Characterizations of Levy Distribution via Sub-Independence of the Random Variables and Truncated Moments

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Following Ahsanullah and Nevzorov (2014), we present certain characterizations of Levy distribution based on: (i) the sub-independence of the random variables; (ii) a simple relationship between two truncated moments; (iii) conditional expectation of certain function of the random variable. In case of independence, characterization (i) reduces to that of Ahsanullah and Nevzorov (2014)

Q-Markov random probability measures and their posterior distributions

In this paper, we use the Markov property introduced in Balan and Ivanoff (J. Theor. Probab. 15, 2002, 553-588) for set-indexed processes and we prove that a Markov prior distribution leads to a Markov posterior distribution. In particular, by proving that a neutral to the right prior distribution leads to a neutral to the right posterior distribution, we extend a fundamental result of Doksum (Ann. Probab. 2,1974, 183-201) to arbitrary sample spaces.Comment: 22 page

On the two-phase framework for joint model and design-based inference

We establish a mathematical framework that formally validates the two-phase ``super-population viewpoint'' proposed by Hartley and Sielken [Biometrics 31 (1975) 411--422] by defining a product probability space which includes both the design space and the model space. The methodology we develop combines finite population sampling theory and the classical theory of infinite population sampling to account for the underlying processes that produce the data under a unified approach. Our key results are the following: first, if the sample estimators converge in the design law and the model statistics converge in the model, then, under certain conditions, they are asymptotically independent, and they converge jointly in the product space; second, the sample estimating equation estimator is asymptotically normal around a super-population parameter.Comment: Published at http://dx.doi.org/10.1214/009053605000000651 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Prognostic Launch Vehicle Probability of Failure Assessment Methodology for Conceptual Systems Predicated on Human Causal Factors

Lessons learned from past failures of launch vehicle developments and operations were used to create a new method to predict the probability of failure of conceptual systems. Existing methods such as Probabilistic Risk Assessments and Human Risk Assessments were considered but found to be too cumbersome for this type of system-wide application for yet-to-be-flown vehicles. The basis for this methodology were historic databases of past failures, where it was determined that various faulty human-interactions were the predominant root causes of failure rather than deficient component reliabilities evaluated through statistical analysis. This methodology contains an expert scoring part which can be used in either a qualitative or a quantitative mode. The method produces two products: a numerical score of the probability of failure or guidance to program management on critical areas in need of increased focus to improve the probability of success. In order to evaluate the effectiveness of this new method, data from a concluded vehicle program (USAF's Titan IV with the Centaur G-Prime upper stage) was used as a test case. Although the theoretical vs. actual probability of failure was found to be in reasonable agreement (4.46% vs. 6.67% respectively) the underlying sub-root cause scoring had significant disparities attributable to significant organizational changes and acquisitions. Recommendations are made for future applications of this method to ongoing launch vehicle development programs