%%writefile distributions/general.py class Distribution: def __init__(self, mu=0, sigma=1): """ Generic distribution class for calculating and visualizing a probability 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 """ self.mean = mu self.stdev = sigma self.data = [] def read_data_file(self, file_name): """ 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. 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

from distributions.general import Distribution # importing python file from directory general1 = Distribution(20, 3) # creating object with 20 mean, 30 standard deviation print("Mean: {}, standard deviation: {}".format(general1.mean, general1.stdev)) general1.read_data_file("data/random.txt") # loading txt file data and checking print("Data Loaded :", general1.data) ## everything is working perfectly

%%writefile distributions/gaussian.py import math import matplotlib.pyplot as plt from .general import Distribution class Gaussian(Distribution): """ 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): Distribution.__init__(self, mu, sigma) 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.calculate_mean() sigma = 0 for d in self.data: sigma += (d - mean) ** 2 sigma = math.sqrt(sigma / n) self.stdev = sigma return self.stdev 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 \n Sample Mean and Sample Standard Deviation') axes[0].set_ylabel('Density') plt.show() return x, y def __add__(self, other): """ Function to add together two Gaussian distributions Args: other (Gaussian): Gaussian instance Returns: Gaussian: Gaussian distribution """ result = Gaussian() result.mean = self.mean + other.mean result.stdev = math.sqrt(self.stdev ** 2 + other.stdev ** 2) return result def __repr__(self): """ Function to output the characteristics of the Gaussian instance Args: None Returns: string: characteristics of the Gaussian """ return "mean {}, standard deviation {}".format(self.mean, self.stdev)

from distributions.gaussian import Gaussian Gaussian(20,3) ## checking the object magic function

gaussian1 = Gaussian(25, 2) gaussian1.read_data_file('data/random.txt')

print("Before pdf : ", round(gaussian1.pdf(25), 5)) # checking pdf on initial mean and stdev print("mean :", round(gaussian1.calculate_mean(), 2)) # calculating mean of data print("Stdev :", round(gaussian1.calculate_stdev(), 2)) # calculating stdev of data print("After pdf : ", round(gaussian1.pdf(75), 5)) # calcuation pdf of data

gaussian1.plot_histogram_pdf();

%%writefile test/test_gaussian.py import unittest from distributions.gaussian import Gaussian class TestGaussianClass(unittest.TestCase): def setUp(self): self.gaussian = Gaussian(35, 6) self.gaussian.read_data_file('data/random.txt') def test_initialization(self): self.assertEqual(self.gaussian.mean, 35, 'incorrect mean') self.assertEqual(self.gaussian.stdev, 6, 'incorrect standard deviation') def test_readdata(self): self.assertEqual(self.gaussian.data,\ [10, 23, 45, 12, 23, 45, 67, 100, 300, 250, 45, 68, 29, 59, 239, 934, 12, 321, 12, 32, 1], 'data not read in correctly') def test_meancalculation(self): self.assertEqual(self.gaussian.calculate_mean(),\ sum(self.gaussian.data) / float(len(self.gaussian.data)), 'calculated mean not as expected') def test_stdevcalculation(self): self.assertEqual(round(self.gaussian.calculate_stdev(), 2), 210.77, 'sample standard deviation incorrect') self.assertEqual(round(self.gaussian.calculate_stdev(0), 2), 205.69, 'population standard deviation incorrect') def test_pdf(self): self.assertEqual(round(self.gaussian.pdf(25), 5), 0.01658,\ 'pdf function does not give expected result') self.gaussian.calculate_mean() self.gaussian.calculate_stdev() self.assertEqual(round(self.gaussian.pdf(75), 5), 0.00184,\ 'pdf function after calculating mean and stdev does not give expected result') def test_add(self): gaussian_one = Gaussian(25, 3) gaussian_two = Gaussian(30, 4) gaussian_sum = gaussian_one + gaussian_two self.assertEqual(gaussian_sum.mean, 55) self.assertEqual(gaussian_sum.stdev, 5) if __name__ == '__main__': unittest.main()

