Related papers: Confidence disc and square for Cauchy distribution…
We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point of the system must remain inside a set of constraints K; the…
In this brief note, we highlight some difficulties that can arise when fitting a continuous, symmetric, unimodal distribution to a set of expert's judgements. A simple analysis shows it is possible to fit a Cauchy distribution to an…
We deal with the orbit determination problem for a class of maps of the cylinder generalizing the Chirikov standard map. The problem consists of determining the initial conditions and other parameters of an orbit from some observations. A…
Portnoy (2019) considered the problem of constructing an optimal confidence interval for the mean based on a single observation $\, X \sim {\cal{N}}(\mu , \, \sigma^2) \,$. Here we extend this result to obtaining 1-sample confidence…
We theoretically determine the probability distribution function of the net field of the random planar structure of dipoles which represent polarized particles. At small surface concentrations c of the point dipoles this distribution is…
We consider a wave equation with a nonlocal logarithmic damping depending on a small parameter $\theta \in (0,1/2)$. This research is a counter part of that was initiated by Charao-D'Abbicco-Ikehata considered in [5] for the large parameter…
In this paper, we consider the Cauchy problem for the fractional Camassa-Holm equation which models the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. Using Kato's…
Consider a set of points sampled independently near a smooth compact submanifold of Euclidean space. We provide mathematically rigorous bounds on the number of sample points required to estimate both the dimension and the tangent spaces of…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…
We present conjectured candidates for the least perimeter partition of a disc into $N \le 10$ regions which take one of two possible areas. We assume that the optimal partition is connected, and therefore enumerate all three-connected…
The regression function is one of the key objects of binary classification, since it not only determines a Bayes optimal classifier, hence, defines an optimal decision boundary, but also encodes the conditional distribution of the output…
Using a Coulomb gas technique, we compute analytically the probability $\mathcal{P}_\beta^{(C)}(N_+,N)$ that a large $N\times N$ Cauchy random matrix has $N_+$ positive eigenvalues, where $N_+$ is called the index of the ensemble. We show…
We represent the product of two correlated normal random variables, and more generally the sum of independent copies of such random variables, as a difference of two independent noncentral chi-square random variables (which we refer to as…
By using the independence structure of points following a determinantal point process, we study the radii of the spherical ensemble, the truncation of the circular unitary ensemble and the product ensemble with parameter n and k. The…
Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…
When using the Focused Information Criterion (FIC) for assessing and ranking candidate models with respect to how well they do for a given estimation task, it is customary to produce a so-called FIC plot. This plot has the different point…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
We obtain an approximate Gaussian distribution from a Poisson distribution after doing a change of variable. A new chi-square function is obtained which can be used for parameter estimations and goodness-of-fit testing when adjusting curves…
We study the peak height distribution of certain non-stationary Gaussian random fields. The explicit peak height distribution of smooth, non-stationary Gaussian processes in 1D with general covariance is derived. The formula is determined…
Estimating high quantiles plays an important role in the context of risk management. This involves extrapolation of an unknown distribution function. In this paper we propose three methods, namely, the normal approximation method, the…