Related papers: A Novel Extension of Randomly Weighted Average
In this paper, an alternative Discrete skew Logistic distribution is proposed, which is derived by using the general approach of discretizing a continuous distribution while retaining its survival function. The properties of the…
We extend the celebrated Stone's theorem to the framework of distributional regression. More precisely, we prove that weighted empirical distribution with local probability weights satisfying the conditions of Stone's theorem provide…
A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…
We study the distribution regression problem assuming the distribution of distributions has a doubling measure larger than one. First, we explore the geometry of any distributions that has doubling measure larger than one and build a small…
In this paper we tackle the problem of comparing distributions of random variables and defining a mean pattern between a sample of random events. Using barycenters of measures in the Wasserstein space, we propose an iterative version as an…
It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are…
In this paper we present the result of successively applying a Chebyshev polynomial to a continuous random variable. In particular we show that under mild assumptions the limiting distribution will be the same as the weight with respect to…
In this work, we derive an Edgeworth expansion for the Bernoulli weighted mean $\hat{\mu} = \frac{\sum_{i=1}^n Y_i T_i}{\sum_{i=1}^n T_i}$ in the case where $Y_1, \dots, Y_n$ are i.i.d. non semi-lattice random variables and $T_1, \dots,…
As a rigorous statistical approach, statistical Taylor expansion extends the conventional Taylor expansion by replacing precise input variables with random variables of known distributions and sample counts to compute the mean, the…
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function…
The skew-normal and the skew-$t$ distributions are parametric families which are currently under intense investigation since they provide a more flexible formulation compared to the classical normal and $t$ distributions by introducing a…
The multidimensional distributions with heavy tails attracted recently the attention of several papers on Applied Probability. However, the most of the works of the last decades are focused on multivariate regular variation, while the rest…
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and…
We derive in this article the exact non-asymptotical exponential and power estimates for self-normalized sums of centered independent random variables (r.v.) under natural norming. We will use also the theory of the so-called Grand Lebesgue…
We consider a model of random tree growth, where at each time unit a new vertex is added and attached to an already existing vertex chosen at random. The probability with which a vertex with degree $k$ is chosen is proportional to $w(k)$,…
A new version of a Strong Law of Large Numbers is proposed in this note for pairwise independent random variables. The main goal is to relax the assumption on a finite expectation for each term.
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime factors of typical integers.
In meta-analysis, the random-effects models are standard tools to address between-study heterogeneity in evidence synthesis analyses. For the random-effects distribution models, the normal distribution model has been adopted in most…
A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson…
This article aims to introduced a new distribution named as extended xgamma (EXg) distribution. This generalization is derived from xgamma distribution (Xg), a special finite mixture of exponential and gamma distributions [see, Sen et al.…