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Plot conventional and reverse CDF on same plot by grouping variable

Apr 10, 2019 3:34 PM
(3088 views)

Hello,

Have a question on CDF plots on the distribution platform

I would like to plot the CDF of two variables say Y1 and Y2 which are on the same numerical scale but differ by the range/. For example Y1 from 0-100 and Y2 from 0 to 1000. I want to plot Y1like a regular CDF plot with the CumProb going from 0 to 1 and X1 values increasing from 0 to 100.

For Y2, I want the X2 to be in decreasing order from 1000 to 0 but the cumprob of Y2 runs from 0 to Y increasing in the Y axis direction.

I want to essentially reverse cdf(Y2) and overplot with cdf(Y1) and plot both on the same cdf plot window. Eventually I want to shade specific areas under the curves based on X1 and X2 values but before that I want to know how I could accomplish this task?

I started with getting the probability score and adding a column for 1-P(X2 > x) for Y2 but was little stuck on how I could get 1-P(X2>x) and P(X1<=x1) on the same X axis and was running around circles with how I could approach this in general. Any thoughts and pointers would be really helpful. I have 5 different categories of a grouping variable and do not mind having 5 different such cdf plots.

2 REPLIES 2

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Re: Plot conventional and reverse CDF on same plot by grouping variable

Attached is a script that I believe simulates your data setup and two methods to create the graph you described. One uses unstacked data ( two columns) and another with stacked data. If you are looking for rows where the Inv Prob of Y2 > Prob Y1 the unstacked (raw) data would be easier to use.

Note, Y1 and Y2 were simulated as uniform distributions.

```
Names Default to Here(1);
dt = New Table("Demo - Raw", Add rows(1000),
New Column("Y1", Numeric, Continuous, <<Set Each Value(Random Integer(0,100)) ),
New Column("Y2", Numeric, Continuous, <<Set Each Value(Random Integer(0,1000)) )
);
dist = dt << Distribution(
Continuous Distribution( Column( :Y1 ) ),
Continuous Distribution( Column( :Y2 ) )
);
dist << Save(Prob Scores);
dist << close window();
dt << New Column("Inv Prob Y2", numeric, continuous, <<Set Each Value(1-:Prob Y2));
//Using Unstacked data and GraphBuilder
gb = dt << Graph Builder(
Size( 534, 454 ),
Show Control Panel( 0 ),
Variables(
X( :Y1 ),
X( :Y2, Position( 1 ) ),
Y( :Prob Y1 ),
Y( :Inv Prob Y2, Position( 1 ) )
),
Elements(
Smoother( X( 1 ), Y( 1 ), Legend( 25 ) ),
Smoother( X( 2 ), Y( 2 ), Legend( 27 ) )
),
SendToReport(
Dispatch(
{},
"Y1",
ScaleBox,
{Min( -100 ), Max( 1100 ), Inc( 50 ), Minor Ticks( 1 ),
Label Row( {Show Major Grid( 1 ), Show Minor Grid( 1 )} )}
),
Dispatch(
{},
"Prob Y1",
ScaleBox,
{Min( -0.1 ), Max( 1.1 ), Inc( 0.1 ), Minor Ticks( 1 ),
Label Row( {Show Major Grid( 1 ), Show Minor Grid( 1 )} )}
)
)
);
//Sometimes it is easier to stack the data and use Bivariate instead of GraphBuilder
dtstck = dt << Stack(
columns( :Y1, :Y2, :Prob Y1, :Inv Prob Y2 ),
Source Label Column( "Label" ),
Stacked Data Column( "Data" ),
Stack By Row( 0 ),
Number of Series( 2 ),
Contiguous,
Output Table Name("Demo - Stacked")
);
dtstck:Data2 << set name("Prob");
//this creates one graph with 2 curves
biv = dtstck << Bivariate(
Y( :Prob ),
X( :Data ),
Group By(:Label),
Fit Each Value( {Report(0)}),
SendToReport(
Dispatch(
{},
"1",
ScaleBox,
{Min( -50 ), Max( 1050 ), Inc( 50 ), Minor Ticks( 1 ),
Label Row( {Show Major Grid( 1 ), Show Minor Grid( 1 )} )}
),
Dispatch(
{},
"2",
ScaleBox,
{Label Row( {Show Major Grid( 1 ), Show Minor Grid( 1 )} )}
),
Dispatch(
{},
"Bivar Plot",
FrameBox,
{Row Legend(
Label,
Color( 1 ),
Color Theme( "JMP Default" ),
Marker( 0 ),
Marker Theme( "" ),
Continuous Scale( 0 ),
Reverse Scale( 0 ),
Excluded Rows( 0 )
)}
)
)
);
```

Here are the two graphs:

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Re: Plot conventional and reverse CDF on same plot by grouping variable

I like Georgia's solution a lot. Here is a simpler and different approach: normalizing the two data sets before combining the plot. It might not be as satisfying.

I used two normal distributions with different parameters to illustrate this approach. You could save the fitted model for a distribution of sample data as a column formula instread of making up the data as I did. Here is the resulting plot:

I attached the data table that I made to produce this plot.

Learn it once, use it forever!