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import math |
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import random |
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4
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from enum import Enum |
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5
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6
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from scipy.stats import norm, t |
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7
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8
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9
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class DistributionFamily(Enum): |
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normal = 1 |
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student_t = 2 |
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fisher = 3 |
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chi_square = 4 |
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simulation = 5 |
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16
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class MeanSamplingDistribution(object): |
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sample_distribution = None |
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point_estimate = None |
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distribution_family = None |
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df = None |
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def __init__(self, sample_distribution=None, sample_mean=None, sample_sd=None, sample_size=None): |
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if sample_mean is not None: |
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self.point_estimate = sample_mean |
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if sample_sd is not None: |
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self.sample_sd = sample_sd |
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if sample_size is not None: |
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self.sample_size = sample_size |
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if sample_distribution is not None: |
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self.sample_distribution = sample_distribution |
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self.point_estimate = sample_distribution.mean |
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self.sample_sd = sample_distribution.sd |
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self.sample_size = sample_distribution.sample_size |
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self.standard_error = MeanSamplingDistribution.calculate_standard_error(self.sample_sd, self.sample_size) |
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self.df = self.sample_size - 1.0 |
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if self.sample_size < 30: |
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self.distribution_family = DistributionFamily.student_t |
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else: |
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self.distribution_family = DistributionFamily.normal |
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@staticmethod |
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def calculate_standard_error(sample_sd, sample_size): |
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return sample_sd / math.sqrt(sample_size) |
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def confidence_interval(self, confidence_level): |
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q = 1 - (1 - confidence_level) / 2 |
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if self.distribution_family == DistributionFamily.normal: |
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z = norm.ppf(q) |
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pf = z * self.standard_error |
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return self.point_estimate - pf, self.point_estimate + pf |
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else: |
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t_df = t.ppf(q, self.df) |
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pf = t_df * self.standard_error + self.point_estimate |
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return self.point_estimate - pf, self.point_estimate + pf |
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63
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class ProportionSamplingDistribution(object): |
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sample_distribution = None |
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point_estimate = None |
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distribution_family = None |
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sample_size = None |
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categorical_value = None |
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standard_error = None |
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simulated_proportions = None |
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72
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def __init__(self, sample_distribution=None, categorical_value=None, sample_proportion=None, sample_size=None): |
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if sample_proportion is not None: |
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self.point_estimate = sample_proportion |
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76
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if sample_size is not None: |
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self.sample_size = sample_size |
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if categorical_value is not None: |
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self.categorical_value = categorical_value |
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82
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if sample_distribution is not None: |
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self.build(sample_distribution) |
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85
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if self.sample_size * self.point_estimate < 10 or self.sample_size * (1 - self.point_estimate) < 10: |
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self.distribution_family = DistributionFamily.simulation |
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self.simulate() |
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else: |
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self.distribution_family = DistributionFamily.normal |
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self.standard_error = math.sqrt(self.point_estimate * (1 - self.point_estimate) / self.sample_size) |
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92
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def build(self, sample_distribution): |
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self.sample_distribution = sample_distribution |
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self.point_estimate = sample_distribution.proportion |
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self.categorical_value = sample_distribution.categorical_value |
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self.sample_size = sample_distribution.sample_size |
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98
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def simulate(self): |
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self.simulated_proportions = [0] * 1000 |
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for iter in range(1000): |
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count = 0 |
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102
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for trials in range(self.sample_size): |
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if random.random() <= self.point_estimate: |
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count += 1 |
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105
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self.simulated_proportions[iter] = float(count) / self.sample_size |
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self.simulated_proportions = sorted(self.simulated_proportions) |
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107
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108
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def confidence_interval(self, confidence_level): |
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109
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q = 1 - (1 - confidence_level) / 2 |
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if self.distribution_family == DistributionFamily.normal: |
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z = norm.ppf(q) |
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pf = z * self.standard_error |
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113
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return self.point_estimate - pf, self.point_estimate + pf |
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else: |
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115
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threshold1 = int(1000 * (1 - confidence_level) / 2) |
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threshold2 = int(1000 * q) |
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return self.simulated_proportions[threshold1], self.simulated_proportions[threshold2] |
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119
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chen0040 /
pysie
