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.
“Hill”1 page
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6 l 0-4 PROBABILITY DE.\JSITY PLI\TTIOJ\" or N
z ' l 0--.,
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1000 2000 3000 4000
N-= !'<umber nf ET Civilin1tin11~ in Galaxy
Figure 4. Comparing lhc two probability density functions of lhc random variabk 11/ found:
I) Al lhc end of Section 3.3. in a purely numcric way and without rcsorling to lhc CLTat all (thick curve) and
2) Analylically by using thc CLT and lhc rclcvant lognormal approximation (lhin curw).
PRO BA BIUTY DENSITY rff\lCTIO"I or Y=ln("I)
0 5
0.4
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2 4 7 8 9 Ill )) )2
lnckpcnt.lcnt vanalllc Y = ln(N)
Figure 5. Comparing lhc two probability density functions of lhc random variabk Y=ln(N) found:
I) Al lhc end of Section 3.3. in a purely numcric way and wilhoul resorting lo thc CLT al all (lhick curvc) and
2) Analylically by using thc CLT and lhc rclcvant normal (Gaussian) appro.xirnalion (thin Gaussian curve).
8. DISTANCE OF THE NEAREST
EXTRATERRESTRIAL CIVILIZATION
AS A PROBABILITY DISTRIBUTION
A\ an application of the Statistical Drake
Equation developed in the previous ~ec!iom of thi\
paper. we now want to consider the problem of
estimating the diqance of the ExtraTerrestrial
Civilization nearest to us in the Galaxy. In all
Astrnbiology tcxtbooh (sec, for in\tancc, ref. [IOJ)
45
and in several web sites, the solution to this
problem is reported with only slight difference~ in
the mathematical proofs among the variom authors.
In the first of the coming two sections (\cction 7.1)
we derive the expression for this ''ET _Distance"
(as we like to denote it) in the cla~sical, non-
probabilistic way: in other words. this is the
cla~sicaL determiniqic derivation. In the second
section (7 .2) we provide the probabilistic
derivation. arising from our Stati\tical Drake
UNCLASSIFIED/ ;raft. &PPI@IAL ~Iii &•lblf Not linked to a story yet.
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.