Related papers: Ordering properties of the smallest order statisti…
In this paper, we use a new partial order, called the f-majorization order. The new order includes as special cases the majorization , the reciprocal majorization and the p-larger orders. We provide a comprehensive account of the…
Dispersive order is a type of variability order for comparing the variability in probability distributions. Star order compares the skewness of probability distributions. This work considers dispersive and star orders of extreme order…
Given low order moment information over the random variables $\mathbf{X} = (X_1,X_2,\ldots,X_p)$ and $Y$, what distribution minimizes the Hirschfeld-Gebelein-R\'{e}nyi (HGR) maximal correlation coefficient between $\mathbf{X}$ and $Y$,…
The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are…
Let $ X_{\lambda_1},\ldots,X_{\lambda_n}$ be a set of dependent and non-negative random variables share a survival copula and let $Y_i= I_{p_i}X_{\lambda_i}$, $i=1,\ldots,n$, where $I_{p_1},\ldots,I_{p_n}$ be independent Bernoulli random…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are independent and identically distributed…
We consider balanced one-, two- and three-way ANOVA models to test the hypothesis that the fixed factor A has no effect. The other factors are fixed or random. We determine the noncentrality parameter for the exact F-test, describe its…
In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The…
In this paper, we analyze the relative errors that crop up in the various reliability measures due to the tacit assumption that the components are independently working associated with a $n$-component series system or a parallel system…
The Gumbel-Softmax probability distribution allows learning discrete tokens in generative learning, while the Gumbel-Argmax probability distribution is useful in learning discrete structures in discriminative learning. Despite the efforts…
Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks…
A measurement strategy is developed for a new kind of hypothesis testing. It assigns, with minimum probability of error, the state of a quantum system to one or the other of two complementary subsets of a set of N given non-orthogonal…
Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…
In this note, we establish the convergence in distribution of the maxima of i.i.d. random variables to the Gumbel distribution with the associated normalizing sequences for several examples that are related to the normal distribution.…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
Stochastic comparisons of series and parallel systems are important in many areas of engineering, operations research and reliability analysis. These comparisons allow for the evaluation of the performance and reliability of systems under…
Let $\bm{x}_1,\cdots,\bm{x}_n$ be a random sample of size $n$ from a $p$-dimensional population distribution, where $p=p(n)\rightarrow\infty$. Consider a symmetric matrix $W=X^\top X$ with parameters $n$ and $p$, where…
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 study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
This paper introduces a new three-parameters model called the Weibull-G exponential distribution (WGED) distribution which exhibits bathtub-shaped hazard rate. Some of it's statistical properties are obtained including quantile, moments,…