Descriptive statistics is the process of summarizing gathered raw data from a research and creating useful statistics, which help the better understanding of data. According to the types of variables, which consist of qualitative and quantitative variables, some descriptive statistics have been introduced. Frequency percentage is used in qualitative data, and mean, median, mode, standard deviat...

Let $p$ be an odd prime. Associated to a pair $(E, \mathcal{F}_\infty)$ consisting of rational elliptic curve $E$ and $p$-adic Lie extension $\mathcal{F}_\infty$ $\mathbb{Q}$, is the $p$-primary Selmer group $Sel_{p^\infty}(E/\mathcal{F}_\infty)$ over $\mathcal{F}_\infty$. In this paper, we study arithmetic statistics for algebraic structure group. The results provide insights into asymptotics ...

Let {X,Xn; n ≥ 1} be a sequence of i.i.d. random variables with distribution function F (x). For each positive integer n, let X1:n ≤ X2:n ≤ · · · ≤ Xn:n be the order statistics of X1, X2, · · · , Xn. Let H(·) be a real Borel-measurable function defined on R such that E|H(X)| < ∞ and let J(·) be a Lipschitz function of order one defined on [0, 1]. Write μ = μ(F, J,H) = E(J(U)H(F←(U))) and Ln(F, ...

There is neither motivation nor need to introduce 'superstatistics.' The authors attempt to generalize the Boltzmann factor so as to obtain a more general statistics, i.e., their so-called superstatistics. The do so by performing a Laplace transform on the probability density function (pdf) of an intensive variable, f (β), where β is the inverse temperature. The criteria they use for choosing f...

Consider a N ×n matrix Σn = 1 √ n R 1/2 n Xn, where Rn is a nonnegative definite Hermitian matrix and Xn is a random matrix with i.i.d. real or complex standardized entries. The fluctuations of the linear statistics of the eigenvalues: Trace f(ΣnΣ ∗ n) = N ∑ i=1 f(λi), (λi) eigenvalues of ΣnΣ ∗ n, are shown to be gaussian, in the regime where both dimensions of matrix Σn go to infinity at the s...

We present quantum bum ps obtained from flash experim ents at the Limulus ventral nerve photoreceptor under voltage clam p conditions. The results are shown and discussed in form o f histogram s for the latency, am plitude and net charge transfer (current time integral) o f the bum p current responses. We argue tha t the experim ental latency histogram s cannot be de­ scribed satisfactorily by ...

It is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions F and based on a probability measure P holds a.s. if and only if F CLT (P ) and ∫ F dP < ∞, where F = supf F |f | and it holds in probability if and only if F ∈ CLT (P ). Thus, for a large class of statistics, no local uniformity of the CLT (about P ) is needed for the bootstrap to w...

BACKGROUND Relative validity (RV), a ratio of ANOVA F-statistics, is often used to compare the validity of patient-reported outcome (PRO) measures. We used the bootstrap to establish the statistical significance of the RV and to identify key factors affecting its significance. METHODS Based on responses from 453 chronic kidney disease (CKD) patients to 16 CKD-specific and generic PRO measures...

Abstract: An important problem in statistics is determining a joint probability distribution from its marginals. In 2D case, the marginal probability density functions f1(x) and f2(y) are related to their joint distribution f (x,y) via the horizontal and vertical line integrals. So, the problem of determining f (x,y) from f1(x) and f2(y) is an ill-posed inverse problem. In statistics the notion...