Statistics in Practice

The Homogeneous Poisson Point Process

Comparing estimators of the galaxy correlation function

We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales, it is known that the correlation function follows reasonably well a power--law expression $\xi(r) \propto r^{-\gamma}$. The accurate determination of the exponent $\gamma$ (the order of the pole) depends on the estimator used for $\xi(r)$; on the other hand, its behavior at large scale gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples and the errors of each estimator. Erro…

Finite Point Processes

Fitting and Testing Point Process Models

Appendix C: Fundamentals of geostatistics

Appendix B: Geometrical Characteristics of Sets

Stationary Point Processes

Stationary Marked Point Processes

Modelling and Simulation of Stationary Point Processes

Appendix A: Fundamentals of statistics