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Normal Probability Plot

Normal Probability Plot
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2015-02-10 10:47
FunctionProbability & StatisticsTransformation
This applet demonstrates the relationship between a cumulative distribution function (CDF) plot and a probability plot. It smoothly animates the vertical quantile scale of a CDF plot into a probability plot. Key mathematical concepts include normal distribution in probability and statistics. Construction highlights the use of GeoGebra commands such as Sequence, Normal, Sort, Translate, etc. Suitable for teaching and learning probability and statistics.

GeoGebra Commands & Parameters

  1. Sequence(RandomUniform[0, 10], i, 1, 19) → dataunif
  2. Sequence(10 - InverseChiSquared[3, RandomUniform[0, 1]], i, 1, 19) → dataleft
  3. Sequence(RandomNormal[5, 2], i, 1, 19) → datanorm
  4. Sequence(InverseChiSquared[3, RandomUniform[0, 1]], i, 1, 19) → dataright
  5. Normal(0.5, 1 / ((2 * InverseNormal[0, 1, scalept])), x) → normf
  6. Sort(If[skewleft, dataleft, If[skewright, dataright, If[norm, datanorm, dataunif]]]) → data
  7. Translate(Rotate[Sequence[(xx, (2 * normf(xx))), xx, -3, 3, 0.05], 1.5708], (axescross - normoffset, 0)) → normpdfpoints
  8. Mean(data) → xbar
  9. SampleSD(data) → s
  10. If(probscale, t2, 1 - t2) → t
  11. Sequence((0.05 * i), i, 0, 20) → ycoords1
  12. Zip(If[yy ≟ 0, -3, If[yy ≟ 1, 3, InverseNormal[0, 1, yy] / ((2 * InverseNormal[0, 1, scalept])) + 0.5]], yy, ycoords1) → ycoords2
  13. Zip(((1 - t) * aa) + (t * bb), aa, ycoords1, bb, ycoords2) → ycoords
  14. Sequence((Element[data, i], Element[ycoords, i + 2]), i, 1, 9) → altPoints
  15. Join(Sequence[{(Element[data, i], Element[ycoords, i + 1]), (Element[data, i + 1], Element[ycoords, i + 1])}, i, 1, 19]) → ogivePoints
  16. PolyLine(ogivePoints) → ogive
  17. Zip(((1 - t) * yy) + (t * (InverseNormal[0, 1, yy] / ((2 * InverseNormal[0, 1, scalept])) + 0.5)), yy, Sequence[(0.1 * i) + 0.05, i, 0, 9]) → altycoords
  18. Polygon({Corner[2], Corner[3], (x(Corner[3]) - (x(Corner[3]) - x(Corner[4])) / 5.5, y(Corner[3])), (x(Corner[2]) - (x(Corner[2]) - x(Corner[1])) / 5.5, y(Corner[2]))}) → filler
  19. Line(normlineP1, normlineP2) → normdragline
  20. Polygon(Join[{KeepIf[y(P) < y(normlineP1), P, normpdfpoints], {(axescross - (2 * normf(y(normlineP1))) - normoffset, y(normlineP1)), (axescross - normoffset, y(normlineP1))}}]) → normarea
  21. PolyLine(normpdfpoints) → normpdf
  22. Segment((0, -0.27), (0, -0.23)) → zerotick
  23. Sequence((Element[data, i], Element[ycoords, i + 1]), i, 1, 19) → dataPoints
  24. Sequence(Ray[(axescross, Element[ycoords, i]), (1, Element[ycoords, i])], i, 1, 21, 2) → gridlines
  25. Sequence(Text[zz, (axescross - normoffset + 0.06, zz / ((2 * InverseNormal[0, 1, scalept])) + 0.49)], zz, -3, 3) → zlabels
  26. Segment((axescross - normoffset, y(normlineP1)), (axescross, y(normlineP1))) → normsegment
  27. Sequence(Segment[(axescross - normoffset - 0.04, zz / ((2 * InverseNormal[0, 1, scalept])) + 0.5), (axescross - normoffset + 0.04, zz / ((2 * InverseNormal[0, 1, scalept])) + 0.5)], zz, -3, 3) → zticks
  28. Sequence(Segment[(axescross - 0.08, Element[ycoords, i]), (axescross + 0.08, Element[ycoords, i])], i, 1, 21, 2) → tickmarks
  29. Sequence(Text[Element[ycoords1, i], (axescross - 0.36, Element[ycoords, i] - 0.015)], i, 1, 21, 2) → ticklabels
  30. Zip(Segment[(axescross - 0.04, yy), (axescross + 0.04, yy)], yy, altycoords) → alttickmarks
  31. Textfield() → inputBox1

AI Drawing Prompt Reference

Draw a probability plot that illustrates the relationship between a cumulative distribution function (CDF) and a probability plot. The plot includes data points generated from uniform, inverse chi-squared, and standard normal distributions, arranged in order. A CDF curve is drawn, along with points that map the data to a probability plot. A standard normal probability density curve is added as reference. The figure also includes zero point markers, grid lines, and labels to annotate data points and curves. The overall graphic should clearly show the correspondence between the CDF curve and the probability plot points, suitable for teaching probability and statistics.
The prompt above was compiled from the original drawing commands and is for reference only.