TSBINOMIAL(1) TSBINOMIAL(1) NAME tsbinomial - generate a binomial distribution time series SYNOPSIS tsbinomial [-f fraction] [-i value] [-n n] [-p probability] [-r] [-s] [-t] [-v] number DESCRIPTION Tsbinomial is for generating binomial distribution noise, with unfair bias, and cumulative sum-generates a time series. The idea is to pro- duce a 1/f squared power spectrum distribution by running a cumulative sum on a binomial distribution. The program accepts a an unfair bias and a wager factor. See "Fractals," Jens Feder, Plenum Press, New York, New York, 1988, ISBN 0-306-42851-2, pp. 154, as suggested by Hurst. This program is a modification of the program tscoin. The wager frac- tion is computed by first calculating the optimal wager fraction, f = 2P - 1, where P is the Shannon probability, and f is the optimal wager fraction, (which is the root mean square = standard deviation of the normalized increments of the time series,) and then reducing this value by the standard deviation of the binomial distribution, which is the square root of the number of elements in the distribution, ie., the root mean square of the normalized increments of the cumulative sum is the same as the standard deviation of the binomial distribution. See "Fractals," Jens Feder, Plenum Press, New York, New York, 1988, ISBN 0-306-42851-2, pp. 155. Note: these programs use the following functions from other references: ran1, which returns a uniform random deviate between 0.0 and 1.0. See "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 210, referencing Knuth. gasdev, which returns a normally distributed deviate with zero mean and unit variance, using ran1 () as the source of uniform deviates. See "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 217. gammln, which returns the log of the results of the gamma function. See "Numerical Recipes in C: The Art of Scientific Computing," William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling, Cambridge University Press, New York, 1988, ISBN 0-521-35465-X, page 168. OPTIONS -f fraction Fraction of reserves to be wagered, (0 <= fraction <= 1) -i value Initial value of cash reserves -n n Number of elements in the binomial distribution. -p probability Shannon probability, (0.5 <= probability <= 1.0) -r Do not normalize the standard deviation = fraction. -s Print the cumulative sum of the binomial distribution time series. -t Sample's time will be included in the output time series. -v Print the version and copyright banner of the program. number Number of data points in the output time series. 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 TSBINOMIAL(1)