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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.
UNCLASSIFIED/ /FOR OFFIEil.t.k W&i Q~lls¥ The bottom line is the classical Drake equation (7). We see that, for this particular set of seven inputs, the classical Drake equation (i.e. the product of the seven numbers) yields a total of 3500 communicating extraterrestrial civilizations existing in the galaxy right now. rs := 350 -109 s := s 0 10 μfp := fpfp := 100 ofp := 100 l ne := 1 μne := ne crne := - /3 0 fl := - μfl := fl crfl := ~ 100 100 fi :=~ μfi := fi on := ~ 100 100 0 fc:= - μfc := fc crfc := ~ 100 100 fL := 10000 crtL := 1000μfl. := tL 1010 1010 _ 1 := Ks -fp -ne-fl -fi .fc .ff, = 3500 Table 2. Input Values (i.e. mean values and standard deviations) for the Seven Drake Uniform Random Variables Di . The first column on the left lists the seven input sheer numbers that also become the mean values (middle column). Finally the last column on the right lists the seven input standard deviations . The bottom line is the classical Drake equation (7). The statistical Drake equation, however, provides a much more articulated answer than just the above sheer number N = 3500. In fact, a MathCad code written by this author and capable of performing all t he numerical calculations required by the statistical Drake equation for a given set of seven input mean va lues plus seven input standard deviations, yields for N the lognormal distribution (thin curve) plotted in Figure 2. We see immediately that the peak of this thin curve (i.e. the mode) falls at about n rmde;;;; npeak = eμ e-a' ""250 (this is equation (99) of Appendix B), while the median (fifty fifty value spl itting the lognormal density in two parts with equal undergoing areas) falls at about nm,d ian;;;; eμ ""1740 . These seem to be smaller values than N = 3500 provided by the classical Drake equations, but it's a wrong impression due to a poor "intuitive" understanding of what statistics is! In fact, neither the mode nor the median are the " really important" values: the really important value for N is the MEAN VALUE! Now if you look at t he thin curve in Figure 2 below (i.e. the lognorma l distribution arisin g from the Central Limit Theorem), you see that this curve has a LONG TAIL ON THE RIGHT! In other words, it does NOT immediately go down to nearly zero beyond the peak of the mode. Thus, when you actually compute the mean value, you should not be too UNCLASSIFIED// POR OPPICll<L ti.!! er~LV 16
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