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Considerable recent attention has focussed on the prospects to use the cosmicmicrowave background (CMB) trispectrum to probe the physics of the earlyuniverse. Here we evaluate the probability distribution function (PDF) for thestandard estimator tau_nle for the amplitude tau_nl of the CMB trispectrum bothfor the null-hypothesis (i.e., for Gaussian maps with tau_nl = 0) and for mapswith a non-vanishing trispectrum (|tau_nl|>0). We find these PDFs to be highlynon-Gaussian in both cases. We also evaluate the variance with which thetrispectrum amplitude can be measured, <tau_nle^2>, as a function of itsunderlying value, tau_nl. We find a strong dependence of this variance ontau_nl. We also find that the variance does not, given the highly non-Gaussiannature of the PDF, effectively characterize the distribution. Detailedknowledge of these PDFs will therefore be imperative in order to properlyinterpret the implications of any given trispectrum measurement. For example,if a CMB experiment with a maximum multipole of lmax = 1500 (such as the Plancksatellite) measures tau_nle = 0 then at the 95% confidence our calculationsshow that we can conclude tau_nl < 1005; assuming a Gaussian PDF but with thecorrect tau_nl-dependent variance we would incorrectly conclude tau_nl < 4225;further neglecting the tau_nl-dependence in the variance we would incorrectlyconclude tau_nl < 361.

The probability distribution for non-Gaussianity estimators constructed from the CMB trispectrum