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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.
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ref. [5]. The advantage of this notation is that it
makes a neat distinction between probabilistic (or
statistical: it's the same thing here) variables,
always denoted by capitals, from non-probabilistic
(or "detenninistic") variables, always denoted by
lower-case letters. Adopting the Papoulis notation
also is a tribute to him by this author, who was a
Fulbright Grantee in the United States with him at
the Polytechnic [nstitute (now Polytechnic
University) of New York in the years 1977-78-79.
We thus introduce seven new (positive)
random variables D; ("D" from "Drake") defined
as
D1 = Ns
D2 =fp
D3 =ne
D4 = fl (2)
Ds =fl
D6 =Jc
D 7 =fL
so that our STATISTICAL Drake equation may be
simply rewritten as
(3)
Of course, N now becomes a (positive) random
variable too, having its own (positive) mean value
and standard deviation. Just as each of the D; has its
own (positive) mean value and standard deviation ...
... the natural question then arises: how are the seven
mean values on the right related to the mean value on
the left?
... and how are the seven standard deviations on the
right related to the standard deviation on the left?
Just take the next step ...
3. STEP 2: INTRODUCING LOGS TO
CHANGE THE PRODUCT INTO A SUM
Products of random variables are not easy to
handle in probability theory. It is actually much
easier to handle sums of random variables, rather
than products, because:
1) The probability density of the sum of two or
more independent random variables is the
convolution of the relevant probabifay
densities (worry not about the equations,
right now) .
2) The Fourier transform of the convolution
simply is the product of the Fourier
transforms (again, worry not about the
equations, at this point)
UNCLASSIFIED//EOR OFFICIO! !!SF ON! X
30 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.