sqrt[2]]], 3] > > Out[4]= 5.8876 > During evaluation of In[4]:= $RecursionLimit::reclim: Recursion depth of 1024 exceeded. >> > ... (more errors) > During evaluation of In[4]:= General::stop: Further output of $RecursionLimit::reclim will be suppressed during this calculation. >> > > Is this a bug or am I missing something? My guess is InverseGammaRegularized is written such that it uses the specified precision and its internal algorithms don't converge at low precision.

**References**:**Possible bug in InverseGammaRegularized?***From:*psycho_dad <s.nesseris@gmail.com>