def poisson_pmf():
rv=Pie(4.5)#the average incident is 4.5
x = np.arange(0, 11, 1)#return evenly spaced values within 1 interval between [1,11)
y = rv.pmf(x)#probability mass function
plt.bar(x, y, width=0.6, color='grey')#make bar chart
plt.savefig('fig.png')
def expon_cdf_pdf():
x = np.linspace(0, 5, 100)##return evenly spaced samples, calculated over the interval [0,5]
rv=E(scale = 1)#the scale is 1
plt.plot(x, rv.pdf(x), color='blue')#make pdf chart
plt.plot(x, rv.cdf(x), color='red') #make cdf chart
plt.savefig('fig.png')
def geom_pmf():
rv=G(0.2)#probability of success is 0.2
x = np.arange(1, 11, 1)#return evenly spaced values within 1 interval between [1,11)
y = rv.pmf(x)#probability mass function
plt.bar(x, y, width=0.6, color='grey')#make bar chart
plt.savefig('fig.png')
def draw():
#get input data
x = get_data()
c = ('b', 'g', 'r', 'c', 'm', 'y', 'k', 'w')
# the pie chart of the data
plt.pie(x, colors=c, shadow=False)
#show image
plt.savefig('fig.png')
def expon_pdf():
x = np.linspace(0, 20, 100)#return evenly spaced samples, calculated over the interval [0,20]
rv1=E(scale = 1.5)#the scale is 1.5
rv2=E(scale = 1.0)#the scale is 1.0
rv3=E(scale = 0.5)#the scale is 0.5
plt.plot(x, rv1.pdf(x), color='green')#make chart
plt.plot(x, rv2.pdf(x), color='blue')#make chart
plt.plot(x, rv3.pdf(x), color='red')#make chart
plt.savefig('fig.png')
def norm_pdf():
x = np.linspace(-10, 10, 100)#return evenly spaced samples, calculated over the interval [-10,10]
rv1=N(loc=0, scale = 1)#the mean is 0, the standard deviation is 1
rv2=N(loc=-5, scale = 1)#the mean is -5, the standard deviation is 1
rv3=N(loc=0, scale = 3)#the mean is 0, the standard deviation is 3
plt.plot(x, rv1.pdf(x), color='green')#make chart
plt.plot(x, rv2.pdf(x), color='blue')#make chart
plt.plot(x, rv3.pdf(x), color='red')#make chart
plt.savefig('fig.png')
def central_limit_theorem():
y = []
n=100
for i in range(1000):
r = expon.rvs(scale=1, size=n)
rsum=np.sum(r)
z=(rsum-n)/np.sqrt(n)
y.append(z)
plt.hist(y,color='grey')
plt.savefig('central_limit_theorem.png')
def second_year():
X=sta.norm(loc=950, scale=20)#generate random data in normal distribution whose expectation is 950 and standard deviation is 20
wbread=[]
for i in range(365):
x=X.rvs(size=100)
wbread.append(max(x))#get the random data for one day
log(numpy.mean(wbread))#print mean value
log(sta.skew(wbread))#print skew value
plt.hist(wbread,color='grey')
plt.savefig('second_year.png')
def law_of_large_numbers():
x = np.arange(1, 1001, 1)
r = bernoulli.rvs(0.3, size=1000)
y = []
rsum =0.0
for i in range(1000):
if r[i]==1:
rsum=rsum+1
y.append(rsum/(i+1))
plt.plot(x, y, color='red')
plt.savefig('law_of_large_numbers.png')
def central_limit_theorem():
y = []
n=100
for i in range(1000):
r = binom.rvs(n, 0.3)
rsum=np.sum(r)
z=(rsum-n*0.3)/np.sqrt(n*0.3*0.7)
y.append(z)
plt.hist(y,color='grey')
plt.savefig('central_limit_theorem.png')
def first_year():
X=sta.norm(loc=950, scale=20)#generate random data in normal distribution whose expectation is 950 and standard deviation is 20
wbread=[]
for i in range(365):
x=X.rvs(size=100)
wbread.append(x[0])#get the random data for one day
log(numpy.mean(wbread))#print mean value
log(sta.skew(wbread))#print skew value
plt.hist(wbread,color='grey')
plt.savefig('first_year.png')
def law_of_large_numbers():
x = np.arange(1, 1001, 1)
r1 = binom.rvs(10, 0.6, size=1000)
r2 = poisson.rvs(mu=6, size=1000)
r3 = norm.rvs(loc=6, size=1000)
y = []
rsum=0.0
for i in range(1000):
rsum=rsum+(r1[i]+r2[i]+r3[i])
y.append(rsum/((i+1)*3)-6)
plt.plot(x, y, color='red')
plt.savefig('law_of_large_numbers.png')
def draw():
#get input data
menMeans = (20, 35, 30, 35, 27)
menStd = (2, 3, 4, 1, 2)
womenMeans = (25, 32, 34, 20, 25)
womenStd = (3, 5, 2, 3, 3)
ind = np.arange(5)
width = 0.35
# the histogram of the data
plt.bar(ind, menMeans, width, color='r')
plt.bar(ind+width, womenMeans, width, color='y')
#show image
plt.savefig('fig.png')
def linregress1():
x = np.linspace(-5, 5, num=150)
y = x + np.random.normal(size=x.size)
y[12:14] += 10
slope, intercept, r_value, p_value, std_err = stats.linregress(x,y)
log(slope)
log(intercept)
log(r_value)
log(p_value)
log(std_err)
plt.plot(x, y, 'b.')
