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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: zeros in the Gamma distribution. |

Date |
Thu, 8 Apr 2010 14:28:42 +0100 |

I agree with Maarten's main point: Precision will bite here because the smallest possible positive value cannot be arbitrarily small. Using -double- will ease this problem but cannot remove it absolutely. Although Sun Samn tells us very little about what is being done, it seems quite likely that a change of measurement units might help (e.g. working in mg rather than kg) and/or that operations should be carried out on a transformed scale, e.g. work with logarithms and simulate gamma distributions rather than vice versa. Nick n.j.cox@durham.ac.uk Maarten buis --- On Thu, 8/4/10, sun samn wrote: > As we all know, the random numbers from Gamma > distributions should be positive; but when I use 'rgamma' to > generate 100 numbers, it has 7 zeros, why is that? Is this > reasonable? is there any way to get rid of these zeros? > You know ,I need to take log of these numbers, the > zeros are really bothering me. It means you are trying to use a too extreme distribution. Basically the numbers become so small that a computer cannot distinguish them from zero. Things become better when you create the variable as doubles, but it still finds a substantial number of zeros in the most extreme distribution. But looking at these distributions you can see that they cannot possible serve any practical purpose: to all intends and purposes they are so extreme that in a real data situaton there would be no way of distinguishing this distribution form a spike at zero and a small scattering of other values. *-------- example using floats ------------ clear set obs 10000 gen x1 = rgamma(1,1) count if x1 == 0 gen x2 = rgamma(.1,1) count if x2 == 0 gen x3 = rgamma(.01,1) count if x3 == 0 gen x4 = rgamma(.001,1) count if x4 == 0 *------------ end example ------------------ *----------- example using doubles ------------ clear set obs 10000 gen double x1 = rgamma(1,1) count if x1 == 0 gen double x2 = rgamma(.1,1) count if x2 == 0 gen double x3 = rgamma(.01,1) count if x3 == 0 gen double x4 = rgamma(.001,1) count if x4 == 0 *-------------- end example ----------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: zeros in the Gamma distribution.***From:*sun samn <shwshang@hotmail.com>

**Re: st: zeros in the Gamma distribution.***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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