AAWSAP DIRD, An Introduction to the Statistical Drake Equation, March 2010

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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that is
(148)
(149)
Since from the definition (147) one obviously has
erf(0)=0, (149) yields
This is the median of the lognormal distribution of
N. Ill other words, this is the number of
ExtraTerrestrial civilizatio11s i11 the Galaxy such
that, with 50% probability the actual value of N will
be lower tha11 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
N in the following Table 2.
NUMERICAL EXAMPLE OF THE
ET_DISTANCE DISTRIBUTION
ln this section we provide a numerical
example of the analytic calculations carried on so
far.
Consider the Drake Equation values reported
(150) in Table 1. Then, the graph of the corresponding
probability density function of the nearest
whence finally ET_Distance, f ET_Distan"' (r), is shown in Figure 6.
Imedian= m= Ce-~ 1. (151)
DISTANCE OF NEAREST Er_CIVILIZA TION
5.63·10-20
500 I000 I500 2000 2500 3000 3500 4000 4500 5000
ET_ Distance from Earth (ligJ,t years)
Figure 6. This is the probability of finding the nearest ExtraTerrestrial Civilization at the distance r from
Earth (in light years) if the values assumed in the Drake Equation are those shown in Table I. The relevant
probability density function f ET_Distano:Cr) is given by equation (113). Its mode (peak abscissa) 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
UNCLASSIFIED/fFQA QFFICiIPL. PP&i ODI! Y
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