Add support for Student's t-distribution

.gitignore

@@ -143,3 +143,4 @@ cython_debug/
 *~
 *.swp
 *.swo
+

.vscode/settings.json

@@ -0,0 +1,5 @@
+{
+ "python.linting.flake8Enabled": true,
+ "python.linting.enabled": true,
+ "python.linting.flake8Args": ["--ignore=E501, F401"]
+}

probdists/Batesdistribution.py

@@ -0,0 +1,148 @@
+import math
+import numpy as np
+from matplotlib import pyplot as plt
+from .Generaldistribution import Distribution
+
+
+class Bates(Distribution):
+
+ def __init__(self, n=20, a=0, b=1):
+ """ Bates distribution class for calculating and
+ visualizing a Bates distribution.
+
+ Attributes:
+
+ mean (float): the mean value of the distribution
+ stdev (float): the standard deviation of the distribution
+
+ data (list of floats): extracted from the data file
+
+ n (int): The number of samples
+ a (int): The lower limit of distribution [Default: 0]
+ b (int): The upper limit of distribution [Default: 1]
+ """
+ self.n = n
+ self.a = a
+ self.b = b
+ Distribution.__init__(self,
+ self.calculate_mean(),
+ self.calculate_stdev())
+
+ def calculate_mean(self, round_to=2):
+ """ Method to calculate the mean from n
+
+ Args:
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: mean of the distribution
+ """
+ self.mean = 0.5 * (self.a + self.b)
+
+ return round(self.mean, round_to)
+
+ def calculate_stdev(self, round_to=2):
+ """ Method to calculate the standard deviation from n
+
+ Args:
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: standard deviation of the distribution
+ """
+ var = (self.b - self.a) / (12 * self.n)
+
+ self.stdev = math.sqrt(var)
+
+ return round(self.stdev, round_to)
+
+ def _fx(self, x):
+ """ Internal function to calculate probability density function at a point.
+ Should not be used by end user.
+
+ Args:
+ x (int): point for calculating the mean value.
+ """
+ if x < 0 or x > 1:
+ value = 0
+ else:
+ g = 0
+ for i in range(0, int(self.n * x + 1)):
+ g += pow(-1, i) * _comb(self.n, i) * pow(x - i / self.n, self.n - 1)
+ value = (self.n**self.n / math.factorial(self.n - 1)) * g
+ return value
+
+ def calculate_pdf(self, x, round_to=2):
+ """ Probability density function calculator for the Bates distribution.
+
+ Args:
+ x (float): point for caluclating the probability density function
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: probability density function
+ """
+ self.pdf = self._fx((x - self.a) / (self.b - self.a)
+ ) / (self.b - self.a)
+ return round(self.pdf, round_to)
+
+ def calculate_cdf(self, x, round_to=2):
+ """ Cumulative distribution function calculator for the Bates distribution.
+ Args:
+ x (float): point for calculating the probability density function
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: cumulative distribution function output
+ """
+ value = 0
+ for i in range(0, int(x) + 1):
+ value += self.calculate_pdf(i)
+ self.cdf = value
+ return round(value, round_to)
+
+ def plot_pdf(self, samples=10**6):
+ """ Method to plot the pdf of the Bates distribution.
+
+ Args:
+ points (int): number of discrete data points
+
+ Returns:
+ F (np.array): list of PDFs for samples
+ """
+ x = np.linspace(self.a, self.b, num=samples)
+ y = (x - self.a) / (self.b - self.a)
+
+ F = np.zeros_like(y)
+
+ for i in range(0, len(y) + 1 // 2):
+ F[i] = self.calculate_pdf(y[i])
+ F[-i - 1] = F[i] # symmetric graph
+
+ plt.plot(x, F, label=f'n={self.n}')
+ plt.legend()
+ plt.title(f"Probability Distribution Function for Bates n={self.n}")
+ plt.show()
+ return F
+
+ def __repr__(self):
+ """ Method to output the characteristics of the Bates instace.
+ Args:
+ None
+ Returns:
+ string: characteristics of the Bates
+ """
+ return "mean {0}, standard deviation {1}, n {2}".format(self.mean,
+ self.stdev, self.n)
+
+
+def _comb(n, k):
+ """Protected function to calculate nCk
+ math.comb(n,k) was added in Python v3.8
+ Hence, for backward compatibility with earlier versions
+ """
+ return math.factorial(n) / (math.factorial(n - k) * math.factorial(k))

probdists/Exponentialdistribution.py

@@ -124,7 +124,7 @@ def plot_bar_pdf(self, points=100):
  #
 
  def __repr__(self):
- """ Method to outputthe characteristics of the Exponential instace.
+ """ Method to output the characteristics of the Exponential instace.
  Args:
  None
  Returns:

