Related papers: Record-biased permutations and their permuton limi…

In this note, we investigate the non-identifiability of the multivariate unified skew-normal distribution under permutation of its latent variables. We show that the non-identifiability issue also holds with other parametrizations and…

For a given permutation or set partition there is a natural way to assign a genus. Counting all permutations or partitions of a fixed genus according to cycle lengths or block sizes, respectively, is the main content of this article. After…

Reliable estimation of feature contributions in machine learning models is essential for trust, transparency and regulatory compliance, especially when models are proprietary or otherwise operate as black boxes. While permutation-based…

Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…

This paper focuses on the size-biased permutation of $n$ independent and identically distributed (i.i.d.) positive random variables. This is a finite dimensional analogue of the size-biased permutation of ranked jumps of a subordinator…

Machine learning systems are increasingly being used to make impactful decisions such as loan applications and criminal justice risk assessments, and as such, ensuring fairness of these systems is critical. This is often challenging as the…

We introduce and study a new random permutation model that generalizes the $k$-card minimum model defined by Travers and the Mallows model. We calculate the permuton limit of such a sequence of random permutations. As a corollary, we deduce…

The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…

We provide an efficient algorithm to generate random samples from the bounded kth order statistic in a sample of independent, but not necessarily identically distributed, random variables. The bounds can be upper or lower bounds and need…

We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises…

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…

The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…

In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary…

We explore the asymptotic distributions of sequences of integer-valued additive functions defined on the symmetric group endowed with the Ewens probability measure as the order of the group increases. Applying the method of factorial…

Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions.…

Fix a base B and let zeta have the standard exponential distribution; the distribution of digits of zeta base B is known to be very close to Benford's Law. If there exists a C such that the distribution of digits of C times the elements of…

Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…

In this work we obtain recurrent formulae for the number of permutations with either increasing or monotonic (i.e., both increasing and decreasing) runs of bounded length. Our formulae allow one to efficiently compute the number of such…

Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…

Machines whose main purpose is to permute and sort data are studied. The sets of permutations that can arise are analysed by means of finite automata and avoided pattern techniques. Conditions are given for these sets being enumerated by…