Related papers: Size bias for one and all
With $X^*$ denoting a random variable with the $X$-size bias distribution, what are all distributions for $X$ such that it is possible to have $X^*=X+Y$, $Y\geq 0$, with $X$ and $Y$ {\em independent}? We give the answer, due to Steutel…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We study the finite-size scaling behaviour at the critical point, resulting from the addition of a homogeneous size-dependent perturbation, decaying as an inverse power of the system size. The scaling theory is first formulated in a general…
The study of sums of finite sets of integers has mostly concentrated on sets with very small sumsets (Freiman's theorem and related work) and on sets with very large sumsets (Sidon sets and $B_h$-sets). This paper considers the full range…
This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression…
Binomial data with unknown sizes often appear in biological and medical sciences and are usually overdispersed. All previous methods used parametric models and only considered overdispersion due to the variation of sizes. The proposed…
A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
We study the large deviation function for the empirical measure of diffusing particles at one fixed position. We find that the large deviation function exhibits anomalous system size dependence in systems that satisfy the following…
The infinite random size-biased order with arbitrary positive size parameters is introduced in terms of independent exponential random variables. We collect basic properties and constructions of the order, some of which belong to the…
Binomial data with unknown sizes often appear in biological and medical sciences. The previous methods either use the Poisson approximation or the quasi-likelihood approach. A full likelihood approach is proposed by treating unknown sizes…
Data can be collected in scientific studies via a controlled experiment or passive observation. Big data is often collected in a passive way, e.g. from social media. In studies of causation great efforts are made to guard against bias and…
Logistic regression with unknown sizes has many important applications in biological and medical sciences. All models about this problem in the literature are parametric ones. A semiparametric regression model is proposed. This model…
Biased-coin designs are used in clinical trials to allocate treatments with some randomness while maintaining approximately equal allocation. More recent rules are compared with Efron's [Biometrika 58 (1971) 403-417] biased-coin rule and…
Let $S$ be a finite set, and $X_1,\ldots,X_n$ an i.i.d. uniform sample from $S$. To estimate the size $|S|$, without further structure, one can wait for repeats and use the birthday problem. This requires a sample size of the order…
We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected…
The thermodynamic dislocation theory developed for non-uniform plastic deformations is used here for the analysis of twisted copper wires. With a small set of physical parameters that we expect to be independent of strain rate and…
In this paper, we explore some links between transforms derived by Stein's method and concentration inequalities. In particular, we show that the stochastic domination of the zero bias transform of a random variable is equivalent to…
Elections constitute a paradigm of decision-making problems that have puzzled experts of different disciplines for decades. We study two decision-making problems, where groups make decisions that impact only themselves as a group. In both…
An early burst of speciation followed by a subsequent slowdown in the rate of diversification is commonly inferred from molecular phylogenies. This pattern is consistent with some verbal theory of ecological opportunity and adaptive…