!python test/test_gaussian.py

%%writefile distributions/binomial.py import math import matplotlib.pyplot as plt from .general import Distribution class Binomial(Distribution): """ Binomial distribution class for calculating and visualizing a Binomial 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 to be extracted from the data file p (float) representing the probability of an event occurring n (int) the total number of trials """ def __init__(self, prob=.5, size=20): self.p = prob self.n = size mu = self.calculate_mean() sigma = self.calculate_stdev() Distribution.__init__(self, mu, sigma) def calculate_mean(self): """Function to calculate the mean from p and n Args: None Returns: float: mean of the data set """ self.mean = self.p*self.n return self.mean def calculate_stdev(self): """Function to calculate the standard deviation from p and n. Args: None Returns: float: standard deviation of the data set """ self.stdev = math.sqrt(self.n * self.p * (1 - self.p)) return self.stdev def replace_stats_with_data(self): """Function to calculate p and n from the data set Args: None Returns: float: the p value float: the n value """ self.n = len(self.data) self.p = sum(self.data)/len(self.data) self.mean = self.calculate_mean() self.stdev = self.calculate_stdev() return self.p,self.n def plot_bar(self): """Function to output a histogram of the instance variable data using matplotlib pyplot library. Args: None Returns: None """ plt.bar(x = ['0', '1'], height = [(1 - self.p) * self.n, self.p * self.n]) plt.title('Bar Chart of Data') plt.xlabel('outcome') plt.ylabel('count') def pdf(self, k): """Probability density function calculator for the gaussian distribution. Args: k (float): point for calculating the probability density function Returns: float: probability density function output """ a = math.factorial(self.n) / (math.factorial(k) * (math.factorial(self.n - k))) b = (self.p ** k) * (1 - self.p) ** (self.n - k) return a * b def plot_bar_pdf(self): """Function to plot the pdf of the binomial distribution Args: None 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(self.n + 1): x.append(i) y.append(self.pdf(i)) # make the plots plt.bar(x, y) plt.title('Distribution of Outcomes') plt.ylabel('Probability') plt.xlabel('Outcome') plt.show() return x, y def __add__(self, other): """Function to add together two Binomial distributions with equal p Args: other (Binomial): Binomial instance Returns: Binomial: Binomial distribution """ try: assert self.p == other.p, 'p values are not equal' except AssertionError as error: raise result = Binomial() result.p = self.p result.n = self.n + other.n result.mean = self.calculate_mean() result.stdev = self.calculate_stdev() return result pass def __repr__(self): """Function to output the characteristics of the Binomial instance Args: None Returns: string: characteristics of the Gaussian """ return "mean {}, standard deviation {}, p {}, n {}".format(self.mean,self.stdev,self.p,self.n) pass

from distributions.binomial import Binomial Binomial(0.6,300)

B1 = Binomial(0.4, 20) # creating object with 0.4 probability, 30 size print("Mean: {}, standard deviation: {}".format(B1.mean, round(B1.stdev,2))) B1.read_data_file("data/binary.txt") # loading txt file data and checking print("Data Loaded :", B1.data)

print("Initial PDF",round(B1.pdf(5), 5)) p, n = B1.replace_stats_with_data() print("Data p: {}, n: {}".format(round(p,3),n)) print("Data PDF",round(B1.pdf(5), 5))

B1.plot_bar()

B1.plot_bar_pdf();

%%writefile test/test_binomial.py import unittest from distributions.binomial import Binomial class TestBinomialClass(unittest.TestCase): def setUp(self): self.binomial = Binomial(0.4, 20) self.binomial.read_data_file('data/binary.txt') def test_initialization(self): self.assertEqual(self.binomial.p, 0.4, 'p value incorrect') self.assertEqual(self.binomial.n, 20, 'n value incorrect') def test_readdata(self): self.assertEqual(self.binomial.data,\ [1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1], 'data not read in correctly') def test_calculatemean(self): mean = self.binomial.calculate_mean() self.assertEqual(mean, 8) def test_calculatestdev(self): stdev = self.binomial.calculate_stdev() self.assertEqual(round(stdev,2), 2.19) def test_replace_stats_with_data(self): p, n = self.binomial.replace_stats_with_data() self.assertEqual(round(p,3), 0.471) self.assertEqual(n, 17) def test_pdf(self): self.assertEqual(round(self.binomial.pdf(5), 5), 0.07465) self.assertEqual(round(self.binomial.pdf(3), 5), 0.01235) self.binomial.replace_stats_with_data() self.assertEqual(round(self.binomial.pdf(5), 5), 0.06923) self.assertEqual(round(self.binomial.pdf(3), 5), 0.00963) def test_add(self): binomial_one = Binomial(.4, 20) binomial_two = Binomial(.4, 60) binomial_sum = binomial_one + binomial_two self.assertEqual(binomial_sum.p, .4) self.assertEqual(binomial_sum.n, 80) if __name__ == '__main__': unittest.main()

!python test/test_binomial.py

%%writefile distributions/__init__.py from .binomial import Binomial from .gaussian import Gaussian

%%writefile setup.py from setuptools import setup setup(name='distributions', version='0.2', description='Gaussian and Binomial distributions', packages=['distributions'], author = "Abid Ali Awan", author_email = "abidaliawan@rocketmail.com", zip_safe=False)