Re: Mathematica 6.0.1: problems with Beta Negative Binomial
- To: mathgroup at smc.vnet.net
- Subject: [mg84681] Re: [mg84662] Mathematica 6.0.1: problems with Beta Negative Binomial
- From: Darren Glosemeyer <darreng at wolfram.com>
- Date: Wed, 9 Jan 2008 03:50:54 -0500 (EST)
- References: <200801080838.DAA04403@smc.vnet.net>
Thank you for the report. The results should be conditional on the value
of alpha (the ith moment is only finite for alpha>i). The Mean result is
correct for alpha>1, Variance and StandardDeviation results for alpha>2,
Skewness for alpha>3, and Kurtosis for alpha>4.
The missing condition will be fixed in a future release of Mathematica.
I apologize for any inconvenience this may have caused.
Darren Glosemeyer
Wolfram Research
Nasser Abbasi wrote:
> When alpha is less than 1, the mean does not work. These 2 commands below
> should give the same answer:
>
> Mean[BetaNegativeBinomialDistribution[0.3, 3, 10]]
> Out[24]= -42.85714285714286
>
>
> In[25]:= ExpectedValue[x, BetaNegativeBinomialDistribution[0.3, 3, 10], x]
> During evaluation of In[25]:= Sum::div:Sum does not converge. >>
>
> In addition, the mean given above as -42 is wrong, as clearly can be seen by
> looking at the PDF. The mean must be positive
>
> ListPlot[Table[PDF[BetaNegativeBinomialDistribution[0.3, 3, 10], k], {k, 0,
> 100}],
> AxesOrigin -> {0, 0}]
>
> A rough estimate of the expected value can be found:
> tbl = Table[{k, PDF[BetaNegativeBinomialDistribution[0.3, 3, 10], k]}, {k,
> 1000000}];
> mean = N[Sum[tbl[[k,1]]*tbl[[k,2]], {k, 1, 1000000}]]
>
> Which gives about 20,000 and not -42
>
> The Variance is also wrong:
>
> In[105]:= Variance[BetaNegativeBinomialDistribution[0.3, 3, 10]]
> Out[105]= -770.3481392557023
>
> (Variance is negative??) Variance is the average of squared quantities, so
> it can not be negative.
>
> I think the formulas for the mean and variance shown in help are wrong.
>
> Nasser
>
>
- References:
- Mathematica 6.0.1: problems with Beta Negative Binomial Distribution
- From: "Nasser Abbasi" <nma@12000.org>
- Mathematica 6.0.1: problems with Beta Negative Binomial Distribution