相关论文: Bad witnesses for a composite number

We investigate the average number of representations of a positive integer as the sum of $k + 1$ perfect $k$-th powers of primes. We extend recent results of Languasco and the last Author, which dealt with the case $k = 2$ [6] and $k = 3$…

We consider the sum of the reciprocals of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an asymptotic expansion in the first case and an asymptotic formula involving an implicit parameter in the…

Given observations from a positive random variable contaminated by multiplicative measurement error, we consider a nonparametric goodness-of-fit testing task for its unknown density in a non-asymptotic framework. We propose a testing…

A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior…

Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…

The strong Lucas test is a widely used probabilistic primality test in cryptographic libraries. When combined with the Miller-Rabin primality test, it forms the Baillie-PSW primality test, known for its absence of false positives,…

Weighted histogram in Monte-Carlo simulations is often used for the estimation of a probability density function. It is obtained as a result of random experiment with random events that have weights. In this paper the bin contents of…

Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are…

We study the problem of constructing positive representations of complex measures. In this paper we consider complex densities on a direct product of $U(1)$ groups and look for representations by probability distributions on the…

In view of the tomographic-probability representation of quantum states, we reconsider the approach to quantumness tests of a single system developed in [Alicki and Van Ryn 2008 J. Phys. A: Math. Theor. 41 062001]. For qubits we introduce a…

In this paper, we study a density version of the Waring-Goldbach problem. Suppose that A is a subset of the primes, and the lower density of A in the primes is larger than 1-1/2k. We prove that every sufficiently large natural number n…

Let $p$ be an odd prime. We give a formula for the bad part of $p$-class groups that is valid for $100\%$ of the abelian $p$-extensions when ordered by product of ramified primes.

Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…

This paper outlines a framework for quantifying the prior's contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual…

Motivated by the forensic problem of determining the strength of evidence of a continuously distributed measurement of evidence, in the situation of composite hypotheses of the prosecutor and the defence concerning a parameter of a…

We study the set $\mathcal{S}$ of odd positive integers $n$ with the property ${2n}/{\sigma(n)} - 1 = 1/x$, for positive integer $x$, i.e., the set that relates to odd perfect and odd "spoof perfect" numbers. As a consequence, we find that…

Tests for proportional hazards assumption concerning specified covariates or groups of covariates are proposed. The class of alternatives is wide: log-hazard rates under different values of covariates may cross, approach, go away. The data…

The number of tuples with positive integers pairwise relatively prime to each other with product at most $n$ is considered. A generalization of $\mu^{2}$ where $\mu$ is the M\"{o}bius function is used to formulate this divisor sum and…

We propose a convergence mode for positive Radon measures which allows a sequence of probability measures to have an improper limiting measure. We define a sequence of vague priors as a sequence of probability measures that converges to an…

The increasing interest in subpopulation analysis has led to the development of various new trial designs and analysis methods in the fields of personalized medicine and targeted therapies. In this paper, subpopulations are defined in terms…