def show_binomial():
"""Show an example of binomial distributions"""
bd1 = stats.binom(20, 0.5)
bd2 = stats.binom(20, 0.7)
bd3 = stats.binom(40, 0.5)
k = np.arange(40)
sns.set_context('paper')
sns.set_style('ticks')
mystyle.set(14)
markersize = 8
plt.plot(k, bd1.pmf(k), 'o-b', ms=markersize)
plt.hold(True)
plt.plot(k, bd2.pmf(k), 'd-r', ms=markersize)
plt.plot(k, bd3.pmf(k), 's-g', ms=markersize)
plt.title('Binomial distribuition')
plt.legend(['p=0.5 and n=20', 'p=0.7 and n=20', 'p=0.5 and n=40'])
plt.xlabel('X')
plt.ylabel('P(X)')
sns.despine()
mystyle.printout_plain('Binomial_distribution_pmf.png')
plt.show()
def show_poisson():
"""Show different views of a Poisson distribution"""
fig, ax = plt.subplots(3,1)
k = np.arange(25)
pd = stats.poisson(10)
mystyle.set(12)
ax[0].plot(k, pd.pmf(k),'x-')
ax[0].set_title('Poisson distribition')
ax[0].set_xticklabels([])
ax[0].set_ylabel('PMF (X)')
ax[1].plot(k, pd.cdf(k))
ax[1].set_xlabel('X')
ax[1].set_ylabel('CDF (X)')
y = np.linspace(0,1,100)
ax[2].plot(y, pd.ppf(y))
ax[2].set_xlabel('X')
ax[2].set_ylabel('PPF (X)')
plt.tight_layout()
plt.show()
def show_poisson_views():
"""Show different views of a Poisson distribution"""
fig, ax = plt.subplots(3,1)
k = np.arange(25)
pd = stats.poisson(10)
mystyle.set(12)
ax[0].plot(k, pd.pmf(k),'x-')
ax[0].set_title('Poisson distribition')
ax[0].set_xticklabels([])
ax[0].set_ylabel('PMF (X)')
ax[1].plot(k, pd.cdf(k))
ax[1].set_xlabel('X')
ax[1].set_ylabel('CDF (X)')
y = np.linspace(0,1,100)
ax[2].plot(y, pd.ppf(y))
ax[2].set_xlabel('X')
ax[2].set_ylabel('PPF (X)')
plt.tight_layout()
plt.show()
def show_binomial():
"""Show an example of binomial distributions"""
bd1 = stats.binom(20, 0.5)
bd2 = stats.binom(20, 0.7)
bd3 = stats.binom(40, 0.5)
k = np.arange(40)
sns.set_context('paper')
sns.set_style('ticks')
mystyle.set(14)
markersize = 8
plt.plot(k, bd1.pmf(k), 'o-b', ms=markersize)
plt.hold(True)
plt.plot(k, bd2.pmf(k), 'd-r', ms=markersize)
plt.plot(k, bd3.pmf(k), 's-g', ms=markersize)
plt.title('Binomial distribuition')
plt.legend(['p=0.5 and n=20', 'p=0.7 and n=20', 'p=0.5 and n=40'])
plt.xlabel('X')
plt.ylabel('P(X)')
sns.despine()
mystyle.printout_plain('Binomial_distribution_pmf.png')
plt.show()
def main():
'''Demonstrate central limit theorem.'''
# Generate data
ndata = 1e5
nbins = 50
data = np.random.random(ndata)
# Show them
fig, axs = plt.subplots(1,3)
mystyle.set(14)
myColor = '#CCCCCC'
#sns.set_context('paper')
#sns.set_style('whitegrid')
axs[0].hist(data,bins=nbins, color=myColor)
axs[0].set_title('Random data')
axs[0].set_xticks([0, 0.5, 1])
axs[0].set_ylabel('Counts')
axs[1].hist( np.mean(data.reshape((ndata/2,2)), axis=1), bins=nbins, color=myColor)
axs[1].set_xticks([0, 0.5, 1])
axs[1].set_title(' Average over 2')
axs[2].hist( np.mean(data.reshape((ndata/10,10)),axis=1), bins=nbins, color=myColor)
axs[2].set_xticks([0, 0.5, 1])
axs[2].set_title(' Average over 10')
plt.tight_layout()
mystyle.printout_plain('CentralLimitTheorem.png')
plt.show()
def main():
# Univariate data -------------------------
# Generate data that are normally distributed
x = randn(500)
# Set the fonts the way I like them
sns.set_context('paper')
sns.set_style('white')
mystyle.set()
# Scatter plot
plot(x, '.')
