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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¥ 1s := 3 · o-109 s := -s cr s := 1-109 ·o 10 μfp := fpfp := 100 crfp := 100 1 ne := 1 μne := ne crne := - ,/3 fl :=~ μfl := fl crt1 = ~ 100 100 fi := 20 μfi := fi crfi := ~ 100 100 fc := 20 -100 μfc := fc 10 crfc := - 100 10000 fl. :=-- μfl. := fl. 1000 crfl. := -- 1010 101 0 s-fp -ne-fl -fi.fc .fl. - = 3500 Table 1. Input values (i.e. mean values and standard devi ations) for the seven Drake uni fo rm random variables D;. The fi rst column on the left lists the seven input sheer numbers that al so become the mean values (middle co lumn). Finally the last column on the right lists the seven input standard dev iations. The bottom line is the cl assical Drake equation ( 1). 3.2 STEP 6: COMPUTING THE LOGS OF THE 7 UNIFORMY DISTRIB UTED DRAKE RANDOM VARIABLES D; Intuiti vely speakiJ1g, the natural log of a unifonnly disuibuted random vari able may not be another uniforml y distributed random variable! This is obvious fro m the tri vial diagram of y = ln (x) shown below: Natural logarithm of x - _,,,,,,,,_,,. ~ r 2 3 4 5 POSITIVE independent variable x Figure 1. The simple function y = ln (x). So, if we have a unifo rml y di stributed random variable D; with lower limit a;and upper limit b;, the random variable Y; =ln(D;) i = l, ...,7 (23) must have its range limited in between the lower limit l11 (a;) and the upper limi t ln(b,). In other words, this are the lower and upper limits of the relevant probability density functio n fr;(y). But what is the actual analytic expression of such a pdf/ . To find it, we must resort to the general transformation law for random variables, defined by equation (9). Here we obviously have y =g(x) =ln(x) (24) That, upon inversion, yields the single root (25) On the other hand, differentiating (24) one gets UNCLASSIFIED//FOR OFFIEil.t.k W&i QNls¥ 35
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