25,774 research outputs found
The Monty Python Method for Generating Gamma Variables
The Monty Python Method for generating random variables takes a decreasing density, cuts it into three pieces, then, using area-preserving transformations, folds it into a rectangle of area 1. A random point (x, y) from that rectangle is used to provide a variate from the given density, most of the time as x itself or a linear function of x. The decreasing density is usually the right half of a symmetric density. The Monty Python method has provided short and fast generators for normal, t and von Mises densities, requiring, on the average, from 1.5 to 1.8 uniform variables. In this article, we apply the method to non-symmetric densities, particularly the important gamma densities. We lose some of the speed and simplicity of the symmetric densities, but still get a method for γα variates that is simple and fast enough to provide beta variates in the form γa(γa + γb). We use an average of less than 1.7 uniform variates to produce a gamma variate whenever α ≥ 1. Implementation is simpler and from three to five times as fast as a recent method reputed to be the best for changing α's.link_to_subscribed_fulltex
Color Transformations of Photometric Measurements of Galaxies in Optical and Near-Infrared Wide-Field Imaging Surveys
Over the past 2 decades, wide-field photometric surveys in optical and
infrared domains reached a nearly all-sky coverage thanks to numerous
observational facilities operating in both hemispheres. However, subtle
differences among exact realizations of Johnson and SDSS photometric systems
require one to convert photometric measurements into the same system prior to
analysis of composite datasets originating from multiple surveys. It turns out
that the published photometric transformations lead to substantial biases when
applied to integrated photometry of galaxies from the corresponding catalogs.
Here we present photometric transformations based on piece-wise linear
approximations of integrated photometry of galaxies in the optical surveys
SDSS, DECaLS, BASS, MzLS, DES, DELVE, KiDS, VST ATLAS, and the near-infrared
surveys UKIDSS, UHS, VHS, and VIKING. We validate our transformations by
constructing k-corrected color-magnitude diagrams of non-active galaxies and
measuring the position and tightness of the "red sequence". We also provide
transformations for aperture magnitudes and show how they are affected by the
image quality difference among the surveys. We present the implementation of
the derived transformations in Python and IDL and also a web-based color
transformation calculator for galaxies. By comparing DECaLS and DES, we
identified systematic issues in DECaLS photometry for extended galaxies, which
we attribute to the photometric software package used by DECaLS. As an
application of our method, we compiled two multi-wavelength photometric
catalogs for over 200,000 low- and intermediate-redshift galaxies originating
from CfA FAST and Hectospec spectral archives.Comment: 24 pages, 21 figures, accepted for publication in PASP. The "Color
transformations" web service and the Python and IDL codes are available at
https://colors.voxastro.org
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