importmatplotlib.pyplotaspltimportnumpyasnpfrommatplotlib.patchesimportPolygon# Fixing random state for reproducibilitynp.random.seed(19680801)# fake up some dataspread=np.random.rand(50)*100center=np.ones(25)*50flier_high=np.random.rand(10)*100+100flier_low=np.random.rand(10)*-100data=np.concatenate((spread,center,flier_high,flier_low))fig,axs=plt.subplots(2,3)# basic plotaxs[0,0].boxplot(data)axs[0,0].set_title('basic plot')# notched plotaxs[0,1].boxplot(data,notch=True)axs[0,1].set_title('notched plot')# change outlier point symbolsaxs[0,2].boxplot(data,sym='gD')axs[0,2].set_title('change outlier\npoint symbols')# don't show outlier pointsaxs[1,0].boxplot(data,sym='')axs[1,0].set_title("don't show\noutlier points")# horizontal boxesaxs[1,1].boxplot(data,sym='rs',orientation='horizontal')axs[1,1].set_title('horizontal boxes')# change whisker lengthaxs[1,2].boxplot(data,sym='rs',orientation='horizontal',whis=0.75)axs[1,2].set_title('change whisker length')fig.subplots_adjust(left=0.08,right=0.98,bottom=0.05,top=0.9,hspace=0.4,wspace=0.3)# fake up some more dataspread=np.random.rand(50)*100center=np.ones(25)*40flier_high=np.random.rand(10)*100+100flier_low=np.random.rand(10)*-100d2=np.concatenate((spread,center,flier_high,flier_low))# Making a 2-D array only works if all the columns are the# same length.  If they are not, then use a list instead.# This is actually more efficient because boxplot converts# a 2-D array into a list of vectors internally anyway.data=[data,d2,d2[::2]]# Multiple box plots on one Axesfig,ax=plt.subplots()ax.boxplot(data)plt.show()

random_dists=['Normal(1, 1)','Lognormal(1, 1)','Exp(1)','Gumbel(6, 4)','Triangular(2, 9, 11)']N=500norm=np.random.normal(1,1,N)logn=np.random.lognormal(1,1,N)expo=np.random.exponential(1,N)gumb=np.random.gumbel(6,4,N)tria=np.random.triangular(2,9,11,N)# Generate some random indices that we'll use to resample the original data# arrays. For code brevity, just use the same random indices for each arraybootstrap_indices=np.random.randint(0,N,N)data=[norm,norm[bootstrap_indices],logn,logn[bootstrap_indices],expo,expo[bootstrap_indices],gumb,gumb[bootstrap_indices],tria,tria[bootstrap_indices],]fig,ax1=plt.subplots(figsize=(10,6))fig.canvas.manager.set_window_title('A Boxplot Example')fig.subplots_adjust(left=0.075,right=0.95,top=0.9,bottom=0.25)bp=ax1.boxplot(data,notch=False,sym='+',orientation='vertical',whis=1.5)plt.setp(bp['boxes'],color='black')plt.setp(bp['whiskers'],color='black')plt.setp(bp['fliers'],color='red',marker='+')# Add a horizontal grid to the plot, but make it very light in color# so we can use it for reading data values but not be distractingax1.yaxis.grid(True,linestyle='-',which='major',color='lightgrey',alpha=0.5)ax1.set(axisbelow=True,# Hide the grid behind plot objectstitle='Comparison of IID Bootstrap Resampling Across Five Distributions',xlabel='Distribution',ylabel='Value',)# Now fill the boxes with desired colorsbox_colors=['darkkhaki','royalblue']num_boxes=len(data)medians=np.empty(num_boxes)foriinrange(num_boxes):box=bp['boxes'][i]box_x=[]box_y=[]forjinrange(5):box_x.append(box.get_xdata()[j])box_y.append(box.get_ydata()[j])box_coords=np.column_stack([box_x,box_y])# Alternate between Dark Khaki and Royal Blueax1.add_patch(Polygon(box_coords,facecolor=box_colors[i%2]))# Now draw the median lines back over what we just filled inmed=bp['medians'][i]median_x=[]median_y=[]forjinrange(2):median_x.append(med.get_xdata()[j])median_y.append(med.get_ydata()[j])ax1.plot(median_x,median_y,'k')medians[i]=median_y[0]# Finally, overplot the sample averages, with horizontal alignment# in the center of each boxax1.plot(np.average(med.get_xdata()),np.average(data[i]),color='w',marker='*',markeredgecolor='k')# Set the axes ranges and axes labelsax1.set_xlim(0.5,num_boxes+0.5)top=40bottom=-5ax1.set_ylim(bottom,top)ax1.set_xticklabels(np.repeat(random_dists,2),rotation=45,fontsize=8)# Due to the Y-axis scale being different across samples, it can be# hard to compare differences in medians across the samples. Add upper# X-axis tick labels with the sample medians to aid in comparison# (just use two decimal places of precision)pos=np.arange(num_boxes)+1upper_labels=[str(round(s,2))forsinmedians]weights=['bold','semibold']fortick,labelinzip(range(num_boxes),ax1.get_xticklabels()):k=tick%2ax1.text(pos[tick],.95,upper_labels[tick],transform=ax1.get_xaxis_transform(),horizontalalignment='center',size='x-small',weight=weights[k],color=box_colors[k])# Finally, add a basic legendfig.text(0.80,0.08,f'{N} Random Numbers',backgroundcolor=box_colors[0],color='black',weight='roman',size='x-small')fig.text(0.80,0.045,'IID Bootstrap Resample',backgroundcolor=box_colors[1],color='white',weight='roman',size='x-small')fig.text(0.80,0.015,'*',color='white',backgroundcolor='silver',weight='roman',size='medium')fig.text(0.815,0.013,' Average Value',color='black',weight='roman',size='x-small')plt.show()

deffake_bootstrapper(n):"""    This is just a placeholder for the user's method of    bootstrapping the median and its confidence intervals.    Returns an arbitrary median and confidence interval packed into a tuple.    """ifn==1:med=0.1ci=(-0.25,0.25)else:med=0.2ci=(-0.35,0.50)returnmed,ciinc=0.1e1=np.random.normal(0,1,size=500)e2=np.random.normal(0,1,size=500)e3=np.random.normal(0,1+inc,size=500)e4=np.random.normal(0,1+2*inc,size=500)treatments=[e1,e2,e3,e4]med1,ci1=fake_bootstrapper(1)med2,ci2=fake_bootstrapper(2)medians=[None,None,med1,med2]conf_intervals=[None,None,ci1,ci2]fig,ax=plt.subplots()pos=np.arange(len(treatments))+1bp=ax.boxplot(treatments,sym='k+',positions=pos,notch=True,bootstrap=5000,usermedians=medians,conf_intervals=conf_intervals)ax.set_xlabel('treatment')ax.set_ylabel('response')plt.setp(bp['whiskers'],color='k',linestyle='-')plt.setp(bp['fliers'],markersize=3.0)plt.show()

x=np.linspace(-7,7,140)x=np.hstack([-25,x,25])fig,ax=plt.subplots()ax.boxplot([x,x],notch=True,capwidths=[0.01,0.2])plt.show()

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