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.

UNCLASSIFIED/ /fOR OFFI&IAk WliF QPU,¥
6 ·10-4
1000 2000 3000 4000
N = Number of ET Civilizations in Galaxy
Figure 4. Comparing the two probability density functions of the random variable N found:
1) At the end of Section 3.3. in a purely numeric way and without resorting to the CLT at all (thick curve) and
2) AnalyticaJly by using the CLT and the relevant lognormal approximation (thin curve).
PROBABILITY DENSITY FUNCTION OF Y=ln(N)
0.5
>- 0.4.....0
g
.B
§ 0.3
.....
•~
5"O 0.2
_q
]
".D
e 0.1
0..
00 2 3 12
Independent variable Y = ln(N )
Figure 5. Comparing the two probability density functions of the random variable Y=ln(N) found:
I) At the end of Section 3.3 . in a purely numeric way and without resorting to the CLTat all (thick curve) and
2) Analytically by using the CLT and the relevant normal (Gaussian) approximation (thin Gauss ian curve).
8. DISTANCE OF THE NEAREST and in several web sites, the solution to this
EXTRA TERRESTRIAL CIVILIZATION problem is reported with only slight differences in
AS A PROBABILITY DISTRIBUTION the mathematical proofs among the various authors .
In the first of the coming two sections (section 7 .1 )
As an application of the Statistical Drake we derive the expression for this "ET_Distance"
Equation developed in the previous sections of this (as we like to denote it) in the classical, non
paper, we now want to consider the problem of probabilistic way: in other words, this is the
estimating the distance of the ExtraTerrestrial classical, deterministic derivation. In the second
Civilization nearest to us in the Galaxy. In all section (7.2) we provide the probabilistic
Astrobiology textbooks (see, for instance, ref. [10)) derivation, arising from our Statistical Drake
UNCLASSIFIED/}FOA OlililCil0L. 1155 ON!¥
45