1999/10/07 by C. R. Contaldi, P. G. Ferreira, J. Magueijo +1 · 2 citations
Physics and Astronomy · #Amplitude #Bayesian probability #Cosmic background radiation #Cosmic microwave background #Cosmology and Gravitation Theories #Electrical and Electromagnetic Research #Galaxies: Formation, Evolution, Phenomena #Gaussian #Kurtosis #Planck #Skewness #Spectral density #astro-ph
paper · pdf · doi:10.1086/308759
published as Astrophys.J.534:25,2000 · submitted to Astrophysical Journal Letters
arxiv created 1999/10/07 · openalex publication_date 2000/05/01 · arxiv updated 2010/04/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose a formalism for estimating the skewness and angular power spectrum of a general cosmic microwave background data set. We use the Edgeworth expansion to define a non-Gaussian likelihood function that takes into account the anisotropic nature of the noise and the incompleteness of the sky coverage. The formalism is then applied to estimate the skewness of the publicly available 4 yr COBE Differential Microwave Radiometer (DMR) data. We find that the data is consistent with a Gaussian skewness, and with isotropy. Inclusion of non-Gaussian degrees of freedom has essentially no effect on estimates of the power spectrum, if each C l is regarded as a separate parameter or if the angular power spectrum is parametrized in terms of an amplitude ( Q ) and spectral index ( n ). Fixing the value of the angular power spectrum at its maximum-likelihood estimate, the best-fit skewness is S = 6.5 ± 6.0 × 10 4 μK 3 ; marginalizing over Q , the estimate of the skewness is S = 6.5 ± 8.4 × 10 4 μK 3 , and marginalizing over n one has S = 6.5 ± 8.5 × 10 4 μK 3 .