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Possible bug in InverseGammaRegularized?

• To: mathgroup at smc.vnet.net
• Subject: [mg129924] Possible bug in InverseGammaRegularized?
• From: psycho_dad <s.nesseris at gmail.com>
• Date: Tue, 26 Feb 2013 01:10:53 -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

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?

Cheers

• Follow-Ups:
  • Re: Possible bug in InverseGammaRegularized?
    • From: Sseziwa Mukasa <mukasa@gmail.com>