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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 OFFI&IAk Wlii QPU,¥ that the mean value of the lognormal random variable N is actually of the same order as the classical N given by the ordinary Drake equation, as one might expect from a good statistical generalization. 1. INTRODUCTION The Drake equation is a now famous result (see ref. [1] for the Wikipedia summary) in the fields of SETI (the Search for ExtraTetTestial Intelligence, see ref. [2]) and Astrobiology (see ref. [3]). Devised in l 960, the Drake equation was the first scientific attempt to estimate the number N of ExtraTerrestrial civilizations in the Galaxy with which we might come in contact. Frank D. Drake (see ref. [4]) proposed it as the product of seven factors: N=Ns-fp-ne·fl·fi·fc·fL. (1) Where: I) Ns is the estimated number of stars in our Galaxy. 2) fp is the fraction (= percentage) of such stars that have planets. 3) ne is the number "Earth-type" such planets around the given star; in other words, ne is number of planets, in a given stellar system, on which the chemical conditions exist for life to begin its course: they are "ready for life," 4) fl is fraction(= percentage) of such "ready for life" planets on which life actually starts and grows up (but not yet to the "intelligence" level). 5) fl is the fraction (= percentage) of such "planets with life fom1S" that actually evolve until some form of "intelligent civilization" emerges (like the first, historic human civilizations on Earth). 6) Jc is the fraction (= percentage) of such "planets with civilizations" where the civilizations evolve to the point of being able to communicate across the interstellar distances with other (at least) similarly evolved civilizations. As far as we know in 2008, this means that they must be aware of the Maxwell equations governing radio waves, as well as of computers and radioastronomy (at least). 7) fl is the fraction of galactic civilizations alive at the time when we, poor humans, attempt to pick up their radio signals (that they throw out into space just as we have done since l 900, when Marconi started the transatlantic transmissions). In other words, fl is the number of civilizations now transmitting and receiving, and this implies an estimate of"how long will a technological civilization live?" that nobody can make at the moment. Also, are they going to destroy themselves in a nuclear war, and thus live only a few decades of technological civi lization? Or are they slowly becoming wiser, reject war, speak a single language (like English today), and merge into a single "nation", thus living in peace for ages? Or will robots take over one day making "flesh animals" disappear forever (the so-called "post-biological universe")? No one knows ... But let us go back to the Drake equation (1). In the fifty years of its existence, a number of suggestions have been put forward about the different numeric values of its seven factors. Of course, every different set of these seven input numbers yields a different value for N, and we can endlessly play that way. But we claim that these are like ... children plays! We claim the classical Drake equation (1), as we shall call it from now on to distinguish it from our statistical Drake equation to be introduced in the coming sections, well, the classical Drake equation is scientifically inadequate in one regard at least: it just handles sheer numbers and does not associate an error bar to each of its seven factors. At the very least, we want to associate an error bar to each D;. Well, we have thus reached STEP ONE in our improvement of the classical Drake equation: replace each sheer number by a probability distribution! The reader is now asked to look at the flow chart in the next page as a guide to this paper, please. 2. STEP 1: LETTING EACH FACTOR BECOME A RANDOM VARIABLE In this paper we adopt the notations of the great book "Probability, Random Variables and Stochastic Processes" by Athanasios Papoulis (1921-2002), now re-published as Papoulis-Pillai, UNCLASSIFIED/ ,'FOR: QFFIGI CL. Wii ODIL:¥ 29
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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.