A Generalized KolmogorovSmirnov Statistic forDetrital Zircon
Analysis of Modern Rivers
Oscar M Lovera, Marty Grove and Sara E. Cina Abstract
The
KolmogorovSmirnov (KS) statistic is widely used to test the null hypothesis that two
distributions drawn from the same population. In
detrital zircon provenance analysis of river systems, it is useful to have an equivalent
statistical measure for comparisons involving composite samples that collectively
represent the contributions of tributaries to regionally extensive river systems. We present a generalized KS statistic that depends
on the proportional contribution and sample size of individual distributions as well as
the nature of the respective individual populations. Our
generalized KS statistic is designed to analyze mixtures of single independent variable
data sets and can be calculated from either error weighted distributions (i.e., cumulative
probability density functions) or raw data series (i.e., cumulative distribution
functions). Analytical expressions are
provided for two limiting cases in which mixtures are derived entirely from either
independent or identical populations. Although
intermediate cases must still be tested by numerical analysis, the limiting cases tightly
bound all possible solutions and thus permit conservative evaluation of the null
hypothesis. We demonstrate how the generalized
KS statistic can be used with an example from the modern Marsyandi River (central Nepal
Himalaya) river system. Our results clarify
the manner in which detrital zircon age distributions from tectonically active areas may
be used to constrain key parameters such as erosion rates within the catchment of major
rivers.


Fortran Subroutines(zip file)  GenKS Program Guidelines (PowerPoint file)  
This work was supported by NSF Award0609911 