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1 ## Copyright (C) 1995, 1996, 1997 Kurt Hornik |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- texinfo -*- |
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20 ## @deftypefn {Function File} {} logncdf (@var{x}, @var{mu}, @var{sigma}) |
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21 ## For each element of @var{x}, compute the cumulative distribution |
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22 ## function (CDF) at @var{x} of the lognormal distribution with |
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23 ## parameters @var{mu} and @var{sigma}. If a random variable follows this |
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24 ## distribution, its logarithm is normally distributed with mean |
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25 ## @var{mu} and standard deviation @var{sigma}. |
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26 ## |
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27 ## Default values are @var{mu} = 1, @var{sigma} = 1. |
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28 ## @end deftypefn |
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29 |
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30 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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31 ## Description: CDF of the log normal distribution |
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32 |
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33 function cdf = logncdf (x, mu, sigma) |
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34 |
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35 if (! ((nargin == 1) || (nargin == 3))) |
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36 print_usage (); |
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37 endif |
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38 |
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39 if (nargin == 1) |
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40 mu = 0; |
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41 sigma = 1; |
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42 endif |
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43 |
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44 ## The following "straightforward" implementation unfortunately does |
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45 ## not work (because exp (Inf) -> NaN etc): |
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46 ## cdf = normal_cdf (log (x), log (mu), sigma); |
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47 ## Hence ... |
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48 |
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49 if (!isscalar (mu) || !isscalar (sigma)) |
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50 [retval, x, mu, sigma] = common_size (x, mu, sigma); |
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51 if (retval > 0) |
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52 error ("logncdf: x, mu and sigma must be of common size or scalars"); |
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53 endif |
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54 endif |
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55 |
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56 cdf = zeros (size (x)); |
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57 |
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58 k = find (isnan (x) | !(sigma > 0) | !(sigma < Inf)); |
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59 if (any (k)) |
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60 cdf(k) = NaN; |
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61 endif |
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62 |
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63 k = find ((x == Inf) & (sigma > 0) & (sigma < Inf)); |
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64 if (any (k)) |
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65 cdf(k) = 1; |
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66 endif |
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67 |
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68 k = find ((x > 0) & (x < Inf) & (sigma > 0) & (sigma < Inf)); |
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69 if (any (k)) |
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70 if (isscalar (mu) && isscalar (sigma)) |
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71 cdf(k) = stdnormal_cdf ((log (x(k)) - mu) / sigma); |
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72 else |
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73 cdf(k) = stdnormal_cdf ((log (x(k)) - mu(k)) ./ sigma(k)); |
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74 endif |
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75 endif |
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76 |
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77 endfunction |
