Documents / Report
This Defense Intelligence Agency reference document, dated 11 March 2010, is one of the advanced technology reports produced in FY 2009 under the Advanced Aerospace Weapon System Applications (AAWSA) program. It introduces the Statistical Drake Equation, which replaces each factor of Frank Drake's 1961 equation with a uniform random variable to estimate how far away the nearest extraterrestrial civilization is. In the worked example, there is a 75% probability that the nearest civilization lies between 1,361 and 3,979 light years from Earth.
that is
erf
UNCLASSIFIED//F81it 8FFIIIAI!: 1!181! &••1::Y
[ C' lIn •_, - p
,,,
flu
I
2 (148)
(149)
This is the median of the log11ormal dfrtributio11 of
N. /11 other word.f, this is the number of
HxtraTerrestrial civilizations in the Galaxy such
that, with 50% probability the actual value of N will
be lower than this median, and with 50% probability
it will be higher.
In conclusion, we feel useful to summarize all the
equations that we derived about the random variable
Nin the following Table 2.
NUMERICAL EXAMPLE OF THE
ET_DISTANCE DISTRIBUTION
Since from the definition (147) one obviously has
erf(0J=0. (149) yields In this section \Ve provide a numerical
example of the analytic calculations carried on so
far.
whence finally
( 150)
Consider the Drake Equation values reported
in Table I. Then, the graph of the corresponding
probability density function of the nearest
ET _Distance. f ET D,wmi,,( r), is shown in Figure 6.
median=m=Ce (151)
-45-1(('0
(l 0
DISTA:-JCE OF NEAREST ET _CIVJLIZA TION
,, ' "
I "'I "I'-
I/ ...... ........
- '500 l(XJ0 J:,00 2000 2500 3000 .,500 4000 4500 5000
ET _Di,lan~e fru,n Earlh (lighl yearsi
Figure 6. This is the probability of finding the nearest Extra Terrestrial Civilization at the diqance r from
Earth (in light years) if the values as~umcd in the Drake Equation arc tho~c shown in Table I. The relevant
probability dcn~ity function (ET 0 ,, 1,,,1.,,(r) i~ given by equation (113). It~ mode (peak absci~sa) equals 1933
light years. but its mean value is higher since the curve has a high tail on the right: the mean value equals in
52
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Report, from the dia collection. The PDF is mirrored here; the original link is above. 55 pages are in the text index: search them above, or from the library's search.