The initial mass function modeled by a left truncated beta distribution
TLDR
In this article, a left truncated beta probability density function was introduced to demonstrate the advantage of introducing a four-parameter initial mass function for the stars and the presence of brown dwarfs.Abstract:
The initial mass function (IMF) for the stars is usually fitted by three straight lines, which means seven parameters. The presence of brown dwarfs (BD) increases to four the straight lines and to nine the parameters. Another common fitting function is the lognormal distribution, which is characterized by two parameters. This paper is devoted to demonstrating the advantage of introducing a left truncated beta probability density function, which is characterized by four parameters. The constant of normalization, the mean, the mode and the distribution function are calculated for the left truncated beta distribution. The normal-beta (NB) distribution which results from convolving independent normally distributed and beta distributed components is also derived. The chisquare test and the K-S test are performed on a first sample of stars and BDs which belongs to the massive young cluster NGC 6611 and on a second sample which represents the star’s masses of the cluster NGC 2362.read more
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Bayesian Models for Astrophysical Data: Using R, JAGS, Python, and Stan
TL;DR: In this article, a comprehensive guide to Bayesian methods in astronomy enables hands-on work by supplying complete R, JAGS, Python, and Stan code, to use directly or to adapt.
Posted Content
A right and left truncated gamma distribution with application to the stars
TL;DR: The gamma density function is usually defined in interval between zero and infinity as discussed by the authors, and an upper and a lower boundary to this distribution is introduced, and the parameters which characterize the truncated gamma distribution are evaluated.
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A Right and Left Truncated Gamma Distribution with Application to the Stars
TL;DR: The gamma density function is usually defined in interval between zero and infinity as mentioned in this paper, and an upper and a lower boundary to this distribution is introduced, and the parameters which characterize the truncated gamma distribution are evaluated.
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On the Number of Galaxies at High Redshift
TL;DR: In this article, the number of galaxies at a given flux as a function of the redshift, z, is derived when the z-distance relation is non-standard, and the same formalism is also applied to the standard cosmology.
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The truncated Lindley distribution with applications in astrophysics
TL;DR: In this article, the scale and double truncation of the Lindley distribution with scale were applied to the luminosity function for the Sloan Digital Sky Survey (SDSS) and to the photometric maximum of the 2MASS Redshift Survey (2MRS) galaxies.
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Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
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Numerical Recipes in FORTRAN
TL;DR: The Diskette v 2.04, 3.5'' (720k) for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.
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The Luminosity function and stellar evolution
TL;DR: In this paper, the evolutionary significance of the observed luminosity function for main-sequence stars in the solar neighborhood is discussed and it is shown that stars move off the main sequence after burning about 10 per cent of their hydrogen mass and that stars have been created at a uniform rate in a solar neighborhood for the last five billion years.