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2011

The Probability Distribution for Non-Gaussianity Estimators

Smith, Tristan L., Kamionkowski, Marc, Wandelt, Benjamin D.

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One of the principle efforts in cosmic microwave background (CMB) research is measurement of the parameter fnl that quantifies the departure from Gaussianity in a large class of non-minimal inflationary (and other) models.

Estimators for fnl are composed of a sum of products of the temperatures in three different pixels in the CMB map.
Since the number ~Npix^2 of terms in this sum exceeds the number Npix of measurements, these ~Npix^2 terms cannot be statistically independent.
Therefore, the central-limit theorem does not necessarily apply, and the probability distribution function (PDF) for the fnl estimator does not necessarily approach a Gaussian distribution for N_pix >> 1.

The Probability Distribution for Non-Gaussianity Estimators · Around

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