相关论文: The inverse of the cumulative standard normal prob…

Chatteerjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of…

This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a…

We investigate asymptotic behaviour of probabilities of large deviations for normalized combinatorial sums. We find a zone in which these probabilities are equivalent to the tail of the standard normal law. Our conditions are similar to the…

We study the complexity of deterministic and probabilistic inversions of partial computable functions on the reals.

In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…

We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…

The distribution function of the sum of i.i.d. random variables of the special form is considered. Such sum describes messages posterior probabilities for random coding in binary symmetric channel. Close non-asymptotic lower and upper…

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…

We collect well known and less known facts about the bivariate normal distribution and translate them into copula language. In addition, we prove a very general formula for the bivariate normal copula, we compute Gini's gamma, and we…

We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…

Stirling numbers of the first kind are common in number theory and combinatorics; through Ewen's sampling formula, these numbers enter into the calculation of several population genetics statistics, such as Fu's Fs. In previous papers we…

In this article, we propose a new three parameter distribution by compounding negative binomial with reciprocal inverse Gaussian model called negative binomial-reciprocal inverse Gaussian distribution. This model is tractable with some…

We determine the asymptotic behavior of the realized power variations, or more generally of sums of a given test function evaluated at the successive increments of a L\'{e}vy process. One can completely elucidate the first order behavior…

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…

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…

We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied,…

This paper develops unified asymptotic distribution theory for dynamic quantile predictive regressions which is useful when examining quantile predictability in stock returns under possible presence of nonstationarity.

In this communication, we introduce a new statistical model and study its various mathematical properties. The expressions for hazard rate, reversed hazard rate, and odd functions are provided. We explore the asymptotic behaviors of the…

We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…

According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…