## 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_cdf (x [, a, v]) ## ## For each element of x, compute the cumulative distribution function ## (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: CDF of the log normal distribution function cdf = lognormal_cdf (x, a, v) if !((nargin == 1) || (nargin == 3)) usage ("lognormal_cdf (x [, a, v])"); endif if (nargin == 1) a = 1; v = 1; endif ## The following "straightforward" implementation unfortunately does ## not work (because exp (Inf) -> NaN etc): ## cdf = normal_cdf (log (x), log (a), v); ## Hence ... [retval, x, a, v] = common_size (x, a, v); if (retval > 0) error (["lognormal_cdf: ", ... "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); cdf = zeros (1, s); k = find (isnan (x) | !(a > 0) | !(a < Inf) ... | !(v > 0) | !(v < Inf)); if any (k) cdf(k) = NaN * ones (1, length (k)); endif k = find ((x == Inf) & (a > 0) & (a < Inf) & (v > 0) & (v < Inf)); if any (k) cdf(k) = ones (1, length (k)); endif k = find ((x > 0) & (x < Inf) & (a > 0) & (a < Inf) ... & (v > 0) & (v < Inf)); if any (k) cdf(k) = stdnormal_cdf ((log (x(k)) - log (a(k))) ./ sqrt (v(k))); endif cdf = reshape (cdf, r, c); endfunction

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