TSSHANNON(1) TSSHANNON(1) NAME tsshannon - calculate the probability, given the Shannon information capacity SYNOPSIS tsshannon [-v] C(p) DESCRIPTION Tsshannon is for calculating the probability, given the Shannon infor- mation capacity. See "Fractals, Chaos, Power Laws," Manfred Schroeder, W. H. Freeman and Company, New York, New York, 1991, ISBN 0-7167-2136-8, pp 128 and pp 151. Uses Newton-Raphson method for an iterative solution for the probability, p, given the Shannon informa- tion capacity, C(p). As a reference on Newton-Raphson Method of root finding, see "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge Uni- versity Press, New York, 1988, ISBN 0-521-35465-X, pp 270. From Schroeder, pp 151: p = 0.55 2^(C(0.55)) = 0.005, (probably a typo, meaning 1.005) by calculator, C(0.55) = 0.0072, (this program gives C(0.549912) = 0.0072) Derivation, starting with Schroeder, pp 151: C(p) = 1 + p ln (p) + (1 - p) ln (1 - p) 2 2 C(p) = 1 + p (ln (p) / ln (2)) + (1 - p) (ln (1 - p) / ln (2)) C(p) = [1 / ln (2)] [ln (2) + p ln (p) + (1 - p) ln (1 - p)] C(p) = [1 / ln (2)] [ ln (2) + p ln (p) + ln (1 - p) - p ln (1 - p)] dC(p) ---- = [1 / ln (2)] [1 + ln (p) - (1 / (1 - p)) - dp {ln (1 - p) - (p / (1 - p))}] = [1 / ln (2)] [1 + ln (p) - (1 / (1 - p)) - ln (1 - p) + (p / (1 - p))] = [1 / ln (2)] [ln (p) - ln (1 - p) + (p / (1 - p)) - (1 / (1 - p))] = [1 / ln (2)] [1 + ln (p) - ln (1 - p) + ((p - 1) / (1 - p))] = [1 / ln (2)] [1 + ln (p) - ln (1 - p) - 1] = [1 / ln (2)] [ln (p) - ln (1 - p)] OPTIONS -v Print the version and copyright banner of the program. C(p) Shannon information capacity. WARNINGS There is little or no provision for handling numerical exceptions. SEE ALSO tsderivative(1), tshcalc(1), tshurst(1), tsintegrate(1), tslogre- turns(1), tslsq(1), tsnormal(1), tsshannon(1), tsblack(1), tsbrown- ian(1), tsdlogistic(1), tsfBm(1), tsfractional(1), tsgaussian(1), tsin- tegers(1), tslogistic(1), tspink(1), tsunfairfractional(1), tswhite(1), tscoin(1), tsunfairbrownian(1), tsfraction(1), tsshannonmax(1), tschangewager(1), tssample(1), tsrms(1), tscoins(1), tsavg(1), tsXsquared(1), tsstockwager(1), tsshannonwindow(1), tsmath(1), tsavg- window(1), tspole(1), tsdft(1), tsbinomial(1), tsdeterministic(1), tsnumber(1), tsrmswindow(1), tsshannonstock(1), tsmarket(1), tsstock(1), tsstatest(1), tsunfraction(1), tsshannonaggregate(1), tsin- stant(1), tsshannonvolume(1), tsstocks(1), tsshannonfundamental(1), tstrade(1), tstradesim(1), tsrunlength(1), tsunshannon(1), tsroot- mean(1), tsrunmagnitude(1), tskurtosis(1), tskurtosiswindow(1), tsroot- meanscale(1), tsscalederivative(1), tsgain(1), tsgainwindow(1) tscauchy(1), tslognormal(1), tskalman(1), tsroot(1), tslaplacian(1) DIAGNOSTICS Error messages for incompatible arguments, failure to allocate memory, inaccessible files, and opening and closing files. AUTHORS ---------------------------------------------------------------------- A license is hereby granted to reproduce this software source code and to create executable versions from this source code for personal, non-commercial use. The copyright notice included with the software must be maintained in all copies produced. THIS PROGRAM IS PROVIDED "AS IS". THE AUTHOR PROVIDES NO WARRANTIES WHATSOEVER, EXPRESSED OR IMPLIED, INCLUDING WARRANTIES OF MERCHANTABILITY, TITLE, OR FITNESS FOR ANY PARTICULAR PURPOSE. THE AUTHOR DOES NOT WARRANT THAT USE OF THIS PROGRAM DOES NOT INFRINGE THE INTELLECTUAL PROPERTY RIGHTS OF ANY THIRD PARTY IN ANY COUNTRY. Copyright (c) 1994-2006, John Conover, All Rights Reserved. Comments and/or bug reports should be addressed to: john@email.johncon.com (John Conover) ---------------------------------------------------------------------- January 17, 2006 TSSHANNON(1)