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)