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1 ## Copyright (C) 1995, 1996, 1997, 2007 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} {} nbinpdf (@var{x}, @var{n}, @var{p}) |
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21 ## For each element of @var{x}, compute the probability density function |
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22 ## (PDF) at @var{x} of the Pascal (negative binomial) distribution with |
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23 ## parameters @var{n} and @var{p}. |
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24 ## |
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25 ## The number of failures in a Bernoulli experiment with success |
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26 ## probability @var{p} before the @var{n}-th success follows this |
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27 ## distribution. |
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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: PDF of the Pascal (negative binomial) distribution |
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32 |
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33 function pdf = nbinpdf (x, n, p) |
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34 |
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35 if (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 (!isscalar(n) || !isscalar(p)) |
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40 [retval, x, n, p] = common_size (x, n, p); |
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41 if (retval > 0) |
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42 error ("nbinpdf: x, n and p must be of common size or scalar"); |
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43 endif |
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44 endif |
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45 |
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46 pdf = zeros (size (x)); |
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47 |
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48 k = find (isnan (x) | (n < 1) | (n == Inf) | (n != round (n)) |
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49 | (p < 0) | (p > 1)); |
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50 if (any (k)) |
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51 pdf(k) = NaN; |
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52 endif |
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53 |
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54 ## Just for the fun of it ... |
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55 k = find ((x == Inf) & (n > 0) & (n < Inf) & (n == round (n)) |
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56 & (p == 0)); |
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57 if (any (k)) |
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58 pdf(k) = 1; |
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59 endif |
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60 |
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61 k = find ((x >= 0) & (x < Inf) & (x == round (x)) & (n > 0) |
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62 & (n < Inf) & (n == round (n)) & (p > 0) & (p <= 1)); |
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63 if (any (k)) |
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64 if (isscalar (n) && isscalar (p)) |
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65 pdf(k) = bincoeff (-n, x(k)) .* (p ^ n) .* ((p - 1) .^ x(k)); |
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66 else |
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67 pdf(k) = bincoeff (-n(k), x(k)) .* (p(k) .^ n(k)) .* ((p(k) - 1) .^ x(k)); |
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68 endif |
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69 endif |
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70 |
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71 endfunction |
