17 citations · 88 across the 18 of their papers we have counts for
24 papers
Strong Convergence of Multivariate Maxima
Michael Falk, Simone A. Padoan, Stefano Rizzelli
It is well known and readily seen that the maximum of independent and uniformly on distributed random variables, suitably standardised, converges in total variation dis…
Conditional Tail Independence in Archimedean Copula Models
Michael Falk, Simone Padoan, Florian Wisheckel
Consider a random vector , whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $U…
Generalized Pareto Copulas: A Key to Multivariate Extremes
Michael Falk, Simone Padoan, Florian Wisheckel
This paper reviews generalized Pareto copulas (GPC), which turn out to be a key to multivariate extreme value theory. Any GPC can be represented in an easy analytic way using a par…
On a class of norms generated by nonnegative integrable distributions
Michael Falk, Gilles Stupfler
We show that any distribution function on with nonnegative, nonzero and integrable marginal distributions can be characterized by a norm on , calle…
Records for Some Stationary Dependent Sequences
Michael Falk, Amir Khorrami, Simone A. Padoan
For a zero-mean, unit-variance second-order stationary univariate Gaussian process we derive the probability that a record at the time , say , takes place and derive its di…
On Multivariate Records from Random Vectors with Independent Components
M. Falk, A. Khorrami, S. A. Padoan
Let be independent copies of a random vector with values in and with a continuous distribution function. T…
Some Results on Joint Record Events
M. Falk, A. Khorrami Chokami, S. A. Padoan
Let be independent and identically distributed random variables on the real line with a joint continuous distribution function . The stochastic behavior of the s…
On generalized max-linear models in max-stable random fields
Michael Falk, Maximilian Zott
In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in by interpolatin…
Asymptotic Independence of Bivariate Order Statistics
Michael Falk, Florian Wisheckel
It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables…
Multivariate Order Statistics: The Intermediate Case
Michael Falk, Florian Wisheckel
Asymptotic normality of intermediate order statistics taken from univariate iid random variables is well-known. We generalize this result to random vectors in arbitrary dimension,…
An Offspring of Multivariate Extreme-Value Theory: The Max-Characteristic Function
Michael Falk, Gilles Stupfler
This paper introduces max-characteristic functions (max-CFs), which are an offspring of multivariate extreme-value theory. A max-CF characterizes the distribution of a random vecto…
On functional records and champions
Clément Dombry, Michael Falk, Maximilian Zott
Records among a sequence of iid random variables on the real line have been investigated extensively over the past decades. A record is defined as a random variabl…
The space of D-norms revisited
Stefan Aulbach, Michael Falk, Maximilian Zott
The theory of -norms is an offspring of multivariate extreme value theory. We present recent results on -norms, which are completely determined by a certain random vector cal…
Testing for a δ-neighborhood of a generalized Pareto copula
Stefan Aulbach, Michael Falk
A multivariate distribution function F is in the max-domain of attraction of an extreme value distribution if and only if this is true for the copula corresponding to F and its uni…
On generalized max-linear models and their statistical interpolation
Michael Falk, Martin Hofmann, Maximilian Zott
We propose a way how to generate a max-stable process in from a max-stable random vector in by generalizing the \emph{max-linear model} established by \citet…
Max-stable processes and the functional D-norm revisited
Stefan Aulbach, Michael Falk, Martin Hofmann +1
Aulbach et al. (2013) introduced a max-domain of attraction approach for extreme value theory in C[0,1] based on functional distribution functions, which is more general than the a…
On Idempotent D-Norms
Michael Falk
Replacing the spectral measure by a random vector $\bfZ$ allows the representation of a max-stable distribution on with standard negative margins via a norm, called \emph{$D…
A multivariate piecing-together approach with an application to operational loss data
Stefan Aulbach, Verena Bayer, Michael Falk
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We…
Testing for a generalized Pareto process
Stefan Aulbach, Michael Falk
We investigate two models for the following setup: We consider a stochastic process X \in C[0,1] whose distribution belongs to a parametric family indexed by \vartheta \in Θ \subse…
Local asymptotic normality in δ-neighborhoods of standard generalized Pareto processes
Stefan Aulbach, Michael Falk
De Haan and Pereira (2006) provided models for spatial extremes in the case of stationarity, which depend on just one parameter β > 0 measuring tail dependence, and they proposed d…
Asymptotic Conditional Distribution of Exceedance Counts: Fragility Index with Different Margins
Michael Falk, Diana Tichy
Let be a random vector, whose components are not necessarily independent nor are they required to have identical distribution functions . Denote…
The multivariate Piecing-Together approach revisited
Stefan Aulbach, Michael Falk, Martin Hofmann
The univariate Piecing-Together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. A m…
Sojourn Times and the Fragility Index
Michael Falk, Martin Hofmann
We investigate the sojourn time above a high threshold of a continuous stochastic process Y on [0,1]. It turns out that the limit, as the threshold increases, of the expected sojou…
On Max-Stable Processes and the Functional D-Norm
Stefan Aulbach, Michael Falk, Martin Hofmann
We introduce a functional domain of attraction approach for stochastic processes, which is more general than the usual one based on weak convergence. The distribution function G of…