Related papers: Expansions of maximum and minimum from Generalized…

In this paper, asymptotic expansions of the distributions and densities of powered extremes for Maxwell samples are considered. The results show that the convergence speeds of normalized partial maxima relies on the powered index.…

The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant…

In this paper, we study the asymptotic behaviors of the extreme of mixed skew-t distribution. We considered limits on distribution and density of maximum of mixed skew-t distribution under linear and power normalization, and further derived…

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…

We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically…

We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.

In this paper, we study second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization. Numerical analysis are given to compare the asymptotic behaviors under power normalization with…

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…

For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…

The max-stable H\"usler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper…

We consider the extremal properties of the highly flexible univariate extended skew-normal distribution. We derive the well-known Mills' inequalities and Mills' ratio for the extended skew-normal distribution and establish the asymptotic…

Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…

In the seminal contribution [4] the joint weak convergence of maxima and minima of weakly dependent stationary sequences is derived under some mild asymptotic conditions. In this paper we address additionally the case of incomplete samples…

The Conway-Maxwell-Poisson (CMP) distribution is a natural two-parameter generalisation of the Poisson distribution which has received some attention in the statistics literature in recent years by offering flexible generalisations of some…

This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…

We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…