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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 2, or (at your option) |
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8 ## 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, write to the Free |
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17 ## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} gampdf (@var{x}, @var{a}, @var{b}) |
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22 ## For each element of @var{x}, return the probability density function |
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23 ## (PDF) at @var{x} of the Gamma distribution with parameters @var{a} |
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24 ## and @var{b}. |
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25 ## @seealso{gamma, gammaln, gammainc, gamcdf, gaminv, gamrnd} |
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26 ## @end deftypefn |
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27 |
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28 ## Author: TT <Teresa.Twaroch@ci.tuwien.ac.at> |
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29 ## Description: PDF of the Gamma distribution |
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30 |
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31 function pdf = gampdf (x, a, b) |
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32 |
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33 if (nargin != 3) |
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34 usage ("gampdf (x, a, b)"); |
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35 endif |
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36 |
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37 if (!isscalar (a) || !isscalar(b)) |
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38 [retval, x, a, b] = common_size (x, a, b); |
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39 if (retval > 0) |
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40 error ("gampdf: x, a and b must be of common size or scalars"); |
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41 endif |
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42 endif |
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43 |
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44 sz = size(x); |
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45 pdf = zeros (sz); |
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46 |
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47 k = find (!(a > 0) | !(b > 0) | isnan (x)); |
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48 if (any (k)) |
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49 pdf (k) = NaN; |
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50 endif |
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51 |
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52 k = find ((x > 0) & (a > 0) & (a <= 1) & (b > 0)); |
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53 if (any (k)) |
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54 if (isscalar(a) && isscalar(b)) |
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55 pdf(k) = ((b .^ a) .* (x(k) .^ (a - 1)) |
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56 .* exp(-b .* x(k)) ./ gamma (a)); |
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57 else |
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58 pdf(k) = ((b(k) .^ a(k)) .* (x(k) .^ (a(k) - 1)) |
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59 .* exp(-b(k) .* x(k)) ./ gamma (a(k))); |
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60 endif |
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61 endif |
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62 |
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63 k = find ((x > 0) & (a > 1) & (b > 0)); |
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64 if (any (k)) |
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65 if (isscalar(a) && isscalar(b)) |
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66 pdf(k) = exp (a .* log (b) + (a-1) .* log (x(k)) |
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67 - b .* x(k) - gammaln (a)); |
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68 else |
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69 pdf(k) = exp (a(k) .* log (b(k)) + (a(k)-1) .* log (x(k)) |
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70 - b(k) .* x(k) - gammaln (a(k))); |
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71 endif |
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72 endif |
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73 |
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74 endfunction |
