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arXiv2022

Scalable random number generation for truncated log-concave distributions

Inverse transform sampling is an exceptionally general method to generate non-uniform-distributed random numbers, but can be rather unstable when simulating extremely truncated distributions. Many famous probability models share a property called log-concavity, which is not affected by truncation, so they can all be simulated via rejection sampling using Devroye's approach. This sampler is based on rejection and thus more stable than inverse transform, and uses a very simple envelope whose acceptance rate is guaranteed to be at least 20\%. The aim of this paper is threefold: firstly, to warn against the risk of wrongly simulating from truncated distributions; secondly, to motivate a more extensive use of rejection sampling to mitigate the issues; lastly, to motivate Devroye's automatic method as a practical standard in the case of log-concave distributions. We illustrate the proposal by means of simulations based on some Tweedie distributions, for their relevance in regression analysis.

stat.ME↗

arXiv2007

The globular cluster system in NGC5866: optical observations from HST Advanced Camera for Surveys

We perform a detailed study of the Globular Cluster (GC) system in the galaxy NGC5866 based on F435W, F555W, and F625W (~ B, V, and R) HST Advanced Camera for Surveys images. Adopting color, size and shape selection criteria, the final list of GC candidates comprises 109 objects, with small estimated contamination from background galaxies, and foreground stars. The color distribution of the final GC sample has a bimodal form. Adopting color to metallicity transformations derived from the Teramo--SPoT simple stellar population model, we estimate a metallicity [Fe/H]~ -1.5, and -0.6 dex for the blue and red peaks, respectively. A similar result is found if the empirical color-metallicity relations derived from Galactic GCs data are used. The two subpopulations show some of the features commonly observed in the GC system of other galaxies, like a ``blue tilt'', higher central concentrations of the red subsystem, and larger half--light radii at larger galactocentric distances. However, we do not find evidence of a substantial difference between the average sizes of red and blue clusters. Our analysis of the GC Luminosity Function indicates a V-band Turn-Over Magnitude V$_0^{TOM}$=23.46+-0.06, or M$_{V,0}^{TOM}\sim-7.29 +- 0.10$ mag, using the distance modulus derived from the average of SBF and the PNLF distances. The absolute Turn-Over Magnitude obtained agrees well with calibrations from literature. The specific frequency is measured to be $S_N=1.4 +- 0.3$, typical for galaxies of this type.

astro-ph↗