# Computational Probability: Algorithms and Applications in the Mathematical Sciences

Springer Science & Business Media, 2008. gada 8. janv. - 222 lappuses

Computational probability encompasses data structures and algorithms that have emerged over the past decade that allow researchers and students to focus on a new class of stochastic problems. COMPUTATIONAL PROBABILITY is the first book that examines and presents these computational methods in a systematic manner. The techniques described here address problems that require exact probability calculations, many of which have been considered intractable in the past. The first chapter introduces computational probability analysis, followed by a chapter on the Maple computer algebra system. The third chapter begins the description of APPL, the probability modeling language created by the authors. The book ends with three applications-based chapters that emphasize applications in survival analysis and stochastic simulation.

The algorithmic material associated with continuous random variables is presented separately from the material for discrete random variables. Four sample algorithms, which are implemented in APPL, are presented in detail: transformations of continuous random variables, products of independent continuous random variables, sums of independent discrete random variables, and order statistics drawn from discrete populations.

The APPL computational modeling language gives the field of probability a strong software resource to use for non-trivial problems and is available at no cost from the authors. APPL is currently being used in applications as wide-ranging as electric power revenue forecasting, analyzing cortical spike trains, and studying the supersonic expansion of hydrogen molecules. Requests for the software have come from fields as diverse as market research, pathology, neurophysiology, statistics, engineering, psychology, physics, medicine, and chemistry.

### Lietotāju komentāri -Rakstīt atsauksmi

Ierastajās vietās neesam atraduši nevienu atsauksmi.

### Saturs

 Four Simple Examples of the Use of APPL 6 Solving Equations 20 Simple Algorithms 37 Examples 50 roducts of Random Variables 55 ata Structures and Simple Algorithms 71
 ums of Independent Random Variables 92 Algorithm 106 rder Statistics 119 teliability and Survival Analysis 135 133 to chastic Simulation 153 152 ther Applications 185

### Populāri fragmenti

69. lappuse - There is always somewhere a weakest spot,  In hub, tire, i'elloe, in spring or thill, In panel or cross-bar or floor or sill, In screw, bolt, thorough-brace,  lurking still, Find it somewhere you must and will,  Above or below, or within or without,  And that's the reason, beyond a doubt, A chaise breaks down, but does n't wear out. 4. But the Deacon swore, (as Deacons do, With an "I dew vurn...
3. lappuse - It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them.
104. lappuse - Col. 1 Col. 2 Col. 3 Col. 4 Col. 5 Col. 6 Col. 7 Col. 8 Col. 9 Col. 10 Col.
219. lappuse - J. & Vlach, M. / GENERALIZED CONCAVITY IN FUZZY OPTIMIZATION AND DECISION ANALYSIS Song, J. & Yao, D. / SUPPLY CHAIN STRUCTURES: Coordination, Information and Optimization Kozan, E. & Ohuchi, A. / OPERATIONS RESEARCH/ MANAGEMENT SCIENCE AT WORK Bouyssou et al. / AIDING DECISIONS WITH MULTIPLE CRITERIA: Essays in Honor of Bernard Roy Cox, Louis Anthony, Jr. / RISK ANALYSIS: Foundations, Models and Methods Dror, M., L'Ecuyer, P. & Szidarovszky, F. / MODELING UNCERTAINTY: An Examination of Stochastic...
89. lappuse - Let X be a binomial random variable with parameters n and p, both unknown.
41. lappuse - Find the expected value of the random variable Y = f(X), when X is a discrete random variable with probability mass function g(x). Let...
126. lappuse - J p(u|a,|a) du (A10) 0 which provides the probability of obtaining a value less than or equal to x. On x, = x|p exp((ji,), PfXjIa.jx) is given through 2-,/2 ""2 Je P(xi|a,n) = j + (27I)" exp(-s2) ds s 0.84 = P(84) (Alia) 0 which is independent of a and ^.; while on x?
157. lappuse - ... of jumping between hyperplanes. With this in mind, we compare the distribution of the distances between consecutive points (ordered pairs) and the distribution of the distances between truly random points on the unit square. The assumption being made is that generators that yield a distribution of distances similar to the purely random points will be better random number generators.
156. lappuse - ... within it. This randomness is not to be found in the structure of the lattice, however, but in the order in which the points are generated. More specifically, the empirical distribution of the distance between consecutive random number pairs should be close to the theoretical distance between consecutive random number pairs for a good random number generator.