In [49]:
from __future__ import print_function
import thinkstats2
import thinkplot
import math
import random
import numpy as np
import pandas as pd
In [24]:
def Estimate1(n=7, m=1000):
"""Evaluates RMSE of sample mean and median as estimators.
n: sample size
m: number of iterations
"""
mu = 0
sigma = 1
means = []
medians = []
for i in range(m):
xs = [random.gauss(mu, sigma) for _ in range(n)]
xbar = np.mean(xs)
median = np.median(xs)
means.append(xbar)
medians.append(median)
if i % 100 == 0:
print(i, " iterations:")
print('Mean error for mean = ', MeanError(means, mu))
print('Mean error for median = ', MeanError(medians, mu))
print('Experiment 1')
print('rmse xbar', RMSE(means, mu))
print('rmse median', RMSE(medians, mu))
In [3]:
def RMSE(estimates, actual):
"""Computes the root mean squared error of a sequence of estimates.
estimate: sequence of numbers
actual: actual value
returns: float RMSE
"""
e2 = [(estimate-actual)**2 for estimate in estimates]
mse = np.mean(e2)
return math.sqrt(mse)
In [25]:
Estimate1(7, 10000)
0 iterations:
Mean error for mean = 0.163930647989
Mean error for median = -0.277193360771
100 iterations:
Mean error for mean = 0.0225932640312
Mean error for median = 0.0188436370281
200 iterations:
Mean error for mean = 0.0120274897561
Mean error for median = 0.0189191296009
300 iterations:
Mean error for mean = 0.00308209622623
Mean error for median = 0.0101249140768
400 iterations:
Mean error for mean = 0.0210421496495
Mean error for median = 0.0308532419184
500 iterations:
Mean error for mean = 0.0128488977334
Mean error for median = 0.0247561362641
600 iterations:
Mean error for mean = 0.00406098870778
Mean error for median = 0.00849843727575
700 iterations:
Mean error for mean = -0.0046478461556
Mean error for median = -0.00424818582617
800 iterations:
Mean error for mean = -0.00456038721257
Mean error for median = -0.00471870397491
900 iterations:
Mean error for mean = -0.00129397960676
Mean error for median = -0.00290393393922
1000 iterations:
Mean error for mean = -0.00328123430094
Mean error for median = -0.00464121441981
1100 iterations:
Mean error for mean = -0.00218285316136
Mean error for median = -0.00263593577425
1200 iterations:
Mean error for mean = -0.00370416590784
Mean error for median = -0.00443503057836
1300 iterations:
Mean error for mean = -0.000894265731013
Mean error for median = -0.00244097676342
1400 iterations:
Mean error for mean = 0.00360492502408
Mean error for median = 0.00271479858454
1500 iterations:
Mean error for mean = 0.000124103625644
Mean error for median = -0.000805279316247
1600 iterations:
Mean error for mean = -0.0031078792772
Mean error for median = -0.00258868764963
1700 iterations:
Mean error for mean = 0.000807709837379
Mean error for median = 0.00151783628577
1800 iterations:
Mean error for mean = 0.00131194434642
Mean error for median = 0.000348973171654
1900 iterations:
Mean error for mean = 0.000123088205485
Mean error for median = 0.000741544405808
2000 iterations:
Mean error for mean = -0.000363614136306
Mean error for median = 0.000293990359035
2100 iterations:
Mean error for mean = 0.000271617915215
Mean error for median = 0.000204337132387
2200 iterations:
Mean error for mean = 0.00261444541356
Mean error for median = 0.00320492033806
2300 iterations:
Mean error for mean = -0.000530780799893
Mean error for median = -0.00216852906395
2400 iterations:
Mean error for mean = -0.00206171199193
Mean error for median = -0.00273016733235
2500 iterations:
Mean error for mean = -0.00111257462636
Mean error for median = -0.00192382423416
2600 iterations:
Mean error for mean = -0.00177778185177
Mean error for median = -0.00252702861877
2700 iterations:
Mean error for mean = -0.00351945081258
Mean error for median = -0.00451034446308
2800 iterations:
Mean error for mean = -0.00436234594768
Mean error for median = -0.00743134627501
