25,774 research outputs found

    The Monty Python Method for Generating Gamma Variables

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    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

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    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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