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')