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# dist2dpdf2

## PURPOSE

Joint 2D PDF computed as f(x1|X2=x2)*f(x2)

## SYNOPSIS

y = dist2dpdf2(v1,h1,phat)

## DESCRIPTION

``` DIST2DPDF2 Joint 2D PDF computed as f(x1|X2=x2)*f(x2)

CALL:  f = dist2dpdf2(x1,x2,phat);

f  = PDF struct with the following fields:
f = PDF evaluated at meshgrid(x1,x2)
x = {x1,x2} (i.e., cellarray containing x1 and x2)
x1,x2  = vectors of evaluation points
phat = structure array containing
x    = cellarray of distribution parameters
dist = cellarray of strings defining the distributions of
X2 and X1 given X2, respectively. Options are:
'tgumbel', 'gumbel', 'lognormal','rayleigh','weibull',
and 'gamma'.

DIST2DPDF2 evaluates f{x1|X2=x2 }*f{x2}.
The parameter(s) of the unconditional distribution of X2,
f{x2}, must be in in phat.x{2}. The parameters of the conditional
distribution of X1 given X2 must be in phat.x{1}. The first column
in phat.x{1} contains the X2 values the parameters in column 2 and 3 are
conditioned on.

Example: 2D Rayleigh
x1=linspace(0,10)';
phat.x={[x1,2*ones(size(x1))] 2 };
phat.dist={'rayl','rayl'};
f = dist2dpdf2(x1,x1,phat);
pdfplot(f);

## CROSS-REFERENCE INFORMATION

This function calls:
 createpdf PDF class constructor dist2dpdf Joint 2D PDF computed as f(x1|X2=x2)*f(x2) qlevels Calculates quantile levels which encloses P% of PDF error Display message and abort function. meshgrid X and Y arrays for 3-D plots.
This function is called by:
 dist2dsmfun2 Smooths the conditional DIST2D distribution parameters. recinit setup all global variables of the RECDEMO

## SOURCE CODE

```001 function y = dist2dpdf2(v1,h1,phat)
002 %DIST2DPDF2 Joint 2D PDF computed as f(x1|X2=x2)*f(x2)
003 %
004 %  CALL:  f = dist2dpdf2(x1,x2,phat);
005 %
006 %      f  = PDF struct with the following fields:
007 %           f = PDF evaluated at meshgrid(x1,x2)
008 %        x = {x1,x2} (i.e., cellarray containing x1 and x2)
009 %  x1,x2  = vectors of evaluation points
010 %    phat = structure array containing
011 %            x    = cellarray of distribution parameters
012 %            dist = cellarray of strings defining the distributions of
013 %                   X2 and X1 given X2, respectively. Options are:
014 %                   'tgumbel', 'gumbel', 'lognormal','rayleigh','weibull',
015 %                   and 'gamma'.
016 %
017 %  DIST2DPDF2 evaluates f{x1|X2=x2 }*f{x2}.
018 %   The parameter(s) of the unconditional distribution of X2,
019 %   f{x2}, must be in in phat.x{2}. The parameters of the conditional
020 %   distribution of X1 given X2 must be in phat.x{1}. The first column
021 %   in phat.x{1} contains the X2 values the parameters in column 2 and 3 are
022 %   conditioned on.
023 %
024 % Example: 2D Rayleigh
025 %    x1=linspace(0,10)';
026 %    phat.x={[x1,2*ones(size(x1))] 2 };
027 %    phat.dist={'rayl','rayl'};
028 %    f = dist2dpdf2(x1,x1,phat);
029 %    pdfplot(f);
030 %
032
033 %tested on: matlab 5.2
034 % history:
035 %  Per A. Brodtkorb 28.10.98
036
037 error(nargchk(3,3,nargin))
038
039 y=createpdf(2);
040 [X1 X2]=meshgrid(v1,h1);
041 y.f=  dist2dpdf(X1,X2,phat);
042 y.x{1}=v1(:);
043 y.x{2}=h1(:);
044 %contour(v1,h1,y.f)
045 %y.f(isinf(y.f)|isnan(y.f))=0;
046 try
047   [y.cl y.pl]=qlevels(y.f);
048 catch
049   y.cl=[];
050   y.pl=[];
051 end
052 y.phat=phat;
053
054
055```

Mathematical Statistics
Centre for Mathematical Sciences
Lund University with Lund Institute of Technology

Comments or corrections to the WAFO group

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