Related papers: Characterization of exponential distribution throu…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
This paper describes the Elliptical Quartic Exponential distribution in $\mathbb{R}^D$, obtained via a maximum entropy construction by imposing second and fourth moment constraints. I discuss relationships to related work, analytical…
For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of random variables satisfying $\mathbb{E} \lvert X_{n} \rvert < \infty$ for all $n \geqslant 1$, a maximal inequality is established, and used to obtain strong law of large numbers for…
Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the…
We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum)…
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…
This paper derives bounds for two omnipresent information theoretic measures, the Shannon entropy and its complementary dual, the extropy. Based on a large size data set from a logconcave model, the said bounds are obtained for the entropy…
Parametric inference for spatial max-stable processes is difficult since the related likelihoods are unavailable. A composite likelihood approach based on the bivariate distribution of block maxima has been recently proposed in the…
We propose and study properties of maximum likelihood estimators in the class of conditional transformation models. Based on a suitable explicit parameterisation of the unconditional or conditional transformation function, we establish a…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
Triangular distributions are a well-known class of distributions that are often used as an elementary example of a probability model. Maximum likelihood estimation of the mode parameter of the triangular distribution over the unit interval…
In this paper, higher-order expansions for distributions and densities of powered extremes of standard normal random sequences are established under an optimal choice of normalized constants. Our findings refine the related results in Hall…
In this paper, we establish the second-order distributional expansions of normalized maxima of n independent observations, where the ith observation follows from a normal copula with its correlation coefficient being a monotone continuous…
Kotlarski (1978) proved a result on identification of the distributions of independent random variables $X,Y$ and $Z$ from the joint distribution of the bivariate random vector $(U,V)$ where $(U,V)= (\max(X,Z),\max(Y,Z)).$ We extend this…
Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables (not necessarily identically distributed), and $\eta$ be a counting random variable independent of this sequence. We obtain sufficient conditions on…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the…
We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $X_{k:n}$ of a random sample of size $n$ from a continuous distribution $F$. For central and intermediate cases,…
The maxima and the minima of a randomly stopped sample of a random variable, $X$, together with two newly defined random variables that make $X$ into the maxima or minima of a randomly stopped sample of them, can be used to define…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…