Gaussian.py

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.stddev = sigma
        self.data = []

    def calculate_mean(self):
        avg = 1.0 * sum(self.data) / len(self.data)
        self.mean = avg
        return self.mean

    def calculate_stddev(self, sample=True):
        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.stddev = sigma

        return self.stddev

    def read_data_file(self, file_name, sample=True):
        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.stddev = self.calculate_stddev(sample)

    def plot_histogram(self):
        plt.hist(self.data)
        plt.title('Histogram of Data')
        plt.xlabel('data')
        plt.ylabel('count')

    def pop_density(self, x):
        return (1.0 / (self.stddev * math.sqrt(2 * math.pi))) * math.exp(-0.5 * ((x - self.mean) / self.stddev) ** 2)

    def plot_histogram_pdf(self, n_spaces=50):
        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):
        result = Gaussian()
        result.mean = self.mean + other.mean
        result.stddev = math.sqrt(self.stddev ** 2 + other.stddev ** 2)

        return result

    def __repr__(self):
        return "mean {}, standard deviation {}".format(self.mean, self.stddev)