Related papers: Expansions of maximum and minimum from Generalized…
We study numerically the maximal and minimal height distributions (MAHD, MIHD) of the nonlinear interface growth equations of second and fourth order and of related lattice models in two dimensions. MAHD and MIHD are different due to the…
Bivariate normal distributions are often used to describe the joint probability density of a pair of random variables. These distributions arise across many domains, from telecommunications, to meteorology, ballistics, and computational…
A single joinpoint changepoint model partitions a time series into two segments, joined at the changepoint time by constraining the estimated piecewise linear regression responses to be continuous. This manuscript derives the exact…
Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…
A finite-size uniform random distribution of vertically aligned field emitters on a planar surface is studied under the assumption that the asymptotic field is uniform and parallel to the emitter axis. A formula for field enhancement factor…
Let $\{X_i,i=1,2,...\}$ be i.i.d. standard gaussian variables. Let $S_n=X_1+...+X_n$ be the sequence of partial sums and $$ L_n=\max_{0\leq i<j\leq n}\frac{S_j-S_i}{\sqrt{j-i}}. $$ We show that the distribution of $L_n$, appropriately…
The normalized maximum likelihood (NML) is one of the most important distribution in coding theory and statistics. NML is the unique solution (if exists) to the pointwise minimax regret problem. However, NML is not defined even for simple…
The paper presents improved mathematical models and methods for statistical regularities in the behavior of some important characteristics of precipitation: duration of a wet period, maximum daily and total precipitation volumes within a…
We propose a generalized entropy maximization procedure, which takes into account the generalized averaging procedures and information gain definitions underlying the generalized entropies. This novel generalized procedure is then applied…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
Let $X=\sum_{k=1}^\infty X_k \beta^{-k}$ be the base-$\beta$ expansion of a continuous random variable $X$ on the unit interval where $\beta$ is the golden ratio. We study the asymptotic distribution and convergence rate of the scaled…
In this article, we proposed a new probability distribution named as power Maxwell distribution (PMaD). It is another extension of Maxwell distribution (MaD) which would lead more flexibility to analyze the data with non-monotone failure…
Computing the embedding distribution of a given graph is a fundamental question in topological graph theory. In this article, we extend our viewpoint to a sequence of graphs and consider their asymptotic embedding distributions, which are…
A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal,…
The purpose of this paper is to study the limiting distribution of special {\it additive functionals} on random planar maps, namely the number of occurrences of a given {\it pattern}. The main result is a central limit theorem for these…
We study local asymptotic normality of M-estimates of convex minimization in an infinite dimensional parameter space. The objective function of M-estimates is not necessary differentiable and is possibly subject to convex constraints. In…
To know the statistical distribution of a variable is an important problem in management of resources. Distributions of the power law type are observed in many real systems. However power law distributions have an infinite variance and thus…
Two new test statistics are introduced to test the null hypotheses that the sampling distribution has an increasing hazard rate on a specified interval [0,a]. These statistics are empirical L_1-type distances between the isotonic estimates,…
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
Regular and singular parts of asymptotic expansions of semi-Markov random evolutions are given. Regularity of boundary conditions is shown. An algorithm for calculation of initial conditions is proposed.