def new_calculator(dic, x): # 計算新的標準差平均值
avg = dic["avg"]
std = dic["std"]
count = dic["count"]
n_count = count+1
if n_count == 1:
n_avg = round(x, 2)
n_std = None
elif n_count == 2:
n_avg = round((avg*count+x)/(count+1), 2)
n_std = round(statistics.sqrt((1/n_count)*(x-avg)**2), 2)
else:
n_avg = round((avg*count+x)/(count+1), 2)
n_std = round(statistics.sqrt(((n_count-2)/(n_count-1))*(std**2)+(1/n_count)*(x-avg)**2), 2)
return {"avg": n_avg, "std": n_std, "count": n_count}
def var_std(data) :
a = avg(data) # 산술평균
# list + for : (x - mu)**2
diff = [(x-a)**2 for x in data]
var = sum(diff) / (len(data) - 1) # 분산
std = sqrt(var) # 표준편차
return var, std
def calculate_mhp_feature(timestamp,x,y,z):
global mhp_buffer
if len(mhp_buffer['timestamp']) == buffer_size:
x_mhp = (x - statistics.mean(mhp_buffer['x']))**2
y_mhp = (y - statistics.mean(mhp_buffer['y']))**2
z_mhp = (z - statistics.mean(mhp_buffer['z']))**2
else:
x_mhp,y_mhp,z_mhp = 0,0,0
return statistics.sqrt(x_mhp+y_mhp+z_mhp)
def EVA(smb, n):
"""
smb: pass an arrary or series here
n : n=12 for monthly data; n=250 for daily data
"""
p = 0.99
name = [
"Annualized Mean", "t-statistics", "Annualized Volatility",
"Sharpe Ratio", "Skewness", "Excess Kurtosis",
"99%VaR(Cornish-Fisher)", "Annualized Downside Volatility",
"Sortino Ratio", "Maximum Drawdown", "Max.Draw. Length", "CER"
]
title = smb.name
#annualized mean
gm = (st.geometric_mean(smb + 1) - 1) * n
mu = st.mean(smb)
#annualized S.D.
sd = st.stdev(smb)
asd = st.sqrt(n) * st.stdev(smb)
#annualized Sharpe
sharpe = gm / asd
#skewness and kurtosis
skew = stats.skew(smb)
kurt = stats.kurtosis(smb)
#t-stats
tvalue = stats.ttest_1samp(smb, 0)[0]
#99% VaR-Cornish_Fisher
inter = stats.norm.isf(p)
zcf = inter + ((inter**2 - 1) * skew / 6) + (
(inter**3 - 3 * inter) * kurt / 24) - ((2 * inter**3 - 5 * inter) *
(skew**2) / 36)
VaR = mu + sd * zcf * (-1)
#downside volatility
nret = smb.loc[smb < 0]
dvola = st.stdev(nret) * st.sqrt(n)
#sortino
sortino = ((1 + mu)**n - 1) / dvola
#maxmium drawdown
uvi = (1 + smb).cumprod()
dif = np.maximum.accumulate(uvi) #return the largest value so far
draw = uvi / dif - 1
maxdraw = min(draw)
ddend = np.argmin(draw)
ddstart = np.argmax(uvi[:ddend])
ddlength = ddend - ddstart
#CER
cer = ((1 + smb)**(1 - 5) - 1) / (-4)
CER = st.mean(cer) * n
#Export
number = [
gm, tvalue, asd, sharpe, skew, kurt, VaR, dvola, sortino, maxdraw,
ddlength, CER
]
output = pd.DataFrame({'Stats': name, title: number})
print(output)
return (output)
function_table=FUNCTION_TABLE,
fit_function=fit_modulo_2,
inputs_num=INPUTS_NUM,
nodes_num=NODES_NUM,
outputs_num=OUTPUTS_NUM,
desired_fit=DESIRED_FIT,
generations_num=GENERATIONS_NUM,
mutation_prob=prob,
)
gens.append(solution.generation)
muts.append(solution.total_mutations)
# Store averages in respective lists
avg_gens.append(mean(gens))
avg_muts.append(mean(muts))
# Standard error is stdev/sqrt(N)
err_gens.append(stdev(gens) / sqrt(10))
err_muts.append(stdev(muts) / sqrt(10))
# Save data to a text file
with open(FILEDIR + '/data.txt', mode='w') as f:
for i, prob in enumerate(probabilities):
f.write(f'{prob} {avg_gens[i]} {err_gens[i]} ' +
f'{avg_muts[i]} {err_muts[i]}\n')
# Draw graphs with pyplot
_, ax1 = plt.subplots(figsize=(12, 5))
ax1.set_ylabel('Generations')
ax1.set_xlabel('Probability')
plt.errorbar(
probabilities,
avg_gens,
