相关论文: On Stochastic Comparisons of Order Statistics from…

Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…

We consider the fundamental problem of selecting $k$ out of $n$ random variables in a way that the expected highest or second-highest value is maximized. This question captures several applications where we have uncertainty about the…

A sequence of real numbers $\{x_{n}\}_{n\in \mathbb{N}}$ is said to be $\alpha \beta$-statistically convergent of order $\gamma$ (where $0<\gamma\leq 1$) to a real number $x$ \cite{a} if for every $\delta>0,$ $$\underset{n\rightarrow…

The concept of "stochastic precedence" between two real-valued random variables has often emerged in different applied frameworks. In this paper we consider a slightly more general, and completely natural, concept of stochastic precedence…

In this paper, we have discussed the usual stochastic ordering relations between two systems. Each system consists of n mutually independent components. The components follow Exponentiated (Extended) Chen distribution with three parameters…

A new characterization of the exponential distribution is obtained. It is based on an equation involving randomly shifted (translated) order statistics. No specific distribution is assumed for the shift random variables. The proof uses a…

In this paper ideas of different types of convergence of a sequence of random variables in probability, namely, statistical convergence of order $\alpha$ in probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$ in…

We prove a conjecture of Haglund which can be seen as an extension of the equidistribution of the inversion number and the major index over permutations to ordered set partitions. Haglund's conjecture implicitly defines two statistics on…

Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…

Precedence order is a natural type of comparison for random variables in numerous engineering applications (e.g., for the stress-strength modeling). In this note, we show that, for a $k$-out-of-$n$ system, redundancy at the component level…

Suppose X is a frequency vector that follows a central multiple hyper-geometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We show that the probability that X…

The stochastic comparisons of parallel and series system are worthy of study. In this paper, we present some stochastic comparisons of parallel and series systems having independent components from Gumble distribution with two parameters…

For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…

In this paper, we have discussed the stochastic comparison of the smallest and largest ordered statistic from independent heterogeneous Weibull-G random variables and Gompertz Makeham random variables. We compare systems arising from taking…

The sample selection bias problem arises when a variable of interest is correlated with a latent variable, and involves situations in which the response variable had part of its observations censored. Heckman (1976) proposed a sample…

In this paper, we discuss stochastic comparisons of parallel systems with independent heterogeneous exponentiated Nadarajah-Haghighi (ENH) components in terms of the usual stochastic order, dispersive order, convex transform order and the…

Spectral statistics of quantum systems have been studied in detail using the nearest neighbour level spacings, which for generic chaotic systems follows random matrix theory predictions. In this work, the probability density of the closest…

We introduce a comprehensive method for establishing stochastic orders among order statistics in the i.i.d. case. This approach relies on the assumption that the underlying distribution is linked to a reference distribution through a…

We study the problem of comparing ageing patterns of the lifetime of k-out-of-n systems. Mathematically, this reduces to being able to decide about a stochastic ordering relationship between different order statistics. We discuss such…

An old conjecture of Kahn and Saks says, roughly, that any poset $P$ of large enough width contains elements $x,y$ which are "balanced" in the sense that the probability that $x$ precedes $y$ in a uniformly random linear extension of $P$ is…