| % rspdfsolv() - sub-function used by rsfit() to searc for optimal | |
| % parameter for Ramberg-Schmeiser distribution | |
| % | |
| % Usage: res = rspdfsolv(l, l3, l4) | |
| % | |
| % Input: | |
| % l - [lambda3 lamda4] parameters to optimize | |
| % skew - expected skewness | |
| % kurt - expected kurtosis | |
| % | |
| % Output: | |
| % res - residual | |
| % | |
| % Author: Arnaud Delorme, SCCN, 2003 | |
| % | |
| % See also: rsget() | |
| % | |
| % Reference: Ramberg, J.S., Tadikamalla, P.R., Dudewicz E.J., Mykkytka, E.F. | |
| % A probability distribution and its uses in fitting data. | |
| % Technimetrics, 1979, 21: 201-214. | |
| % Copyright (C) 2003 Arnaud Delorme, SCCN, arno@salk.edu | |
| % | |
| % This program is free software; you can redistribute it and/or modify | |
| % it under the terms of the GNU General Public License as published by | |
| % the Free Software Foundation; either version 2 of the License, or | |
| % (at your option) any later version. | |
| % | |
| % This program is distributed in the hope that it will be useful, | |
| % but WITHOUT ANY WARRANTY; without even the implied warranty of | |
| % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the | |
| % GNU General Public License for more details. | |
| % | |
| % You should have received a copy of the GNU General Public License | |
| % along with this program; if not, write to the Free Software | |
| % Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA | |
| function res = rspdfsolv( l, a3, a4); | |
| A = 1/(1 + l(1)) - 1/(1 + l(2)); | |
| B = 1/(1 + 2*l(1)) + 1/(1 + 2*l(2)) - 2*beta(1+l(1), 1+l(2)); | |
| C = 1/(1 + 3*l(1)) - 1/(1 + 3*l(2)) ... | |
| - 3*beta(1+2*l(1), 1+l(2)) + 3*beta(1+l(1), 1+2*l(2)); | |
| D = 1/(1 + 4*l(1)) + 1/(1 + 4*l(2)) ... | |
| - 4*beta(1+3*l(1), 1+l(2)) - 4*beta(1+l(1), 1+3*l(2)) ... | |
| + 6*beta(1+2*l(1), 1+2*l(2)); | |
| estim_a3 = (C - 3*A*B + 2*A^3)/(B-A^2)^(3/2); | |
| estim_a4 = (D - 4*A*C + 6*A^2*B - 3*A^4)/(B-A^2)^2; | |
| res = (estim_a3 - a3)^2 + (estim_a4 - a4)^2; | |
| % the last term try to ensures that l(1) and l(2) are of the same sign | |
| if sign(l(1)*l(2)) == -1, res = 2*res; end; | |
| return; | |
| % original equations | |
| % $$$ A = 1(1 + l(3)) - 1/(1 + l(4)); | |
| % $$$ B = 1(1 + 2*l(3)) + 1/(1 + 2*l(4)) - 2*beta(1+l(3), 1+l(4)); | |
| % $$$ C = 1(1 + 3*l(3)) - 1/(1 + 3*l(4)) ... | |
| % $$$ - 3*beta(1+2*l(3), 1+l(4)) + 3*beta(1+l(3), 1+2*l(4)); | |
| % $$$ D = 1(1 + 4*l(3)) + 1/(1 + 4*l(4)) ... | |
| % $$$ - 4*beta(1+3*l(3), 1+l(4)) - 4*beta(1+l(3), 1+3*l(4)) ... | |
| % $$$ + 6*beta(1+2*l(3), 1+2*l(4)); | |
| % $$$ | |
| % $$$ R(1) = l(1) + A/l(2); | |
| % $$$ R(2) = (B-A^2)/l(2)^2; | |
| % $$$ R(3) = (C - 3*A*B + 2*A^3)/l(2)^3; | |
| % $$$ R(4) = (D - 4*A*C + 6*A^2*B - 3*A^4)/l(2)^4; | |