import math
import matplotlib.pyplot as plt
class Gaussian():
""" Gaussian distribution class for calculating and
visualizing a Gaussian distribution.
Attributes:
mean (float) representing the mean value of the distribution
stdev (float) representing the standard deviation of the distribution
data_list (list of floats) a list of floats extracted from the data file
"""
def __init__(self, mu = 0, sigma = 1):
self.mean = mu
self.stdev = sigma
self.data = []
def calculate_mean(self):
"""Function to calculate the mean of the data set.
Args:
None
Returns:
float: mean of the data set
"""
avg = 1.0 * sum(self.data) / len(self.data)
self.mean = avg
return self.mean
def calculate_stdev(self, sample=True):
"""Function to calculate the standard deviation of the data set.
Args:
sample (bool): whether the data represents a sample or population
Returns:
float: standard deviation of the data set
"""
if sample:
n = len(self.data) - 1
else:
n = len(self.data)
mean = self.mean
sigma = 0
for d in self.data:
sigma += (d - mean) ** 2
sigma = math.sqrt(sigma / n)
self.stdev = sigma
return self.stdev
def read_data_file(self, file_name, sample=True):
"""Function to read in data from a txt file. The txt file should have
one number (float) per line. The numbers are stored in the data attribute.
After reading in the file, the mean and standard deviation are calculated
Args:
file_name (string): name of a file to read from
Returns:
None
"""
with open(file_name) as file:
data_list = []
line = file.readline()
while line:
data_list.append(int(line))
line = file.readline()
file.close()
self.data = data_list
self.mean = self.calculate_mean()
self.stdev = self.calculate_stdev(sample)
def plot_histogram(self):
"""Function to output a histogram of the instance variable data using
matplotlib pyplot library.
Args:
None
Returns:
None
"""
plt.hist(self.data)
plt.title('Histogram of Data')
plt.xlabel('data')
plt.ylabel('count')
def pdf(self, x):
"""Probability density function calculator for the gaussian distribution.
Args:
x (float): point for calculating the probability density function
Returns:
float: probability density function output
"""
return (1.0 / (self.stdev * math.sqrt(2*math.pi))) * math.exp(-0.5*((x - self.mean) / self.stdev) ** 2)
def plot_histogram_pdf(self, n_spaces = 50):
"""Function to plot the normalized histogram of the data and a plot of the
probability density function along the same range
Args:
n_spaces (int): number of data points
Returns:
list: x values for the pdf plot
list: y values for the pdf plot
"""
mu = self.mean
sigma = self.stdev
min_range = min(self.data)
max_range = max(self.data)
# calculates the interval between x values
interval = 1.0 * (max_range - min_range) / n_spaces
x = []
y = []
# calculate the x values to visualize
for i in range(n_spaces):
tmp = min_range + interval*i
x.append(tmp)
y.append(self.pdf(tmp))
# make the plots
fig, axes = plt.subplots(2,sharex=True)
fig.subplots_adjust(hspace=.5)
axes[0].hist(self.data, density=True)
axes[0].set_title('Normed Histogram of Data')
axes[0].set_ylabel('Density')
axes[1].plot(x, y)
axes[1].set_title('Normal Distribution for
Sample Mean and Sample Standard Deviation')
axes[0].set_ylabel('Density')
plt.show()
return x, y