2900 iterations:
Mean error for mean = -0.00445826287825
Mean error for median = -0.00698430643934
3000 iterations:
Mean error for mean = -0.00545682473206
Mean error for median = -0.00843078499135
3100 iterations:
Mean error for mean = -0.00435066111783
Mean error for median = -0.00828380461403
3200 iterations:
Mean error for mean = -0.00732315046741
Mean error for median = -0.0107928861629
3300 iterations:
Mean error for mean = -0.00840651147263
Mean error for median = -0.0128821450044
3400 iterations:
Mean error for mean = -0.0100491153365
Mean error for median = -0.0150759061295
3500 iterations:
Mean error for mean = -0.00960422505879
Mean error for median = -0.0151313613762
3600 iterations:
Mean error for mean = -0.00806987801779
Mean error for median = -0.0139793846084
3700 iterations:
Mean error for mean = -0.0078615014912
Mean error for median = -0.0129779912299
3800 iterations:
Mean error for mean = -0.00847522929486
Mean error for median = -0.0129116167226
3900 iterations:
Mean error for mean = -0.0092363926742
Mean error for median = -0.0146424570219
4000 iterations:
Mean error for mean = -0.00972049336054
Mean error for median = -0.0157401331097
4100 iterations:
Mean error for mean = -0.00935674550377
Mean error for median = -0.0147796644146
4200 iterations:
Mean error for mean = -0.00945942059752
Mean error for median = -0.0156352543829
4300 iterations:
Mean error for mean = -0.00994020473043
Mean error for median = -0.0167781857928
4400 iterations:
Mean error for mean = -0.0105076961382
Mean error for median = -0.0173977003216
4500 iterations:
Mean error for mean = -0.0118030466691
Mean error for median = -0.0195564611044
4600 iterations:
Mean error for mean = -0.0130923174601
Mean error for median = -0.0205498345408
4700 iterations:
Mean error for mean = -0.0125941629046
Mean error for median = -0.0203371705858
4800 iterations:
Mean error for mean = -0.0117006553582
Mean error for median = -0.0187332969244
4900 iterations:
Mean error for mean = -0.0118980061272
Mean error for median = -0.0179312073204
5000 iterations:
Mean error for mean = -0.0108313387482
Mean error for median = -0.0163800078057
5100 iterations:
Mean error for mean = -0.0103876928773
Mean error for median = -0.0156260075882
5200 iterations:
Mean error for mean = -0.00992691873029
Mean error for median = -0.0148508050902
5300 iterations:
Mean error for mean = -0.00884649991078
Mean error for median = -0.0145120170083
5400 iterations:
Mean error for mean = -0.0079817942773
Mean error for median = -0.01363986804
5500 iterations:
Mean error for mean = -0.00799033733749
Mean error for median = -0.0137056552637
5600 iterations:
Mean error for mean = -0.00773844447754
Mean error for median = -0.0131373754517
5700 iterations:
Mean error for mean = -0.0076770145348
Mean error for median = -0.0128121145752
5800 iterations:
Mean error for mean = -0.00768780761088
Mean error for median = -0.0136652690127
5900 iterations:
Mean error for mean = -0.00843668591502
Mean error for median = -0.0145715744231
6000 iterations:
Mean error for mean = -0.00862482082165
Mean error for median = -0.0147521071854
6100 iterations:
Mean error for mean = -0.0092020901001
Mean error for median = -0.0145893024747
6200 iterations:
Mean error for mean = -0.00952095447649
Mean error for median = -0.0145314923662
6300 iterations:
Mean error for mean = -0.00780056399862
Mean error for median = -0.013030641261
6400 iterations:
Mean error for mean = -0.00794771293576
Mean error for median = -0.0127542411014
6500 iterations:
Mean error for mean = -0.00632689247514
Mean error for median = -0.0113746595544
6600 iterations:
Mean error for mean = -0.00559079911794
Mean error for median = -0.01022725031
6700 iterations:
Mean error for mean = -0.00661290471129
Mean error for median = -0.0111472678338
6800 iterations:
Mean error for mean = -0.00614627353355
