## Copyright (C) 1995, 1996, 1997 Kurt Hornik ## ## 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, 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 file. If not, write to the Free Software Foundation, ## 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. ## usage: lognormal_inv (x [, a, v]) ## ## For each element of x, compute the quantile (the inverse of the CDF) ## at x of the lognormal distribution with parameters a and v. If a ## random variable follows this distribution, its logarithm is normally ## distributed with mean log (a) and variance v. ## ## Default values are a = 1, v = 1. ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> ## Description: Quantile function of the log normal distribution function inv = lognormal_inv (x, a, v) if !((nargin == 1) || (nargin == 3)) usage ("lognormal_inv (x [, a, v])"); endif if (nargin == 1) a = 1; v = 1; endif ## The following "straightforward" implementation unfortunately does ## not work (because exp (Inf) -> NaN): ## inv = exp (normal_inv (x, log (a), v)); ## Hence ... [retval, x, a, v] = common_size (x, a, v); if (retval > 0) error (["lognormal_inv: ", ... "x, a and v must be of common size or scalars"]); endif [r, c] = size (x); s = r * c; x = reshape (x, 1, s); a = reshape (a, 1, s); v = reshape (v, 1, s); inv = zeros (1, s); k = find (!(x >= 0) | !(x <= 1) | !(a > 0) | !(a < Inf) ... | !(v > 0) | !(v < Inf)); if any (k) inv(k) = NaN * ones (1, length (k)); endif k = find ((x == 1) & (a > 0) & (a < Inf) & (v > 0) & (v < Inf)); if any (k) inv(k) = Inf * ones (1, length (k)); endif k = find ((x > 0) & (x < 1) & (a > 0) & (a < Inf) ... & (v > 0) & (v < Inf)); if any (k) inv(k) = a(k) .* exp (sqrt (v(k)) .* stdnormal_inv (x(k))); endif inv = reshape (inv, r, c); endfunction

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