Related papers: On the computation and inversion of the cumulative…
A symmetry-preserving approach to the continuum bound-state problem in quantum field theory is used to calculate the masses, leptonic decay constants and light-front distribution amplitudes of empirically accessible heavy-light mesons. The…
In quantitative finance, it is often necessary to analyze the distribution of the sum of specific functions of observed values at discrete points of an underlying process. Examples include the probability density function, the hedging…
Simple asymptotic expansions for the Jacobi functions $P_\nu^{(\alpha, \beta)}(z)$ and $Q_\nu^{(\alpha, \beta)}(z)$ for large degree $\nu$, with fixed parameters $\alpha$ and $\beta$, are surprisingly rare in the literature, with only a few…
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral…
Ratios of integrals can be bounded in terms of ratios of integrands under certain monotonicity conditions. This result, related with L'H\^{o}pital's monotone rule, can be used to obtain sharp bounds for cumulative distribution functions. We…
We propose a general approach, named by us hyperstatistics, to treat complex systems, in which Boltzmann-Gibbs statistics breaks down in domains of the system. Hyperstatistics preserves the concavity of nonadditive $q$-entropy. We obtain…
We consider a particular generalized Lambert function, $y(x)$, defined by the implicit equation $y^\beta = 1 - e^{-xy}$, with $x>0$ and $ \beta > 1$. Solutions to this equation can be found in terms of a certain continued exponential.…
The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the…
In this paper we study a broad class of distribution functions which is defined by means of reflected generalized beta distribution. This class includes that of Beta-generated distribution as a special case. In particular, we use this class…
We continue the study of the fractional variation following the distributional approach developed in the previous works arXiv:1809.08575, arXiv:1910.13419 and arXiv:2011.03928. We provide a general analysis of the distributional space…
The beta distribution is a two-parameter family of probability distributions whose distribution function is the (regularised) incomplete beta function. In this paper, the inverse incomplete beta function is studied analytically as…
Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable…
We present decidability results for a sub-class of "non-interactive" simulation problems, a well-studied class of problems in information theory. A non-interactive simulation problem is specified by two distributions $P(x,y)$ and $Q(u,v)$:…
The maximum entropy method (MEM) and the Gaussian process (GP) regression, which are both well-suited for the treatment of inverse problems, are used to reconstruct net-baryon number distributions based on a finite number of cumulants of…
Motivated by applications in Bayesian analysis we introduce a multidimensional beta distribution in an ordered simplex. We study properties of this distribution and connect them with the generalized incomplete beta function. This function…
The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple…
We study the recovery of the distribution function $F_X$ of a random variable $X$ that is subject to an independent additive random error $\varepsilon$. To be precise, it is assumed that the target variable $X$ is available only in the form…
In this paper our aim is to establish new integral representations for the Fox--Wright function ${}_p\Psi_q[^{(\alpha_p,A_p)}_{(\beta_q,B_q)}|z]$ when $$\mu=\sum_{j=1}^q\beta_j-\sum_{k=1}^p\alpha_k+\frac{p-q}{2}=-m,\;\;m\in\mathbb{N}_0.$$…
Let $X$ and $Y$ be two independent identically distributed random variables with density $p(x)$ and $Z=\alpha X+\beta Y$ for some constants $\alpha>0$ and $\beta>0$. We consider the problem of estimating $p(x)$ by means of the samples from…
Recent work has developed a non-parametric Bayesian approach to the calibration of a computer model, which abstractly amounts to the inversion of a pushforward of stochastic input parameters by a smooth map. The framework has been used in…