Showing papers on "Probability mass function published in 1977"

On the Possible Orderings in the Measurement Selection Problem

Abstract: An aspect of the measurement selection problem?the existence of anomalous orderings on the probability of error obtained by selected subsets of measurements?is discussed. It is shown that for any ordering on the probability of error as a function of the subset of measurements (subject to an obvious set monotonicity condition), there exists a multivariate normal two-hypothesis problem N(?,K) versus N(??,K) that exhibits this ordering. Thus no known nonexhaustive sequential k-measurement selection procedure is optimal, even for jointly normal measurements.

Probability and Statistics

Abstract: 1. Introduction to Probability 2. Conditional Probability 3. Random Variables and Distributions 4. Expectation 5. Special Distributions 6. Large Random Samples 7. Estimation 8. Sampling Distributions of Estimators 9. Testing Hypotheses 10. Categorical Data and Nonparametric Methods 11. Linear Statistical Models 12. Simulation

The Probability that a Random Polytope is Bounded

Abstract: A formula for the probability that a randomly generated n-polytope defined by m half-spaces is bounded is presented. Results of a simulation giving i the probability that all m constraints are relevant and ii a formula for the expected number of vertices of a polytope, are presented.

The probability density and level-crossings of first-order non-linear systems driven by the random telegraph signal†

Abstract: We consider the probability density function p(y) of the output y(t) of the first-order non linear system [ydot] + β ƒ(y) = βx, where x = x(t) is the random telegraph signal and ƒ(·) is a non-linear function Employing extended forms of the Fokker-Planck-Kolmogorov equation, the so-called vth-order equations, a general expression is derived for p(y) and some specific eases are investigated These results are applied to find the average number of zero and level-crossings per unit time of the output process

On the support of symmetric infinitely divisible and stable probability measures on LCTVS

Abstract: It is shown that the topological support (supp.) of a r-regular, symmetric, infinitely divisible (resp. stable of any index a E (0, 2)) probability measure on a Hausdorff LCTVS E is a subgroup (resp. a subspace) of E. The part regarding the support of a stable probability measure of this theorem completes a result of A. De-Acosta [Ann. of Probability 3 (1975), 865-875], who proved a similar result for a E (1, 2), and the author [Proc. Amer. Math. Soc. 63 (1977), 306-312], who proved it for a E [1, 2). Further, it provides a complete affirmative solution to the question, raised by J. Kuelbs and V. Mandrekar [Studia Math. 50 (1974), 149-162], of whether the supp. of a symmetric stable probability measure of index a E (0, 1] on a separable Hilbert space H is a subspace of H.

Applications of a probability inequality to ranking and selection and other related problems

Abstract: A probability inequality of conditionally independent and identically distributed (i.i.d.) random variables obtained recently by the author is applied to ranking and selection problems. It is shown that under both the indifference-zone and the subset formulations, the probability of a correct selection (PCS) is a cumulative probability of conditionally i.i.d, random variables. Therefore bounds on both the PCS and the sample size required can be obtained from that probability inequality. Applications of that inequality to other multiple decision problems are also considered. It is illustrated that general results concerning conditionally i.i.d. random variables are applicable to many problems in multiple decision theory.

Probability density function of a stochastic linear programming problem

Abstract: A stochastic linear programming problem under the “wait-and-see” situation is studied. After the conditions for the interchange of the order of integration and differentiation are surveyed, an explicit form of the probability density function of the stochastic linear programming problem is found. An example is also given to illustrate the result.

Reliability of a structure using chance constrained programming

Abstract: In the evaluation of a structural reliability, it is important to seek the probability distribution of the structure, but in many cases, it is difficult to determine it for complex structures. In this paper the limit analysis of a structure with probabilistic natures is rewritten to a stochastic mathematical programming problem (i.e. chance-constrained programming problem), where it is assumed that the probability that the structure is within the yield loci is equal to the probability that the collapse does not occur, and then the probability distribution of strengths is estimated. As an example, a reinforced circular cylindrical silo subject to loading by its contents with, and the probability distribution of the strengths and the reliability of the structure are numerically calculated.