mystyle.printout('scatterPlot.png',
xlabel='x',
ylabel='y',
title='Scatter')
# Histogram
hist(x, color='#999999')
mystyle.printout('histogram_plain.png',
xlabel='Data Values',
ylabel='Frequency',
title='Histogram, default settings')
hist(x, 25, color='#999999')
mystyle.printout('histogram.png',
xlabel='Data Values',
ylabel='Frequency',
title='Histogram, 25 bins')
# Cumulative probability density
numbins = 20
plot(stats.cumfreq(x, numbins)[0])
mystyle.printout('CumulativeFrequencyFunction.png',
xlabel='Data Values',
ylabel='Cumulative Freuqency')
# Boxplot
# The ox consists of the first, second (middle) and third quartile
boxplot(x, sym='*')
mystyle.printout('boxplot.png', xlabel='Values', title='Boxplot')
boxplot(x, sym='*', vert=False)
title('Boxplot, horizontal')
xlabel('Values')
show()
# Violinplot
nd = stats.norm
data = nd.rvs(size=(100))
nd2 = stats.norm(loc=3, scale=1.5)
data2 = nd2.rvs(size=(100))
# Use pandas and the seaborn package for the violin plot
df = pd.DataFrame({'Girls': data, 'Boys': data2})
sns.violinplot(df, color=["#999999", "#DDDDDD"])
mystyle.printout('violinplot.png')
import seaborn as sns
import os.path
import mystyle
# Define the skewed distribution
chi2 = stats.chi2(3)
# Generate the data
x = np.linspace(0,10, 100)
y = chi2.pdf(x)
data = chi2.rvs(100)
# Arrange subplots
sns.set_context('paper')
sns.set_style('white')
mystyle.set(11)
fig, axs = plt.subplots(1,2)
# Plot distribution
axs[0].plot(x,y)
axs[0].set_xlabel('X')
axs[0].set_ylabel('PDF(X)')
axs[0].set_title('chi2(x), k=3')
sns.set_style('white')
x0, x1 = axs[0].get_xlim()
y0, y1 = axs[0].get_ylim()
axs[0].set_aspect((x1-x0)/(y1-y0))
#sns.despine()
grandMean = np.mean(groupMean)
ax.axhline(grandMean)
ax.plot([80, 220], [groupMean[1], groupMean[1]], 'b')
ax.plot([80, 120], [groupMean[1]+0.2, groupMean[1]+0.2], 'b')
ax.annotate('', xy=(210, grandMean), xytext=(210,groupMean[1]),
arrowprops=dict(arrowstyle='<->, head_width=0.1', facecolor='black'))
ax.annotate('', xy=(90, groupMean[1]), xytext=(90,groupMean[1]+0.2),
arrowprops=dict(arrowstyle='<->, head_width=0.1', facecolor='black'))
ax.text(210, (grandMean + groupMean[1])/2., '$SS_{Treatment}$', fontsize=24)
ax.text(90, groupMean[1]+0.1, '$SS_{Error}$', ha='right', fontsize=24)
if __name__ == '__main__':
centers = [5, 5.3, 4.7]
colors = 'brg'
#sns.set_context('paper')
#sns.set_style('white')
np.random.seed(123)
mystyle.set(18)
fig = plt.figure()
ax = fig.add_subplot(111)
std = 0.1
numData = 100
show_fig(0.1, ax, 'Sum-Squares')
mystyle.printout_plain('anova_annotated.png')
plt.show()
def show_fig(std, ax, title):
'''Create plot of 3 different, normally distributed data groups'''
for ii in range(3):
data = stats.norm(centers[ii], std).rvs(numData)
offset = ii*numData
ax.plot( offset+np.arange(numData), data, '.', color=colors[ii], ms=10)
ax.xaxis.set_ticks([50,150,250])
ax.set_xticklabels(['Group1', 'Group2', 'Group3'])
ax.set_title(title)
sns.despine()
if __name__ == '__main__':
centers = [5, 5.3, 4.7]
colors = 'brg'
sns.set_context('paper')
sns.set_style('whitegrid')
mystyle.set(14)
fig, axs = plt.subplots(1, 2)
stds = [0.1, 2]
numData = 100
show_fig(0.1, axs[0], 'SD=0.1')
show_fig(2, axs[1], 'SD=2.0')
mystyle.printout_plain('anova_oneway.png')
plt.show()
import seaborn as sns
import os.path
import mystyle
# Define the skewed distribution
chi2 = stats.chi2(3)
# Generate the data
x = np.linspace(0, 10, 100)
y = chi2.pdf(x)
data = chi2.rvs(100)
# Arrange subplots
sns.set_context('paper')
sns.set_style('white')
mystyle.set(11)
fig, axs = plt.subplots(1, 2)
# Plot distribution
axs[0].plot(x, y)
axs[0].set_xlabel('X')
axs[0].set_ylabel('PDF(X)')
axs[0].set_title('chi2(x), k=3')
sns.set_style('white')
x0, x1 = axs[0].get_xlim()
y0, y1 = axs[0].get_ylim()
axs[0].set_aspect((x1 - x0) / (y1 - y0))
#sns.despine()
