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This Defense Intelligence Reference Document, dated 11 March 2010, was prepared by the Defense Intelligence Agency's Defense Warning Office under the Advanced Aerospace Weapon System Applications Program. It introduces the Statistical Drake Equation, which treats each Drake factor as a random variable with a mean value and a standard deviation. Using its example inputs, the paper estimates that the nearest extraterrestrial civilization lies between 1,361 and 3,979 light years away with 75% probability. The author's 2008 International Astronautical Congress paper is attached as an appendix.
From the source:Release of 2026-09-18 Incident: 3/11/10, Las Vegas, Nevada. Released with redactions. This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD introduces the Drake Equation, a well-known thought framework for estimating how many communicative extraterrestrial civilizations might exist in the galaxy. It reformulates the equation in statistical terms, arguing that the usual approach of assigning fixed values to its variables is too simplistic because major inputs are uncertain and are better modeled as probability distributions. Using that approach, it concludes that, if one accepts the underlying logic of the Drake Equation, the estimated number of communicating civilizations should be treated as a range of possible values, and that the likely distance between neighboring civilizations can likewise be expressed statistically rather than as a single figure. The document is primarily a mathematical and methodological exercise, and its worked examples rely on assumed values to illustrate the framework rather than to establish a firm astrophysical estimate. Overall, it is an attempt to formalize uncertainty within the Drake framework rather than an attempt to bound the actual likelihood, prevalence, or proximity of extraterrestrial civilizations.
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In other words, there is a factor of ✓3 = 1.732
included in the two equations (17) that is not obvious
at all to human intuition, and must indeed be taken
into account.
The application of this result to the Statistical Drake
equation is discussed in the next section.
3.1 STEP 5: A NUMERICAL EXAMPLE
OF THE STATISTICAL DRAKE
EQUATION WITH UNIFORM
DISTRIBUTIO S FOR THE DRAKE
RANDOM VARIABLES D;
The first variable Ns in the classical Drake
equation (1) is the number of stars in our Galaxy.
Nobody knows how many they are exactly (!). Only
statistical estimates can be made by astronomers, and
they oscillate (say) around a mean value of 350
billions (if this value is indeed correct!). This being
the situation, we assume that our uniformly
distributed random variable Ns has a mean value of
350 billions minus or plus a standard deviation of
(say) one billion (we don't care whether this number
is scientifically the best estimate as of August 2008:
we just want to set up a numerical example of our
Statistical Drake equation). ln other words, we now
assume that one has:
(uniform_D 1) = 350 ~109
{ (18)
a unilomLD, =l • 10 •
Therefore, according to equations (17) the lower and
upper limit of our uniform distribution for the
random variable Ns=D1 are, respectively
aNs = 1 uniform_D 1 ) - ✓3auni "'" rm O = 348.3-109
{ \ . ,v - I 9 ( ( 9)
bNs =(umform_D 1) + ,fj aunii:>rTTLD, =351.7 -10
Similarly we proceed for all the other six random
variables in the Statistical Drake equation (3).
For instance, we assume that the fraction of stars
that have planets is 50%, i.e. 50/100, and thi s will be
the mean value of the random variable fp=D2. We
also assume that the relevant standard deviation will
be 10%, i. e. that a fr =10 /100 . Therefore, the
relevant lower and upper limits for the uniform
distribution offp=D2 tum out to be
a fp : ( un~orm_D2 )- ,fj a unitbrnLD2 : 0.327 (20)
{ b.fp - ( uniform_D 2 ) + ,fj a unitomLD2 - 0.673
The next Drake random variable is the number
ne of "Earth-type" planets in a given star system.
Taking example from the Solar System, since only
the Earth is truly "Earth-type", the mean value of ne
is clearly I, but the standard deviation is not zero if
we assume that Mars also may be regarded as Earth
type. Since there are thus two Earth-type planets in
the Solar System, we must assume a standard
deviation of 1/ ,fj =0.577 to compensate the ,fj
appearing in ( 17) in order to finally yield two "Earth
type" planets (Earth and Mars) for the upper limit of
the random variable ne. In other words, we assume
that
The next four Drake random variables have even
more "arbitrarily" assumed values that we simply
assume for the sake of making up a numerical
example of our Statistical Drake equation with
uniform entry distributions. So, we really make no
assumption about the astronomy, or the biology, or
the sociology of the Drake equation: we just care
about its mathematics.
All our assumed entries are given in Table l.
Please notice that, had we assumed all the
standard deviations to equal zero in Table I, then our
Statistical Drake equation (3) would have obviously
reduced to the classical Drake equation (1), and the
resulting number of civilizations in the Galaxy would
have turned out to be 3500:
IN =3500 1. (22)
This is the important deterministic number that we
will use in the sequel of this paper for comparison
with our statistical results on the mean value of N,
i.e. (N). This will be explained in Sections 3.3 and 5.
UNCLASSIFIED// POil OFFI@IAb W&i 01'11.¥
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