# we can see here:- # ['Counter', 'Decimal', 'Fraction', 'NormalDist', 'StatisticsError', '__all__', '__builtins__', # '__cached__', '__doc__', '__file__', '__loader__', '__name__', '__package__', '__spec__', '_coerce', # '_convert', '_exact_ratio', '_fail_neg', '_find_lteq', '_find_rteq', '_isfinite', '_normal_dist_inv_cdf', # '_ss', '_sum', 'bisect_left', 'bisect_right', 'erf', 'exp', 'fabs', 'fmean', 'fsum', 'geometric_mean', # 'groupby', 'harmonic_mean', 'hypot', 'itemgetter', 'log', 'math', 'mean', 'median', 'median_grouped', # 'median_high', 'median_low', 'mode', 'multimode', 'numbers', 'pstdev', 'pvariance', 'quantiles', 'random', # 'sqrt', 'stdev', 'tau', 'variance'] # lets discover some of the methods and attributes. a = [20, 20, 20, 23, 34, 40, 45, 56, 67, 67, 67, 77] # we can see we have exp, sqrt, log here. we also have the value of tau. print(stat.exp(45)) # it raises e to the power of the input print(stat.sqrt(90)) print(stat.log(100)) print(stat.tau) # here we have different types of mean such as mean, harmonic_mean, geometric_men, fmean. print(stat.mean(a)) print(stat.harmonic_mean(a)) # The harmonic mean, sometimes called the subcontrary mean, is the # reciprocal of the arithmetic mean of the reciprocals of the data, # and is often appropriate when averaging quantities which are rates # or ratios, for example speeds. Example: # Suppose an investor purchases an equal value of shares in each of # three companies, with P/E (price/earning) ratios of 2.5, 3 and 10. # What is the average P/E ratio for the investor's portfolio? # >>> harmonic_mean([2.5, 3, 10]) # For an equal investment portfolio. # 3.6
def calculateinterval(data):
l = 3.66
s = statistics.stdev(data)
n = len(data)
mean = statistics.mean(data)
return [mean - l*s/statistics.sqrt(n), mean + l*s/statistics.sqrt(n)]
# 변수 선택 x = data['cost'] x[:10] # 1. 대표값 x.mean() lst = x.to_list() # pandas 객체 -> list 객체로 lst st.mean(lst) st.mean(x) st.median(x) st.median_low(x) st.median_high(x) st.mode(x) x.value_counts() # 2. 산포도: 분산, 표준편차 var = st.variance(x) var std = st.stdev(x) std std2 = st.sqrt(var) std2
def cohend(mean1, mean2, array1, array2):
return abs(mean1 - mean2) / statistics.sqrt(
(numpy.std(array1)**2 + numpy.std(array2)**2) / 2)
import statistics import math agesData = [10, 13, 14, 12, 11, 10, 11, 10, 15] print(statistics.mean(agesData)) print(statistics.mode(agesData)) print(statistics.median(agesData)) print(statistics.variance(agesData)) print(statistics.stdev(agesData)) print(statistics.sqrt(statistics.variance(agesData)))
import math import statistics import cube abc = dir(statistics) #print(abc) print(statistics.sqrt(4)) cube.cube(2)
```
Let's try out the built-in **math** and **statistics** packages to do some calculating!
What is the mean of all the integers from 1 to 6?
"""
import statistics as stat
a_list = [1, 2, 3, 4, 5, 6]
stat.mean(a_list)
"""What is the standard deviation of the integers from 1 to 6?"""
stat.stdev(a_list)
"""What is the square root of 72?"""
stat.sqrt(72)
"""What is pi?"""
import math
pi = math.pi
print(pi)
"""What how many radians are in 360 degrees?"""
math.radians(360)
"""Can you find a package that might have functions for random numbers? Use it to generate a couple random numbers!"""
import random
for i in range(3):
random.randint(i + 1, 10)
"""Look for names of some more built-in packages online! Try importing them here."""
def update_event(self, inp=-1):
self.set_output_val(0, statistics.sqrt(self.input(0)))
rerata = statistics.mean(data)
print(f"rerata = ({' + '.join(f'{x}' for x in data)}) / {len(data)}")
print(f'rerata = {rerata}')
print('\n===== Hitung varian =====')
# varian = [(bilangan - rerata) ** 2 for bilangan in data]
# mode verbose
list_varian = []
for bilangan in data:
item = (bilangan - rerata)**2
list_varian.append(item)
print(f'({bilangan} - {rerata}) ^ 2 = {item}')
varian = sum(list_varian) / (len(data) - 1)
print('\ntotal =', ' + '.join(f'{item}' for item in list_varian))
print('total =', sum(list_varian))
print(f'\nvarian = {sum(list_varian)} / ({len(data) - 1})')
print(f'varian = {varian}')
simpangan_baku = statistics.sqrt(varian)
print('\n===== Simpangan Baku =====')
print('s = akar kuadrat dari varian')
print(f's = akar kuadrat({varian})')
print(f's = {simpangan_baku}')
# print(statistics.stdev(data))