# Plot probplot
# Don't worry that in Python it is called "weibull_min": the "weibull_max" is
# simply mirrored about the origin.
showDistribution(arange(0,5,0.02), stats.weibull_min(1), stats.weibull_min(2),
'Weibull Distribution', 'X', 'P(X)',['k=1', 'k=2'], xmin=0, xmax=4)
# Uniform distribution
showDistribution(x, stats.uniform,'' ,
'Uniform Distribution', 'X', 'P(X)','')
# Logistic distribution
showDistribution(x, stats.norm, stats.logistic,
'Logistic Distribution', 'X', 'P(X)',['Normal', 'Logistic'])
# Lognormal distribution
x = logspace(-9,1,1001)+1e-9
showDistribution(x, stats.lognorm(2), '',
'Lognormal Distribution', 'X', 'lognorm(X)','', xmin=-0.1)
# The log-lin plot has to be done by hand:
plot(log(x), stats.lognorm.pdf(x,2))
xlim(-10, 4)
title('Lognormal Distribution')
xlabel('log(X)')
ylabel('lognorm(X)')
show()
#----------------------------------------------------------------------
if __name__ == '__main__':
mystyle.set()
show_continuous()
facecolor='black'))
ax.annotate('',
xy=(90, groupMean[1]),
xytext=(90, groupMean[1] + 0.2),
arrowprops=dict(arrowstyle='<->, head_width=0.1',
facecolor='black'))
ax.text(210, (grandMean + groupMean[1]) / 2.,
'$SS_{Treatment}$',
fontsize=24)
ax.text(90, groupMean[1] + 0.1, '$SS_{Error}$', ha='right', fontsize=24)
if __name__ == '__main__':
centers = [5, 5.3, 4.7]
colors = 'brg'
#sns.set_context('paper')
#sns.set_style('white')
np.random.seed(123)
mystyle.set(18)
fig = plt.figure()
ax = fig.add_subplot(111)
std = 0.1
numData = 100
show_fig(0.1, ax, 'Sum-Squares')
mystyle.printout_plain('anova_annotated.png')
plt.show()
import seaborn as sns
import mystyle
# Calculate the values
nd = stats.norm()
x = np.linspace(-3,3,100)
yp = nd.pdf(x)
y = nd.cdf(x)
x1 = np.linspace(-3, 1)
y1 = nd.pdf(x1)
# Make the plot
sns.set_context('paper')
sns.set_style('white')
mystyle.set(12)
figs, axs = plt.subplots(1,2)
axs[0].plot(x,yp, 'k')
axs[0].fill_between(x1, y1, facecolor='#CCCCCC')
axs[0].text(0, 0.1, 'CDF(x)', family='cursive', fontsize=14, horizontalalignment='center', style='italic')
axs[0].set_xlabel('x')
axs[0].set_ylabel('PDF(x)')
sns.despine()
axs[1].plot(x, y, '#999999', lw=3)
axs[1].set_xlabel('x')
axs[1].set_ylabel('CDF(x)')
plt.vlines(0, 0, 1, linestyles='--')
sns.despine()
# additional packages
import mystyle
# Calculate the values
nd = stats.norm()
x = np.linspace(-3,3,100)
yp = nd.pdf(x)
y = nd.cdf(x)
x1 = np.linspace(-3, 1)
y1 = nd.pdf(x1)
# Make the plot
sns.set_context('paper')
sns.set_style('white')
mystyle.set(12)
figs, axs = plt.subplots(1,2)
axs[0].plot(x,yp, 'k')
axs[0].fill_between(x1, y1, facecolor='#CCCCCC')
axs[0].text(0, 0.1, 'CDF(x)', family='cursive', fontsize=14, horizontalalignment='center', style='italic')
axs[0].set_xlabel('x')
axs[0].set_ylabel('PDF(x)')
sns.despine()
axs[1].plot(x, y, '#999999', lw=3)
axs[1].set_xlabel('x')
axs[1].set_ylabel('CDF(x)')
plt.vlines(0, 0, 1, linestyles='--')
sns.despine()
'')
# Logistic distribution
showDistribution(x, stats.norm, stats.logistic, 'Logistic Distribution',
'X', 'P(X)', ['Normal', 'Logistic'])
# Lognormal distribution
x = logspace(-9, 1, 1001) + 1e-9
showDistribution(x,
stats.lognorm(2),
'',
'Lognormal Distribution',
'X',
'lognorm(X)',
'',
xmin=-0.1)
# The log-lin plot has to be done by hand:
plot(log(x), stats.lognorm.pdf(x, 2))
xlim(-10, 4)
title('Lognormal Distribution')
xlabel('log(X)')
ylabel('lognorm(X)')
show()
#----------------------------------------------------------------------
if __name__ == '__main__':
mystyle.set()
show_continuous()
offset = ii * numData
ax.plot(offset + np.arange(numData),
data,
'.',
color=colors[ii],
ms=10)
ax.xaxis.set_ticks([50, 150, 250])
ax.set_xticklabels(['Group1', 'Group2', 'Group3'])
ax.set_title(title)
sns.despine()
if __name__ == '__main__':
centers = [5, 5.3, 4.7]
colors = 'brg'
sns.set_context('paper')
sns.set_style('whitegrid')
mystyle.set(14)
fig, axs = plt.subplots(1, 2)
stds = [0.1, 2]
numData = 100
show_fig(0.1, axs[0], 'SD=0.1')
show_fig(2, axs[1], 'SD=2.0')
mystyle.printout_plain('anova_oneway.png')
plt.show()