(Weighted) Sum of 'n' Correlated Lognormals: Probability Density Function – Numerical calculation

2010 ◽  
Author(s):  
Tamas Nagy
Keyword(s):  
Numerical Calculation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Weighted Sum

scholarly journals Ensemble age inversions for large spectroscopic surveys

2019 ◽  
Vol 629 ◽  
pp. A127
Author(s):  
Alexey Mints ◽  
Saskia Hekker ◽  
Ivan Minchev
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Age Distribution ◽  
Simulated Data ◽  
Probability Density Functions ◽  
Inversion Method ◽  
Weighted Sum ◽  
Stellar Ages ◽  
The Galaxy

Context. Galactic astrophysics is now in the process of building a multi-dimensional map of the Galaxy. For such a map, stellar ages are an essential ingredient. Ages are measured only indirectly however, by comparing observational data with models. It is often difficult to provide a single age value for a given star, as several non-overlapping solutions are possible. Aims. We aim at recovering the underlying log(age) distribution from the measured log(age) probability density function for an arbitrary set of stars. Methods. We build an age inversion method, namely we represent the measured log(age) probability density function as a weighted sum of probability density functions of mono-age populations. Weights in that sum give the underlying log(age) distribution. Mono-age populations are simulated so that the distribution of stars on the log g-[Fe/H] plane is close to that of the observed sample. Results. We tested the age inversion method on simulated data, demonstrating that it is capable of properly recovering the true log(age) distribution for a large (N > 103) sample of stars. The method was further applied to large public spectroscopic surveys. For RAVE-on, LAMOST and APOGEE we also applied age inversion to mono-metallicity samples, successfully recovering age–metallicity trends present in higher-precision APOGEE data and chemical evolution models. Conclusions. We conclude that applying an age inversion method as presented in this work is necessary to recover the underlying age distribution of a large (N > 103) set of stars. These age distributions can be used to explore age–metallicity relations, for instance.

Sign in / Sign up

Export Citation Format

Share Document