Related papers: The distribution of the maximum of an ARMA(1, 1) p…
A method that uses order statistics to construct multivariate distributions with fixed marginals and which utilizes a representation of the Bernstein copula in terms of a finite mixture distribution is proposed. Expectation-maximization…
We present a generalization of the maximal inequalities that upper bound the expectation of the maximum of $n$ jointly distributed random variables. We control the expectation of a randomly selected random variable from $n$ jointly…
The EM algorithm is a generic tool that offers maximum likelihood solutions when datasets are incomplete with data values missing at random or completely at random. At least for its simplest form, the algorithm can be rewritten in terms of…
In this paper we use an iterative algorithm for solving Fredholm equations of the first kind. The basic algorithm is known and is based on an EM algorithm when involved functions are non-negative and integrable. With this algorithm we…
We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the matrices becomes large. Their limit distributions can be expressed as Fredholm…
In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the…
We prove limit theorems of an entirely new type for certain long memory regularly varying stationary infinitely divisible random processes. These theorems involve multiple phase transitions governed by how long the memory is. Apart from one…
Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The spectral radius is defined as the maximum absolute value of the $n$ eigenvalues of the product matrix. When $m=1$, the…
We study the correlations between the maxima $m$ and $M$ of a Brownian motion (BM) on the time intervals $[0,t_1]$ and $[0,t_2]$, with $t_2>t_1$. We determine exact forms of the distribution functions $P(m,M)$ and $P(G = M - m)$, and…
Following some recent works on risk aggregation and capital allocation for mixed Erlang risks joined by Sarmanov's multivariate distribution, in this paper we present some closed-form formulas for the same topic by considering, however, a…
Let $M_n$ be the maximum of $n$ zero-mean gaussian variables $X_1,..,X_n$ with covariance matrix of minimum eigenvalue $\lambda$ and maximum eigenvalue $\Lambda$. Then, for $n \ge 70$, $$\Pr\{M_n \ge \lambda \left (2 \log n - 2.5 - \log(2…
Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…
Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
Let $\alpha$ be a Steinhaus or a Rademacher random multiplicative function. For a wide class of multiplicative functions $f$ we show that the sum $\sum_{n \le x}\alpha(n) f(n)$, normalised to have mean square $1$, has a non-Gaussian…
We present supremum Lagrange Multiplier tests to compare a linear ARMA specification against its threshold ARMA extension. We derive the asymptotic distribution of the test statistics both under the null hypothesis and contiguous local…
We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…
Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of…
We offer a new perspective on risk aggregation with FGM copulas. Along the way, we discover new results and revisit existing ones, providing simpler formulas than one can find in the existing literature. This paper builds on two novel…
Zero inflation is a common nuisance while monitoring disease progression over time. This article proposes a new observation driven model for zero inflated and over-dispersed count time series. The counts given the past history of the…