QUANTILE AND PROBABILITY PLOTS PAUL HOBSON GEOSYNTEC CONSULTANTS PDX DATA VISUALIZATION 2017-02-09 

BASICS WAYS TO VISUALIZE THE DISTRIBUTION OF A SAMPLE ▸Histogram ▸Boxplot ▸KDE/Violin Plot ▸Swarmplot ▸Quantile/Probability Plots 

COMPUTING PLOTTING POSITIONS HOW TO MAKE A PERCENTILE PLOT ▸ Sort your data ▸ Compute the ranks and plotting positions ▸ Create a scatter plot of the plotting positions vs. value Alpha and Beta independently range from 0 to 1 and are selected based on the applications. 

JUST SOME PSEUDORANDOM DATA SOME MIGHT CALL THIS A PERCENTILE PLOT 

QUANTILE PLOTS HOW TO MAKE A QUANTILE PLOT ▸ Pick a distribution for your data or use N(0, 1) ▸ Use the plotting positions from the percentile plot to compute the quantiles with the distribution’s percent- point function (inverse of the CDF) ▸ Linearity of a quantile plot is a suggests that your data might fit that distribution scipy.stats.norm.ppf(positions) [ -1.65285363, -1.12098304, -0.79566030, -0.53859848, -0.31323996, -0.10291203, 0.10291203, 0.31323996, 0.53859848, 0.79566030, 1.12098304, 1.65285363] 

QUANTILE PLOTS DON’T HAVE TO USE A STANDARD NORMAL DISTRIBUTION dist = scipy.stats.norm(5, 2.5) # <- theoretical distribution dist.ppf(positions) [ 0.86786592 2.1975424 3.01084925 3.65350379 4.2169001 4.74271992 5.25728008 5.7830999 6.34649621 6.98915075 7.8024576 9.13213408] 

QUANTILE PLOTS LOOK AGAIN AT A STANDARD NORMAL QUANTILE PLOT 

FINALLY PROBABILITY PLOTS ▸ Preserve the shape of the quantile plots ▸ Provide a readable probability axis 

PROBABILITY SCALES ASYMPTOTICALLY APPROACH ZERO & ONE fig, ax = pyplot.subplots(figsize=(3, 10)) ax.set_yticks([]) ax.set_xscale('prob') ax.set_xlim(0.01, 99.99) seaborn.despine(fig=fig, left=True) 

PROBABILITY SCALES MPL-PROBSCALE ▸ Legit probability scales for matplotlib ▸ Similar to a quantile plot, but expressed as a probability instead of a z- score ▸ Simply import probscale and you’re set ▸ Uses MPL’s scale and transform APIs to implement and register the scale with MPL’s internals. ▸ Distribution agnostic. ▸ Format tick labels as percents or fractions (0 - 1) ▸ GET IT! $ conda install mpl-probscale --channel=conda-forge 

PROBABILITY SCALES MPL-PROBSCALE import probscale ax1.set_xscale('prob') ax1.set_xlim(left=2, right=98) ax1.set_xlabel('Normal scale') ax2.set_xscale('prob', dist=beta(a=3, b=2)) ax2.set_xlim(left=2, right=98) ax2.set_xlabel('Beta scale (α=3, β=2)') 

PROBABILITY PLOTS MPL-PROBSCALE ▸ Can fit linear regression in log- probability space ▸ Bootstrapped confidence intervals ▸ Top-level functions for easy plotting import probscale fig = probscale.probplot( data, ax=ax, # optional Axes plottype='prob', # or ‘qq’, 'pp' probax='y', # or 'x' problabel=ylabel, datascale='log', datalabel=xlabel, bestfit=True, estimate_ci=True ) 

MPL-PROBSCALE, ETC LINK DUMP ▸ Source code: https://github.com/matplotlib/mpl- probscale ▸ Docs: matplotlib.org/mpl-probscale/ ▸ Me ▸ https://twitter.com/pmhobson ▸ https://github.com/phobson 

DEMOS & QUESTIONS. Thank for having me, Meli!