Custom Grid Lines for ProbabilityScalePlot

Question

I'm plotting up some data using a ProbabilityScalePlot in Mathematica 8. It currently looks like so:

Code:

ProbabilityScalePlot[data, "Normal", AspectRatio -> 0.9, Frame -> True, 
    GridLines -> Automatic, GridLinesStyle -> LightGray, Axes -> False, 
    LabelStyle -> font, 
    PlotStyle -> Directive[PointSize -> Large, Thick, Purple], 
    FrameLabel -> {"Value", "Cum. Prob."}, ImageSize -> 250]

I'd like to change the y grid lines to only show up on the ticks {1, 5, 10, 25, 50, 75, 90, 95, 99} but when I change GridLines -> Automatic to GridLines -> {Automatic,Ticks} I get an error.

The error is "A GridLines specification should be None, Automatic, or a list of grid line specifications."

What's odd is that doing the same thing on a different style plot, Histogram for example, works just fine.

Is this a quirk of ProbabilityScalePlot or am I missing something?

If I simplify the input to it's bare-bones (and change the data, sorry):

ProbabilityScalePlot[data, "Normal", GridLines -> {Automatic, Automatic}]

and then look at the GridLines part of InputForm (formatted and comments added to hopefully make it easier to read):

GridLines ->
    {
     (* X-axis *)
     Charting`ScaledTickValues[
       {#1 & , #1 & },
       Charting`ScaledTickValues[{#1 & , #1 & }][##1]
     ] & ,

     (* Y-axis *)
     Charting`ScaledTickValues[
       {1 + SpecialFunctions`Probit[#1] & ,
        (1*Erfc[(1*(Sqrt[2.] - Sqrt[2.]*#1))/2.])/2. &
       },
       Charting`ScaledTickValues[{#1*0.01 & , #1 & }][##1]
     ] &
    }

It appears that it's correctly assigning something to the x and y axis, but based on the error I assume that it's not evaluating to a list of numbers or grid line specifications. Sadly that InputForm is a bit too complicated for me to read fully, but I can tell that it's using the Z-score of the data point as the actual grid lines or tick marks, but then transforming it to cumulative probability when displaying the y-axis.

Answer 1

A problem still exists with the scaling of grid lines in version 10.0.2. I'll try to explore this later if I have time but for now here is a work-around. Specify the horizontal lines in the plot command and the vertical lines in Show, then combine with Overlay.

gr = ProbabilityScalePlot[data, "Normal", GridLines -> {None, {1, 5, 50, 95, 99}}];

Overlay[{
  gr,
  Show[gr, GridLines -> {{-2, -1, 1, 2, 3}, None}]
}]

As a for-your-information example one must realize that the actual y scale of the Graphics is not what the plot shows:

Show[gr, FrameTicks -> Automatic]

The actual plot range is revealed with;

PlotRange[gr]  (* undocumented usage *)

{{-4.38919, 5.86036}, {-1.4587, 3.4587}}

Answer 2

Looks like it's a bug:

After more research and test cases, it appears that this is a bug in Mathematica 8. I have no way of checking older or newer versions. Perhaps someone could execute the following test case code and verify?

In Mathematica 8:

The GridLines->{x, y} option of ProbabilityScalePlot does not work as expected under the following circumstances:

+-------------------------------+--------------------------------+
|                               | X GridLine spec has value <= 0 |
+                               +--------------------------------+
|                               |   True       |  False          |
+-------------------------------+--------------+-----------------+
| One or Both GridLine  |  True | No gridlines | Error           |
| specs are "Automatic" |       | displayed;   |                 |
|                       |       | No Error     |                 |
|                       +-------+--------------+-----------------+
|                       | False | No gridlines | OK              |
|                       |       | displayed;   |                 |
|                       |       | No Error     |                 |
+-----------------------+-------+--------------+-----------------+

Go ahead and try out the following Test Cases and see what you get:

First, generate some data from the Normal distribution. The data should have both positive and negative values in order to really see where things freak out.

data = RandomVariate[NormalDistribution[0, 2], 100];

These result in an error:

ProbabilityScalePlot[data, "Normal", GridLines -> {Automatic, Automatic}]
ProbabilityScalePlot[data, "Normal", GridLines -> {Automatic, {1, 2, 3}}]
ProbabilityScalePlot[data, "Normal", GridLines -> {{1, 2, 3}, Automatic}]

These result in no gridlines being displayed and no error thrown:

ProbabilityScalePlot[data, "Normal", GridLines -> {{0, 1, 2, 3}, {1, 5, 50, 95, 99}}]
ProbabilityScalePlot[data, "Normal", GridLines -> {{-1, 1, 2, 3}, {1, 5, 50, 95, 99}}]
ProbabilityScalePlot[data, "Normal", GridLines -> {{0, 1, 2, 3}, Automatic}]

And these test cases work as expected:

ProbabilityScalePlot[data, "Normal", GridLines -> Automatic]
ProbabilityScalePlot[data, "Normal", GridLines -> {None, {1, 5, 50, 95, 99}}]
ProbabilityScalePlot[data, "Normal", GridLines -> {{1, 2, 3}, {10, 50, 95, 99}}]

Answer 3

ProbabilityScalePlot uses FrameTicks.

data = RandomVariate[NormalDistribution[1, 2], 100];
ProbabilityScalePlot[data, "Normal", 
FrameTicks -> {{Automatic, None}, {Range[-3, 4, .5], None}}]

So if you want to choose your x-axis ticks (here, between -4 and 4 in steps of 0.5), then make the ticks go across the figure in this way:

ProbabilityScalePlot[data, "Normal", 
 FrameTicks -> {Table[{x, x, {.5, 0}}, {x, -4, 4, .5}], Automatic}]