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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 OFFIEiIAk Wlii QPU,¥ (N) =eμ e 2 "'4589 .559 . (95) In other words, there are 4590 ET Civilizatio11s in the Galaxy according the Central Limit Theorem of Statistics with the inputs of Table 1. This ,mmber 4590 is HIGHER than the 3500 foreseen by the classical Drake equation working with sheer numbers only, rather than with probability distributions. Thus equation (95) IS GOOD FOR NEWS FOR SETI, since it shows that the expected number of ETs is HIGHER with an adequate statistical treatment than just with the too simple Drake sheer numbers of (1). 2) Variance of N. The variance of the Iognormal distribution is given by (62) and turns out to be a huge number: 3) Standard deviation of N. The standard deviation of the lognormal distribution is given by (63) and turns out to be: (97) Again, this is GOOD NEWS FOR SETI. In fact, such a high standard deviation means that N may range from very low values (zero, theoretically, and one since Humanity exists) up to tens of thousands (4590+11195=15785 is (95)+(97)). 4) Mode of N. The mode (= peak abscissa) of the lognormal distribution of N is given by (81 ), and has a surprisingly low numeric value: This is well shown in Figure 4: the mode peak is very pronounced and close to the origin, but the right tail is high, and this means that the mean value of the distribution is much higher than the mode: 4590»250. 5) Median of N. The median (= fifty -fifty abscissa, splitting the pdf in two exactly equi-probable parts) of the lognormal distribution of N is given by (89), and has the numeric value: (99) Tn words, assuming the input values listed in Table 1, we have exactly a 50% probability that the actual value of N is lower than 1740, and 50% that it is higher than 1740. 7. COMPARING THE CLT RESULTS WITH THE NON-CLT RESULTS The time is now ripe to compare the CLT based results about the lognormal distribution of N, just described in Section 5, against the Non-CLT based results obtained numerically in Section 3.3 To do so in a simple, visual way, let us plot on the same diagram two curves: 1) The numeric curves appearing in Figure 2 and obtained after laborious Fourier transform calculations in the complex domain, and 2) The lognormal distribution (56) with numeric μ and a given by (91) and (94) respectively. We see that the two curves are virtually coincident for values of N larger than 1500. This is a consequence of the law of large numbers, of which the CLT is just one ofthe 111a11y facets. Similarly it happens for natural log of N, i.e. the random variable Y of (5), that is plotted in Figure 5 both in its normal curve version (thin curve) and in its numeric version, obtained via Fourier transforms and already shown in Figure 2. The conclusion is simple: from now 011 we shall discard forever the 1111meric calc11lations a11d we'll stick only to the equations derived by virtue of the CLT, i.e. to the lognormal (56) and its co11seque11ces. UNCLASSIFIED//509 OFFICIO! 11SF QN 1X 44
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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.