We present a method for distance calibration without using standard fitting procedures. Instead we use random resampling to reconstruct the probability density function (PDF) of calibration data points in the fitting plane. The resulting PDF is then
used to estimate distance-related properties. The method is applied to samples of radio surface brightness to diameter (Sigma-D) data for the Galactic supernova remnants (SNRs) and planetary nebulae (PNe), and period-luminosity (PL) data for the Large Magellanic Cloud (LMC) fundamental mode classical Cepheids. We argue that resulting density maps can provide more accurate and more reliable calibrations than those obtained by standard linear fitting procedures. For the selected sample of the Galactic SNRs, the presented PDF method of distance calibration results in a smaller average distance fractional error of up to $approx 16$ percentage points. Similarly, the fractional error is smaller for up to $approx 8$ and $approx 0.5$ percentage points, for the samples of Galactic PNe and LMC Cepheids, respectively. In addition, we provide a PDF-based calibration data for each of the samples.
The radio surface brightness-to-diameter ({Sigma} - D) relation for supernova remnants (SNRs) in the starburst galaxy M82 is analyzed in a statistically more robust manner than in the previous studies that mainly discussed sample quality and related
selection effects. The statistics of data fits in log {Sigma} - log D plane are analyzed by using vertical (standard) and orthogonal regressions. As the parameter values of D - {Sigma} and {Sigma} - D fits are invariant within the estimated uncertainties for orthogonal regressions, slopes of the empirical {Sigma} - D relations should be determined by using the orthogonal regression fitting procedure. Thus obtained {Sigma} - D relations for samples which are not under severe influence of the selection effects could be used for estimating SNR distances. Using the orthogonal regression fitting procedure {Sigma} - D slope {beta} approx 3.9 is obtained for the sample of 31 SNRs in M82. The results of implemented Monte Carlo simulations show that the sensitivity selection effect does not significantly influence the slope of M82 relation. This relation could be used for estimation of distances to SNRs that evolve in denser interstellar environment, with number denisty up to 1000 particles per cm3 .
