Documents / Official release
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 Wlii QPU,¥ Put in loose terms, the CLT states that, if one has a sum of random variables eve11 NOT identically distributed, this sum tends to a normal distribution whe11 the 11umber of tenns maki11g up the sum te11ds to infinity. Also, the normal distribution mean value is the sum of the mean values of the addend random variables, and the normal distribution variance is the sum of the variances of the addend random variables. Let us now write down the equations of the CLT in the form needed to apply it to our Statistical Drake equation (3). The idea is to apply the CLT to the sum of random variables given by (4) and (5) whatever their probability distributions ca11 possibly be. Tn other words, the CLT applied to the Statistical Drake equation (3) leads immediately to the following three equations: I) The sum of the (arbitrarily distributed) independent random variables Y; makes up the new random variable Y. 2) The sum of their mean values makes up the new mean value of Y. 3) The sum of their variances makes up the new variance of Y. In equations: 7 y = :~::vii =I 7 (Y) = I(Y; ) (48) i = I 7 2 ="'O'y L..Jo-r2, i= I This completes our synthetic description of the CLT for sw11s of random variables . 6. THE LOGNORMAL DISTRIBTIO IS THE DISTRIBUTION OF THE NUMBER N OF EXT RATERRESTRIAL CIVILIZATIONS IN THE GALAXY The CLT may of course be exte11ded to products of random variables upon taki11g the logs of both sides, just as we did in equatio11 (3). It then follows that the exponent random variable, like Y i11 (6), tends to a 11ormal random variable, and, as a co 11seque 11ce, it follows that the base random variable, like N i11 (6), te11ds to a lognormal random variable. To understand this fact better in mathematical terms consider again of the transformation law (9) of random variables. The question is: what is the probability density function of the random variable N in equation (6), that is, what is the probability density function of the lognormal distribution? To find it, set (49) This, upon inversion, yields the single root x1(y) =x(y) =!n(y). (50) On the other hand, differentiating (49) one gets where (50) was already used in the last step. The general transformation law (9) finally yields ( ) "' fx(x;(y)) 1 ( ( )) fNY= L..J i '( ()~=- /ylny • (52) i g X; )' ~ 11 y Therefore, replacing the probability density on the right by virtue of the well-known normal (or Gaussian) distribution given by equation (7), the lognormal distribution of equation (47) is found , and the derivation of the lognormal distribution from the normal distribution is proved. In view of future calculations, it is also useful to point out the so-called "Gaussian integral", that is: B2 f"' e - Ax2 e 8 ·x dx = ~ •e 4 A A> 0 B = real. (53) L ., VA ' ' This follows immediately from the normalization condition of the Gaussian (7), that is oo (x- pf 1 -- ,- J-- e lu· dx=l (54) &a- '--Oj just upon expanding the square at the exponent and making the two replacements (we skip all steps) l A=-- >0,2 2 a- (55)lB = ; 2 = real. UNCLASSIFIED/ /FOR 8FFIGl.t.k W&i ,n11.¥ 39
Not linked to a story yet.
Official release, from the pursue collection. The PDF is mirrored here; the original link is above. 55 pages are in the text index: search them above, or from the library's search.