probdists/Generaldistribution.py

@@ -58,7 +58,9 @@ def read_data_file(self, file_name, separator='\\n', header=None):
  'demo_gamma_data': 'numbers_gamma.txt',
  'demo_uniform_data': 'numbers_uniform.txt',
  'demo_bernoulli_data': 'numbers_bernoulli.txt',
- 'demo_triangular_data': 'numbers_triangular.txt'
+ 'demo_triangular_data': 'numbers_triangular.txt',
+ 'demo_poisson_data': 'numbers_poisson.txt',
+ 'demo_bates_data': 'numbers_bates.txt'
  }
  if file_name in file_name_map:
  dirname = Path(__file__).parent.parent.absolute()
@@ -78,7 +80,7 @@ def read_data_file(self, file_name, separator='\\n', header=None):
  for i in df.iterrows():
  try:
  data_list.append(float(df.iat[i[0], 0]))
- except: # pylint: disable=W0702
+ except Exception: # pylint: disable=W0702
  traceback.print_exc()
  print('Could not convert', df.iat[i[0], 0], ' to int.')
  else:
@@ -102,7 +104,7 @@ def read_data_file(self, file_name, separator='\\n', header=None):
  for number in line:
  try:
  data_list.append(float(number))
- except: # pylint: disable=W0702
+ except Exception: # pylint: disable=W0702
  traceback.print_exc()
  print('Could not convert', number, ' to int.')
  line = file.readline()

probdists/Poissondistribution.py

@@ -0,0 +1,138 @@
+import math
+import matplotlib.pyplot as plt
+from .Generaldistribution import Distribution
+
+
+class Poisson(Distribution):
+ """ Poisson distribution class for calculating and
+ visualizing a Poisson distribution.
+
+ Attributes:
+
+ mean (float): the mean value of the distribution
+ stdev (float): the standard deviation of the distribution
+
+ data (list of floats): extracted from the data file
+
+ lmbda (float): rate of the poisson distribution
+ (missing an 'a' to prevent name clash with Python keyword)
+
+ """
+ def __init__(self, lmbda):
+
+ self.lmbda = lmbda
+
+ Distribution.__init__(self,
+ self.calculate_mean(),
+ self.calculate_stdev())
+
+ def calculate_mean(self, round_to=2):
+ """ Method to calculate the mean from lambda
+
+ Args:
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: mean of the distribution
+ """
+ self.mean = math.sqrt(self.lmbda)
+
+ return round(self.mean, round_to)
+
+ def calculate_stdev(self, round_to=2):
+ """ Method to calculate the standard deviation from lmbda
+
+ Args:
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: standard deviation of the distribution
+ """
+ self.stdev = math.sqrt(self.lmbda)
+
+ return round(self.stdev, round_to)
+
+ def calculate_pdf(self, x, round_to=2):
+ """ Probability density function calculator for the Poisson distribution.
+
+ Args:
+ x (float): point for calculating the probability density function
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: probability density function
+ """
+
+ self.pdf = self._calc_discrete_pdf(x)
+ return round(self.pdf, round_to)
+
+ def calculate_cdf(self, x, round_to=2):
+ """ Cumulative distribution function calculator for the Poisson distribution.
+ Args:
+ x (float): point for calculating the probability density function
+ round_to (int): Round the mean value.
+ [Default value: 2 floating point]
+
+ Returns:
+ float: cumulative distribution function output
+ """
+ value = 0
+ for i in range(0, x + 1):
+ value += self._calc_discrete_pdf(i)
+ self.cdf = value
+ return round(value, round_to)
+
+ def _calc_discrete_pdf(self, x):
+ """ Internal function to calculate probability density function at a point.
+ Should not be used by end user.
+
+ Args:
+ x (int): point for calculating the mean value.
+ """
+ fact = math.factorial(x)
+ pdf = (math.exp(-self.lmbda) * self.lmbda ** x) / fact
+ return pdf
+
+ def plot_pdf(self, points=100):
+ """ Method to plot the pdf of the Poisson distribution.
+
+ Args:
+ points (int): number of discrete data points
+
+ Returns:
+ list: x values for the pdf plot
+ list: y values for the pdf plot
+
+ """
+
+ x = []
+ y = []
+
+ # calculate the x values to visualize
+ for i in range(points + 1):
+ x.append(i)
+ y.append(self._calc_discrete_pdf(i))
+
+ # make the plots
+ plt.bar(x, y)
+ plt.title("Probability Mass Plt for Poisson Distribution")
+ plt.ylabel("Probability")
+ plt.xlabel("x")
+
+ plt.show()
+
+ return x, y
+
+ def __repr__(self):
+ """ Method to output the characteristics of the Poisson instace.
+ Args:
+ None
+ Returns:
+ string: characteristics of the Poisson
+ """
+
+ return "mean {0}, standard deviation {1}, lambda {2}".format(self.mean,
+ self.stdev, self.lmbda)