Overview

해당 문서는 SciPy 라이브러리의 stats 모듈에 대해 자세히 다룬다.

Confidence Interval

Hypothesis

Statistics

SciPy에서 stats 모듈은 확률 분포, 통계적 추론, 가설 검정에 대한 기법을 제공한다.

import scipy.stats as stats

Descriptive Statistics

Descriptive Statistics(기술 통계)는 수집된 데이터를 정리하여 중심 경향성, 분포 등 전반적인 특성을 쉽게 파악하는 기법이다.

import numpy as np
a = np.array([1, 2, 2, 3, 3, 3, 4, 5, 9])

• Descriptive Statistics: stats.describe(a)

  stats.describe(a)
  # DescribeResult(nobs=np.int64(9),
  #                minmax=(np.int64(1),
  #                np.int64(9)),
  #                mean=np.float64(3.5555555555555554),
  #                variance=np.float64(5.527777777777778),  # 표본 분산
  #                skewness=np.float64(1.42567921722749),
  #                kurtosis=np.float64(1.3153834499128827)
  #                )
  

• Trimmed Mean(절사평균): stats.tmean(a, limits=None)

  • limits=(lower bound, upper bound)

  stats.tmean(a, limits=(2, 5))
  # np.float64(3.142857142857143)
  

Probability Distributions

Probability Distributions(확률분포)는 확률변수가 특정한 값을 가질 확률을 나타낸 함수이다.

• Discrete Probability Distribution
  • Bernoulli Distribution
  • Binomial Distribution
  • Geometric Distribution
  • Negative Binomial Distribution
  • Poisson Distribution
• Continuous Probability Distribution
  • Continuous Uniform Distribution
  • Normal Distribution
  • Exponential Distribution
  • Gamma Distribution
  • Beta Distribution
  • Student’s t Distribution
  • F Distribution
  • Chi-squared Distribution

Discrete Probability Distribution

Discrete Probability Distribution(이산형 확률 분포)은 확률변수가 취하는 값들이 유한하고 셀 수 있는 경우, 그 값을 가질 확률에 대응시켜주는 확률 분포이다.

• Bernoulli Distribution: stats.bernoulli(p)

  p = 0.3
  
  # Descriptive Statistics
  stats.bernoulli.mean(p)    # np.float64(0.3)
  stats.bernoulli.median(p)  # np.float64(0.0)
  stats.bernoulli.var(p)     # np.float64(0.21)
  stats.bernoulli.std(p)     # np.float64(0.458257569495584)
  
  # Moments
  mean, var, skew, kurt = stats.bernoulli.stats(p, moments='mvsk')
  
  # Probability Mass Function
  stats.bernoulli.pmf(k=1, p=p)  # 성공 확률
  # np.float64(0.3)
  stats.bernoulli.pmf(k=0, p=p)  # 실패 확률
  # np.float64(0.7)
  
  # Cumulative Distribution Function
  stats.bernoulli.cdf(k=0, p=p)
  # np.float64(0.7)
  
  # Random Variates
  stats.bernoulli.rvs(p, size=10, random_state=54)
  # array([0, 0, 0, 0, 0, 1, 1, 1, 0, 0])
  

  # 확률 변수 지정
  rv = stats.bernoulli(p=0.3)
  
  # Descriptive Statistics
  rv.mean()    # np.float64(0.3)
  rv.median()  # np.float64(0.0)
  rv.var()     # np.float64(0.21)
  rv.std()     # np.float64(0.458257569495584)
  
  # Moments
  mean, var, skew, kurt = rv.stats(moments='mvsk')
  
  # Probability Mass Function
  rv.pmf(k=1)  # 성공 확률
  # np.float64(0.3)
  rv.pmf(k=0)  # 실패 확률
  # np.float64(0.7)
  
  # Cumulative Distribution Function
  rv.cdf(x=0)
  # np.float64(0.7)
  
  # Random Variates
  rv.rvs(10, random_state=54)
  # array([0, 0, 0, 0, 0, 1, 1, 1, 0, 0])
  

• Binomial Distribution: stats.binom()

  n = 10
  p = 0.3
  
  # Descriptive Statistics
  stats.binom.mean(n, p)    # np.float64(3.0)
  stats.binom.median(n, p)  # np.float64(3.0)
  stats.binom.var(n, p)     # np.float64(2.1)
  stats.binom.std(n, p)     # np.float64(1.449137674618944)
  
  # Moments
  mean, var, skew, kurt = stats.binom.stats(n, p, moments='mvsk')
  
  # Probability Mass Function
  stats.binom.pmf(k=3, n=n, p=p)  # k번 성공할 확률
  # np.float64(0.26682793199999977)
  
  # Cumulative Distribution Function
  stats.binom.cdf(k=3, n=n, p=p)
  # np.float64(0.6496107184000002)
  
  # Random Variates
  stats.binom.rvs(n, p, size=10, random_state=54)
  # array([3, 2, 2, 3, 0, 6, 4, 4, 4, 1])
  

  # 확률 변수 지정
  rv = stats.binom(n = 10, p = 0.3)
  
  # Descriptive Statistics
  rv.mean()    # np.float64(3.0)
  rv.median()  # np.float64(3.0)
  rv.var()     # np.float64(2.1)
  rv.std()     # np.float64(1.449137674618944)
  
  # Moments
  mean, var, skew, kurt = rv.stats(moments='mvsk')
  
  # Probability Mass Function
  rv.pmf(k=3)  # k번 성공할 확률
  # np.float64(0.26682793199999977)
  
  # Cumulative Distribution Function
  rv.cdf(x=3)
  # np.float64(0.6496107184000002)
  
  # Random Variates
  rv.rvs(size=10, random_state=54)
  # array([3, 2, 2, 3, 0, 6, 4, 4, 4, 1])