Mean error for median = -0.0107393046986
6900 iterations:
Mean error for mean = -0.00579379177661
Mean error for median = -0.0102934446648
7000 iterations:
Mean error for mean = -0.0060065409545
Mean error for median = -0.0104888635764
7100 iterations:
Mean error for mean = -0.0052059278235
Mean error for median = -0.00939857843918
7200 iterations:
Mean error for mean = -0.0042361061634
Mean error for median = -0.00822751192857
7300 iterations:
Mean error for mean = -0.00422449819927
Mean error for median = -0.00833558178877
7400 iterations:
Mean error for mean = -0.00464391642073
Mean error for median = -0.00852215147888
7500 iterations:
Mean error for mean = -0.00451854260748
Mean error for median = -0.00887701105673
7600 iterations:
Mean error for mean = -0.00422597209142
Mean error for median = -0.00880801465995
7700 iterations:
Mean error for mean = -0.00380942720718
Mean error for median = -0.00853018741638
7800 iterations:
Mean error for mean = -0.00344473827331
Mean error for median = -0.00761395800685
7900 iterations:
Mean error for mean = -0.0034982817626
Mean error for median = -0.0076896005668
8000 iterations:
Mean error for mean = -0.0034527209981
Mean error for median = -0.0081023385364
8100 iterations:
Mean error for mean = -0.00337154816561
Mean error for median = -0.00855609532388
8200 iterations:
Mean error for mean = -0.00412049858409
Mean error for median = -0.00925580890583
8300 iterations:
Mean error for mean = -0.00391660794538
Mean error for median = -0.00882302716041
8400 iterations:
Mean error for mean = -0.00381658685189
Mean error for median = -0.00888896694519
8500 iterations:
Mean error for mean = -0.00388610819403
Mean error for median = -0.00931698484726
8600 iterations:
Mean error for mean = -0.00413039210799
Mean error for median = -0.00986426182772
8700 iterations:
Mean error for mean = -0.00439677666398
Mean error for median = -0.0101181975586
8800 iterations:
Mean error for mean = -0.00417067121612
Mean error for median = -0.00999614387586
8900 iterations:
Mean error for mean = -0.00436985733076
Mean error for median = -0.00953100197598
9000 iterations:
Mean error for mean = -0.00491913985914
Mean error for median = -0.00997031996117
9100 iterations:
Mean error for mean = -0.00447959762773
Mean error for median = -0.00946698813512
9200 iterations:
Mean error for mean = -0.0052049843778
Mean error for median = -0.00956596534439
9300 iterations:
Mean error for mean = -0.00425583786025
Mean error for median = -0.00826758190258
9400 iterations:
Mean error for mean = -0.00384491997472
Mean error for median = -0.00808968981984
9500 iterations:
Mean error for mean = -0.00324631490671
Mean error for median = -0.00747173513289
9600 iterations:
Mean error for mean = -0.00289600696521
Mean error for median = -0.00719638892437
9700 iterations:
Mean error for mean = -0.002956494322
Mean error for median = -0.00680919092361
9800 iterations:
Mean error for mean = -0.0028033146839
Mean error for median = -0.00707020239611
9900 iterations:
Mean error for mean = -0.00266416721588
Mean error for median = -0.00706317912614
Experiment 1
rmse xbar 0.378940788253
rmse median 0.456294183792
In [45]:
def Estimate2(n=7, m=1000):
"""Evaluates S and Sn-1 as estimators of sample variance.
n: sample size
m: number of iterations
"""
mu = 0
sigma = 1
estimates1 = []
estimates2 = []
for i in xrange(m):
xs = [random.gauss(mu, sigma) for _ in range(n)]
biased = np.var(xs)
unbiased = np.var(xs, ddof=1)
estimates1.append(biased)
estimates2.append(unbiased)
if i % 100 == 0:
print(i, " iterations:")
print('Mean error for S_n = ', MeanError(estimates1, sigma))
print('Mean error for S_n-1 = ', MeanError(estimates2, sigma))
print('RMSE for S_n =', RMSE(estimates1, sigma))
print('RMSE for S_n-1 =', RMSE(estimates2, sigma))
In [11]:
def MeanError(estimates, actual):
"""Computes the mean error of a sequence of estimates.
