Characterization Of Random Variables Research Articles

Characterization of random variables with stationary digits

AbstractLet $q\ge2$ be an integer, $\{X_n\}_{n\geq 1}$ a stochastic process with state space $\{0,\ldots,q-1\}$ , and F the cumulative distribution function (CDF) of $\sum_{n=1}^\infty X_n q^{-n}$ . We show that stationarity of $\{X_n\}_{n\geq 1}$ is equivalent to a functional equation obeyed by F, and use this to characterize the characteristic function of X and the structure of F in terms of its Lebesgue decomposition. More precisely, while the absolutely continuous component of F can only be the uniform distribution on the unit interval, its discrete component can only be a countable convex combination of certain explicitly computable CDFs for probability distributions with finite support. We also show that $\mathrm{d} F$ is a Rajchman measure if and only if F is the uniform CDF on [0, 1].

Reliability-based load and resistance factor design for piping: an exploratory case study

This paper presents an exploratory case study on the application of Load and Resistance Factor Design (LRFD) approach to the Section III of ASME Boiler and Pressure Vessel code for piping design. The failure criterion for defining the performance function is considered as plastic instability. Presently used design equation is calibrated by evaluating the minimum reliability levels associated with it. If the target reliability in the LRFD approach is same as that evaluated for the presently used design equation, it is shown that the total safety factors for the two design equations are identical. It is observed that the load and resistance factors are not dependent upon the diameter to thickness ratio. A sensitivity analysis is also conducted to study the variations in the load and resistance factors due to changes in (a) coefficients of variation for pressure, moment, and ultimate stress, (b) ratio of mean design pressure to mean design moment, (c) distribution types used for characterizing the random variables, and (d) statistical correlation between random variables. It is observed that characterization of random variables by log-normal distribution is reasonable. Consideration of statistical correlation between the ultimate stress and section modulus gives higher values of the load factor for pressure but lower value for the moment than the corresponding values obtained by considering the variables to be uncorrelated. Since the effect of statistical correlation on the load and resistance factors is relatively insignificant for target reliability values of practical interest, the effect of correlated variables may be neglected.

A characterization of random variables with minimum L2-distance

A complete characterization of multivariate random variables with minimum L 2 Wasserstein-distance is proved by means of duality theory and convex analysis. This characterization allows to determine explicitly the optimal couplings for several multivariate distributions. A partial solution of this problem has been found in recent papers by Knott and Smith.

Theory, Simulation and Reality

Click to increase image sizeClick to decrease image size Additional informationNotes on contributorsPeter FlusserPeter Flusser was born in Vienna, Austria. He spent the years during WW II as a refugee in Shanghai, China. After coming to the United States, he received his B.A. from Ottawa University in Ottawa, Kansas, his M.A. from the University of Kansas, and his Ed. D. from Oklahoma State University, writing his thesis under Professor I. I. Kotlarski on the characterization of random variables with values in a compact abelian group. Dr. Flusser spent most of his teaching career at small liberal arts colleges in Kansas and Iowa. He is currently Professor of Mathematics at Kansas Wesleyan University. His hobbies include chess, bridge, listening to classical music and reading. He has four children and three grandchildren.