#### November 7 (Wed), 14:15 in A315

#### Jean-Claude Waizmann (Bologna)

#### Order statistics applied to extreme observations of galaxy clusters

In my talk I present an analytic framework for calculating the individual and joint distributions of the n-th most massive or n-th highest redshift galaxy cluster for a given survey characteristic allowing to formulate ΛCDM exclusion criteria. Having introduced the theory, I discuss the application of the order-statistical analysis both in mass and redshift to the SPT massive cluster sample and the MCXC catalogue.

In the second part of the talk, I will focus on the application of order statistics on strong lensing observations. I show how distributions of the largest Einstein radii can be derived based on semi-analytic modelling of the strong lensing signal and how sensitive they are to the underlying assumptions like the mass function, axis-ratio distribution etc.. After the discussion of the statistical modelling of the Einstein radius distribution, I compare the observed Einstein radii of the MACS sample with the LCDM expectations.