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Published online by Cambridge University Press: 30 August 2012
We estimate the parameters of the radio surface brightness to diameter (Σ – D) relation for the sample of Galactic planetary nebulae (PNe). The bootstrap re-sampling and orthogonal offsets fitting procedure are applied. The orthogonal fitting procedure provides that the parameter values of D – Σ and Σ – D fits are invariant within the estimated uncertainties. We discuss the probability statistics of the fitted (log Σ = log A - β log D) relation and the resulting fit parameters which is indicative for PN distance determination.