Plotting a joint density function using DAD and the free software GnuPlot

1. Use DAD and launch the application Distribution => Joint density function
2. Select the appropriate vectors (in this example X: Gross income, Y: Net income)
3. Click on the button RANGE and choose:
• min and max of x and y
• the number of partitions of x and y: example : if min_x=0, max_x=100, # of partions =5: we have the x values {0,20,40,60,80,100}

4. Click on the button graph
5. Choose where you would like to save the ASCII files of the graph coordinates. This data will have the appropriate format to be used with GnuPlot to draw the 3D graph.

ASCII format

0.0 0.0 4.3596391219107303E-10
0.0 2000.0 5.163158311939581E-10
0.0 4000.0 5.891313258199563E-10
0.0 6000.0 6.476806317153927E-10
0.0 8000.0 6.86080129056403E-10
0.0 10000.0 7.002655982746375E-10
0.0 12000.0 6.88704414202037E-10
0.0 14000.0 6.526731803306815E-10
0.0 16000.0 5.960298892786326E-10
0.0 18000.0 5.245357512644426E-10
0.0 20000.0 4.4489129805950077E-10
0.0 22000.0 3.6371010005821217E-10
0.0 24000.0 2.8664615795719816E-10
0.0 26000.0 2.178262384684533E-10
0.0 28000.0 1.5964303084639936E-10
0.0 30000.0 1.1287221027596754E-10
0.0 32000.0 7.701275915731387E-11
0.0 34000.0 5.072690368766997E-11
0.0 36000.0 3.2269788845388605E-11
0.0 38000.0 1.983533648806619E-11
0.0 40000.0 1.1786781054602485E-11

2000.0 0.0 4.668565107490192E-10
2000.0 2000.0 5.556559994590353E-10
2000.0 4000.0 6.372835960909553E-10
2000.0 6000.0 7.043520426273741E-10
2000.0 8000.0 7.502371736355579E-10
2000.0 10000.0 7.70156910997408E-10
etc...

6. Launch the free package GnuPlot  (v 4.0)

7. type the following commands:

# To set the Graph title
set title "Joint density function: Canada 1994"

# To set the X axis title
set xlabel "Gross income"

# To set the Y title
set ylabel "Net axis income"

# No hide the legends
unset key

# To set the tocs level at 0
set ticslevel 0

# To plot the 3D graph
splot "c:/data_graphs/graph1.dat" using 1:2:3 with lines 1
 

# drawing with palette-mapped
set pm3d
splot "dat3d.dat" using 1:2:3 with lines 1

Another example with a higher number of partitions

Remarks : You can change some options for the plotted graph. For this, click on the left button of the mouse when the cursor is on the top panel and select the item Options. You can also rotate the graph by pressing the right button of the mouse and at the same time moving the cursor to the desired direction.