plt.plot(x, slope * x + intercept, 'r-')
plt.savefig('linregress1.png')
def sampling_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
df = 10
x=np.linspace(t.ppf(0.01, df), t.ppf(0.99, df), 100)
ax.plot(x, t.pdf(x, df))
#simulate the sampling distribution
y = []
for i in range(1000):
r = norm.rvs(loc=5, scale=2, size=df+1)
rt =(np.mean(r)-5)/np.sqrt(np.var(r)/df)
y.append(rt)
ax.hist(y, normed=True, alpha=0.2)
plt.savefig('sampling_distribution.png')
def t_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
df = 10
x=np.linspace(-4, 4, 100)
ax.plot(x, t.pdf(x,df))
#simulate the t-distribution
y = []
for i in range(1000):
rx = norm.rvs()
ry = chi2.rvs(df)
rt = rx/np.sqrt(ry/df)
y.append(rt)
ax.hist(y, normed=True, alpha=0.2)
plt.savefig('t_distribution.png')
def sampling_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
dfn, dfm = 10, 5
x=np.linspace(f.ppf(0.01, dfn, dfm), f.ppf(0.99, dfn, dfm), 100)
ax.plot(x, f.pdf(x, dfn, dfm))
#simulate the sampling distribution
y = []
for i in range(1000):
r1 = norm.rvs(loc=5, scale=2, size=dfn+1)
r2 = norm.rvs(loc=3, scale=2, size=dfm+1)
rf =np.var(r1)/np.var(r2)
y.append(rf)
ax.hist(y, normed=True, alpha=0.2)
plt.savefig('sampling_distribution.png')
def sampling_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
x = np.linspace(-4, 4, 100)
ax.plot(x, norm.pdf(x))
#simulate the sampling distribution
y = []
n=100
for i in range(1000):
r = expon.rvs(scale=1, size=n)
rsum=np.sum(r)
z=(rsum-n)/np.sqrt(n)
y.append(z)
ax.hist(y, normed=True, alpha=0.2)
plt.savefig('sampling_distribution.png')
def F_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
dfn, dfm = 10, 5
x = np.linspace(f.ppf(0.01, dfn, dfm), f.ppf(0.99, dfn, dfm), 100)
ax.plot(x, f.pdf(x, dfn, dfm))
#simulate the F-distribution
y = []
for i in range(1000):
rx = chi2.rvs(dfn)
ry = chi2.rvs(dfm)
rf = np.sqrt(rx/dfn)/np.sqrt(ry/dfm)
y.append(rf)
ax.hist(y, normed=True, alpha=0.2)
plt.savefig('F_distribution.png')
def chi2_distribution():
fig, ax = plt.subplots(1, 1)
#display the probability density function
df = 10
x=np.linspace(chi2.ppf(0.01, df), chi2.ppf(0.99, df), 100)
ax.plot(x, chi2.pdf(x,df))
#simulate the chi2 distribution
y = []
n=10
for i in range(1000):
chi2r=0.0
r = norm.rvs(size=n)
for j in range(n):
chi2r=chi2r+r[j]**2
y.append(chi2r)
ax.hist(y, normed=True, alpha=0.2)
plt.savefig('chi2_distribution.png')
