SKKU-통계 by SGLee

기초통계 관련 Sage 명령어 정리 by SGLee

1. mean(v) # v는 list. 평균

2. median(v) # v는 list. 중앙값

3. mode(v) # v는 list. 최빈값

4. moving_average(v, n) # 이동평균

sage: moving_average([1..10], 1)

[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

sage: moving_average([1..10], 4)

[5/2, 7/2, 9/2, 11/2, 13/2, 15/2, 17/2]

sage: moving_average([], 1)

[]

sage: moving_average([pi, e, I, sqrt(2), 3/5], 2)

[1/2*pi + 1/2*e, 1/2*e + 1/2*I, 1/2*sqrt(2) + 1/2*I, 1/2*sqrt(2) + 3/10]

5. std(v, bias=False) # 표준편차

sage: std([1..6], bias=True)

1/2*sqrt(35/3)

sage: std([1..6], bias=False)

sqrt(7/2)

sage: std([e, pi])

sqrt(1/2)*sqrt((pi - e)^2)

sage: std([])

NaN

sage: std([I, sqrt(2), 3/5])

sqrt(1/450*(10*sqrt(2) - 5*I - 3)^2 + 1/450*(5*sqrt(2) - 10*I + 3)^2 + 1/450*(5*sqrt(2) + 5*I - 6)^2)

sage: std([RIF(1.0103, 1.0103), RIF(2)])

0.6998235813403261?

6. variance(v, bias=False) # 분산

sage: variance([1..6])

7/2

sage: variance([1..6], bias=True)

35/12

sage: variance([e, pi])

1/2*(pi - e)^2

sage: variance([])

NaN

sage: variance([I, sqrt(2), 3/5])

1/450*(10*sqrt(2) - 5*I - 3)^2 + 1/450*(5*sqrt(2) - 10*I + 3)^2 + 1/450*(5*sqrt(2) + 5*I - 6)^2

sage: variance([RIF(1.0103, 1.0103), RIF(2)])

0.4897530450000000?

 7. GeneralDiscreteDistribution(P) # P는 확률 list. 이산확률분포 생성

sage: P = [0.3, 0.4, 0.3] # P(0)=0.3, P(1)=0.4, P(2)=0.3

sage: X = GeneralDiscreteDistribution(P)

sage: X.get_random_element() # random

2

sage: from sage.gsl.probability_distribution import GeneralDiscreteDistribution

sage: P = [0.3, 0.4, 0.3]

sage: X = GeneralDiscreteDistribution(P)

sage: h, b = X.generate_histogram_data(bins = 10) # histogram data 생성

sage: h # random

[1.5249999999999995, 0.0, 0.0, 0.0, 0.0, 1.8649999999999995, 0.0, 0.0, 0.0, 1.6099999999999994]

sage: b # random

[0.0, 0.20000000000000001, 0.40000000000000002, 0.60000000000000009, 0.80000000000000004, 1.0, 1.2000000000000002, 1.4000000000000001, 1.6000000000000001, 1.8, 2.0]

8. # 균등분포 Uniform distribution on the interval [a, b]:

sage: a = 0

sage: b = 2

sage: T = RealDistribution('uniform', [a, b])

sage: T.get_random_element() # random

0.416921074037

sage: T.distribution_function(0)

0.5

sage: T.cum_distribution_function(1)

0.5

sage: T.cum_distribution_function_inv(.5)

1.0

9. 가우스 분포 The standard gaussian distribution has sigma = 1:

sage: sigma = 1

sage: T = RealDistribution('gaussian', sigma)

sage: T.get_random_element() # random

0.818610064197

sage: T.distribution_function(0)

0.398942280401

sage: T.cum_distribution_function(1)

0.841344746069

sage: T.cum_distribution_function_inv(.5)

0.0

10. t-분포 The t-distribution has one parameter nu:

sage: nu = 1

sage: T = RealDistribution('t', nu)

sage: T.get_random_element() # random

-0.994514581164

sage: T.distribution_function(0)

0.318309886184

sage: T.cum_distribution_function(1)

0.75

sage: T.cum_distribution_function_inv(.5)

0.0

11. F-분포 The F-distribution has two parameters nu1 and nu2:

sage: nu1 = 9; nu2 = 17

sage: F = RealDistribution('F', [nu1,nu2])

sage: F.get_random_element() # random

1.65211335491

sage: F.distribution_function(1)

0.669502550519

sage: F.cum_distribution_function(3.68)

0.98997177723

sage: F.cum_distribution_function_inv(0.99)

3.68224152405

12. 카이제곱분포 The chi-squared distribution has one parameter nu:

sage: nu = 1

sage: T = RealDistribution('chisquared', nu)

sage: T.get_random_element() # random

0.103230507883

sage: T.distribution_function(0)

+infinity

sage: T.cum_distribution_function(1)

0.682689492137

sage: T.cum_distribution_function_inv(.5)

0.45493642312

13. 지수분포 The exponential power distribution has two parameters a and b:

sage: a = 1

sage: b = 2.5

sage: T = RealDistribution('exppow', [a, b])

sage: T.get_random_element() # random

0.570108609774

sage: T.distribution_function(0)

0.563530248993

sage: T.cum_distribution_function(1)

0.940263052543

14. 회귀직선 

R = [[1,2],[3.45,4],[6,5],[4,3]]

http://sage.math.canterbury.ac.nz/home/pub/76/

http://sage.math.canterbury.ac.nz/home/pub/72/