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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 intervals =[[-2.0,-1.1],[-1.0,-0.6],[-0.5,-0.1],[0.0,0.4],[0.5,0.9],[1.0,1.4],
       [1.5,1.9],[2.0,2.4],[2.5,2.9],[3.0,3.4],[3.5,3.9],[4.0,5.0]]
Step1:  bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])
orig_hist = np.array(h).astype(float)
norm_hist = orig_hist/float(sum(orig_hist))
mid_points = (bins[1
Step2:  h = df.iloc[10,mask]
bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])
orig_hist = np.array(h).astype(float)
norm_hist = orig_hist/float(sum(orig_hist))
mid_points = (bins[1
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Python Code:
def fit_normal_to_hist(h):
    if not all(h==0):
        bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])  
        orig_hist = np.array(h).astype(float)
        norm_hist = orig_hist/float(sum(orig_hist))
        mid_points = (bins[1:] + bins[:-1])/2
        popt,pcov = opt.curve_fit(lambda x,mu,sig: stats.norm.pdf(x,mu,sig), mid_points,norm_hist)
    else:
        popt = [float('nan'),float('nan')]
    return popt[1]
def ZL_std(h):
    intervals =[[-2.0,-1.1],[-1.0,-0.6],[-0.5,-0.1],[0.0,0.4],[0.5,0.9],[1.0,1.4],
           [1.5,1.9],[2.0,2.4],[2.5,2.9],[3.0,3.4],[3.5,3.9],[4.0,5.0]]
    if not all(h==0):
        sum_i1 = 0
        sum_i2 = 0
        for i in range(1,len(h)):
            p = h[i]/100
            v1,v2 = intervals[i]
            sum_i1 += p*(v2**3 - v1**3)/(3*(v2-v1))
            sum_i2 += p*(v2**2 - v1**2)/(2*(v2-v1))
            zl_std = np.sqrt(sum_i1 - sum_i2**2)
    else:
            zl_std = float('nan')    
    return zl_std
def Hist_std(h):
    if not all(h==0):
        bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])  
        orig_hist = np.array(h).astype(float)
        norm_hist = orig_hist/float(sum(orig_hist))
        mid_points = (bins[1:] + bins[:-1])/2
        MeanCrude = np.dot(norm_hist,mid_points)
        VarCrude  = np.dot(norm_hist,(mid_points-MeanCrude)**2)
        bin_widths = np.diff(bins)
        BinWidth = bin_widths.mean()
        VarSheppard = VarCrude - (BinWidth**2)/12       #variance, Sheppard's correction
        hist_std = np.sqrt(VarSheppard)
    else:
        hist_std = float('nan')
    return hist_std  
Explanation: intervals =[[-2.0,-1.1],[-1.0,-0.6],[-0.5,-0.1],[0.0,0.4],[0.5,0.9],[1.0,1.4],
       [1.5,1.9],[2.0,2.4],[2.5,2.9],[3.0,3.4],[3.5,3.9],[4.0,5.0]]
End of explanation
mask = df.columns.str.contains(',')
mask
df.columns[mask]
Explanation: bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])
orig_hist = np.array(h).astype(float)
norm_hist = orig_hist/float(sum(orig_hist))
mid_points = (bins[1:] + bins[:-1])/2
bin_widths = np.diff(bins)
MeanCrude = np.dot(norm_hist,mid_points)
MeanCrude
VarCrude  = np.dot(norm_hist,(mid_points-MeanCrude)**2)
VarCrude
total = 0
for i in range(0,len(norm_hist)):
    total += norm_hist[i]*mid_points[i]
total    
for i in range(0,len(norm_hist)):
    tt[i] = (mid_points[i] - MeanCrude)**2
tt    
VarSheppard = VarCrude - (BinWidth**2)/12
VarSheppard
MeanCrude = sum(Prob . CatMid);                    %crude mean and variance
VarCrude  = sum(Prob . (CatMid-MeanCrude).^2);
BinWidth    = mean(diff(CatBounds(:)));
VarSheppard = VarCrude - BinWidth^2/12;       %variance, Sheppard's correction
def Entr(h):
    if not all(h==0):
        bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])
        orig_hist = np.array(h).astype(float)
        norm_hist = orig_hist/float(sum(orig_hist))     
        bin_widths = np.diff(bins)
    np.dot(h,np.log(h/bin_widths))
    bin_density = h.astype(float) / np.dot(bin_widths, h)
    popt
else:
    popt = [float('nan'),float('nan')]
return popt[1]
End of explanation
df['GA_std'] = df.iloc[:,mask].apply(fit_normal_to_hist,axis=1)
df['ZL_std'] = df.iloc[:,mask].apply(ZL_std,axis=1)
df['Hist_std'] = df.iloc[:,mask].apply(Hist_std,axis=1)
df.head(10)
dfList = []
writer = pd.ExcelWriter(out_data + 'PointForecasts.xlsx')
years = [2014,2015,2016]
quarters = [1,2,3,4]
for year in years:
    for q in quarters:
        f = str(year) + 'Q' + str(q)
        fname = f + '.csv'
        if os.path.isfile(raw_data_path + '\\' + fname):
            raw_df = pd.read_csv(raw_data_path + '\\' + fname,header = True)
            # find the row where the growth expectations start
            dum = raw_df[raw_df['TARGET_PERIOD'] == 'GROWTH EXPECTATIONS; YEAR-ON-YEAR CHANGE IN REAL GDP'].index[0]
            mask_columns = ~raw_df.columns.str.contains('Unnamed')
            df = raw_df.iloc[0:dum-1,[0,1,2]]    
            df['source'] = str(year) + '-Q' + str(q)
            df = df.rename(columns={'TARGET_PERIOD':'target','FCT_SOURCE':'id','POINT':'point'})
            df = df[['source','target','id','point']]
            df['id'] = df['id'].astype('int')
            df['point'] = df['point'].astype('float32')
            df.to_excel(writer,f,index=False)
            dfList.append(df)  
writer.save()      
Explanation: h = df.iloc[10,mask]
bins =np.array([-2.0,-1.0,-0.5,0.0,0.5,1.0,1.5,2.0,2.5,3.0,3.5,4.0,5.0])
orig_hist = np.array(h).astype(float)
norm_hist = orig_hist/float(sum(orig_hist))
mid_points = (bins[1:] + bins[:-1])/2
popt,pcov = opt.curve_fit(lambda x,mu,sig: stats.norm.pdf(x,mu,sig), mid_points,norm_hist)
popt
for i in range(0,10):
    print(i,fit_normal_to_hist(df.iloc[i,mask].astype(float)))
End of explanation
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