In [1]:

    

%matplotlib inline
from scipy.stats import binom
from numpy import array
from pandas import Series
from matplotlib.pyplot import figure, savefig, ylim, legend, gca, plot, bar
from matplotlib import rc
from seaborn import barplot
from matplotlib.ticker import FormatStrFormatter
rc('text', usetex=True)
rc('font', family='serif', serif='Times', size=20)


    

In [2]:

    

def f(n=20, p=0.5, k=13, tail='upper', error='I'):  
    y = Series( binom.pmf(range(n+1),n,p) )   
    figure( figsize=(12,5) )
    palette = ['gray']*(n+1)
    q = y
    
    if ( tail=='upper' or tail=='two'):
        plot([k-0.5]*2, [0,1], linestyle='--', color='black')
        gca().annotate( 'Rifiuto', 
                    xy=(0.66, 0.9),  
                    color='red', 
                    xycoords='axes fraction' )
        
    if ( tail=='lower' or tail=='two' ):
        plot([n-k+0.5]*2, [0,1], linestyle='--', color='black') 
        gca().annotate( 'Rifiuto', 
                        xy=(0.33, 0.9),  
                        color='red', 
                        horizontalalignment='right', 
                        xycoords='axes fraction' )
    
    palette = ['gray'] * len(y)
    palette = ['red' if (tail=='lower' and i <=n-k )            else palette[i] for i in range(len(y))]
    palette = ['red' if (tail=='upper' and i >= k  )            else palette[i] for i in range(len(y))]
    palette = ['red' if (tail=='two'   and (i <=n-k or i >= k)) else palette[i] for i in range(len(y))]
    if (error=='II'):
        palette = ['blue' if (palette[i]== 'gray') else 'gray' for i in range(len(y))]
        
    q = [0 if (palette[i]=='gray') else y[i] for i in range(len(y))] 
    
    if (error=='I'):
        gca().annotate(r'$\alpha= P(T_+|H_0)\ \simeq\ ${:.2f}'.format(sum(q)), 
                       xy=(0.98,0.25), 
                       color='red', 
                       horizontalalignment='right', 
                       xycoords='axes fraction')
    if (error=='II'):
        if (p>0.5): 
            gca().annotate(r'$\beta=P(T_-|H_3 _/ _4)\ \simeq\ ${:.2f}'.format(sum(q)),
                    color='blue',  
                    xy=(0.02,0.25), 
                    horizontalalignment='left', 
                    xycoords='axes fraction') 
        else:
            gca().annotate(r'$\beta=P(T_-|H_1 _/ _4)\ \simeq\ ${:.2f}'.format(sum(q)),
                    color='blue',  
                    xy=(0.98,0.25), 
                    horizontalalignment='right',
                    xycoords='axes fraction')          
    gca().annotate( '$n={}$\n $p={}$'.format(n,p), 
                    xy=(0.02, 0.72), 
                    linespacing=1.8, 
                    xycoords='axes fraction' )
    gca().annotate( 'Non Rifiuto', xy=(0.5, 0.9), 
                    horizontalalignment='center', 
                    xycoords='axes fraction' )
    return y, palette, sum(q)


    

In [3]:

    

n=20; k=13; p=0.5
y, palette, q = f(n=n, k=k, p=p,  tail='upper', error='I')
ylim(0, 0.25)

barplot(x=y.index, y=y, palette=palette)
savefig('B-test_01.pdf',bbox_inches='tight')


    

In [4]:

    

n=20; k=13; p=0.75
y, palette, q = f(n=n, k=k, p=p,  tail='upper', error='II')   
ylim( 0, 0.25 )

barplot(x=y.index, y=y, palette=palette)
savefig('B-test_02.pdf',bbox_inches='tight')


    

In [5]:

    

n=20; k=13; p=0.25
y, palette, q = f(n=n, k=k, p=p,  tail='upper', error='II')  
ylim( 0, 0.25 )  

barplot(x=y.index, y=y, palette=palette)
savefig('B-test_03.pdf',bbox_inches='tight')


    

In [6]:

    

n=20; k=13; p=0.5
y, palette, q = f(n=n, k=k, p=p,  tail='two', error='I')   
ylim(0, 0.25)

barplot(x=y.index, y=y, palette=palette)
savefig('B-test_04.pdf',bbox_inches='tight')


    

In [7]:

    

n=20; k=13; p=0.75
y, palette, q = f(n=n, k=k, p=p,  tail='two', error='II')   
ylim(0, 0.25)

barplot(x=y.index, y=y, palette=palette)
savefig('B-test_05.pdf',bbox_inches='tight')


    

In [8]:

    

n=20; k=13; p=0.25
y, palette, q = f(n=n, k=k, p=p,  tail='two', error='II')   
ylim(0, 0.25)

barplot(x=y.index, y=y, palette=palette)
savefig('B-test_06.pdf',bbox_inches='tight')


    

In [9]:

    

n=40; k=26; p=0.5
y, palette, q = f(n=n, k=k, p=p,  tail='two', error='I')  
ylim(0, 0.20)

barplot(x=y.index, y=y, palette=palette)
savefig( 'B-test_07.pdf', bbox_inches='tight' )


    

In [10]:

    

n=40; k=26; p=0.75
y, palette, q = f(n=n, k=k, p=p,  tail='two', error='II')  
ylim(0, 0.20)

barplot(x=y.index, y=y, palette=palette)
savefig( 'B-test_08.pdf', bbox_inches='tight' )


    

In [11]:

    

n=40; k=26; p=0.25
y, palette, q = f(n=n, k=k, p=p,  tail='two', error='II')
ylim(0, 0.20)

barplot(x=y.index, y=y, palette=palette)
savefig( 'B-test_09.pdf', bbox_inches='tight' )