estimate: sequence of numbers
actual: actual value
returns: float mean error
"""
errors = [estimate-actual for estimate in estimates]
return np.mean(errors)
In [46]:
Estimate2(m=10000)
0 iterations:
Mean error for S_n = -0.568722564739
Mean error for S_n-1 = -0.496842992195
RMSE for S_n = 0.568722564739
RMSE for S_n-1 = 0.496842992195
100 iterations:
Mean error for S_n = -0.127294602168
Mean error for S_n-1 = 0.0181562974709
RMSE for S_n = 0.636922448408
RMSE for S_n-1 = 0.728310747717
200 iterations:
Mean error for S_n = -0.194969641874
Mean error for S_n-1 = -0.0607979155193
RMSE for S_n = 0.565771551452
RMSE for S_n-1 = 0.622610989368
300 iterations:
Mean error for S_n = -0.183274777267
Mean error for S_n-1 = -0.047153906811
RMSE for S_n = 0.579818137659
RMSE for S_n-1 = 0.643502086749
400 iterations:
Mean error for S_n = -0.179765334558
Mean error for S_n-1 = -0.0430595569849
RMSE for S_n = 0.568601071998
RMSE for S_n-1 = 0.630813784175
500 iterations:
Mean error for S_n = -0.176381523249
Mean error for S_n-1 = -0.0391117771241
RMSE for S_n = 0.552229512132
RMSE for S_n-1 = 0.611772764275
600 iterations:
Mean error for S_n = -0.171147827238
Mean error for S_n-1 = -0.033005798444
RMSE for S_n = 0.55527216961
RMSE for S_n-1 = 0.617161116041
700 iterations:
Mean error for S_n = -0.160372144846
Mean error for S_n-1 = -0.020434168987
RMSE for S_n = 0.558805766
RMSE for S_n-1 = 0.624849321699
800 iterations:
Mean error for S_n = -0.16390708797
Mean error for S_n-1 = -0.0245582692986
RMSE for S_n = 0.548966156102
RMSE for S_n-1 = 0.611739980964
900 iterations:
Mean error for S_n = -0.165113363523
Mean error for S_n-1 = -0.0259655907765
RMSE for S_n = 0.545418109992
RMSE for S_n-1 = 0.607018618865
1000 iterations:
Mean error for S_n = -0.165485581527
Mean error for S_n-1 = -0.0263998451153
RMSE for S_n = 0.540490892523
RMSE for S_n-1 = 0.600869548117
1100 iterations:
Mean error for S_n = -0.163106567652
Mean error for S_n-1 = -0.0236243289279
RMSE for S_n = 0.537205911538
RMSE for S_n-1 = 0.597620918286
1200 iterations:
Mean error for S_n = -0.160296049457
Mean error for S_n-1 = -0.0203453910334
RMSE for S_n = 0.534497768885
RMSE for S_n-1 = 0.59522546358
1300 iterations:
Mean error for S_n = -0.160234390197
Mean error for S_n-1 = -0.0202734552302
RMSE for S_n = 0.533317573667
RMSE for S_n-1 = 0.593803012182
1400 iterations:
Mean error for S_n = -0.16250260123
Mean error for S_n-1 = -0.0229197014347
RMSE for S_n = 0.530793800183
RMSE for S_n-1 = 0.589969971931
1500 iterations:
Mean error for S_n = -0.160153241801
Mean error for S_n-1 = -0.020178782101
RMSE for S_n = 0.526663049701
RMSE for S_n-1 = 0.585689978736
1600 iterations:
Mean error for S_n = -0.15446736735
Mean error for S_n-1 = -0.0135452619086
RMSE for S_n = 0.527144245902
RMSE for S_n-1 = 0.588161651072
1700 iterations:
Mean error for S_n = -0.155733851794
Mean error for S_n-1 = -0.0150228270928
RMSE for S_n = 0.522922211985
RMSE for S_n-1 = 0.582586675107
1800 iterations:
Mean error for S_n = -0.156840320035
Mean error for S_n-1 = -0.0163137067073
RMSE for S_n = 0.521438881562
RMSE for S_n-1 = 0.580403651985
1900 iterations:
Mean error for S_n = -0.156050365164
Mean error for S_n-1 = -0.0153920926918
RMSE for S_n = 0.520739954123
RMSE for S_n-1 = 0.579813901631
2000 iterations:
Mean error for S_n = -0.156453905102
Mean error for S_n-1 = -0.0158628892856
RMSE for S_n = 0.519251184193
RMSE for S_n-1 = 0.577857949446
2100 iterations:
Mean error for S_n = -0.157999528682
Mean error for S_n-1 = -0.0176661167954
RMSE for S_n = 0.516996443466
RMSE for S_n-1 = 0.574576834715
2200 iterations:
Mean error for S_n = -0.15756676035
Mean error for S_n-1 = -0.0171612204082
RMSE for S_n = 0.51617693173
RMSE for S_n-1 = 0.57371978189
2300 iterations:
Mean error for S_n = -0.159624686381
Mean error for S_n-1 = -0.0195621341106
RMSE for S_n = 0.515153136108
RMSE for S_n-1 = 0.571766495636
2400 iterations:
Mean error for S_n = -0.158568904498
Mean error for S_n-1 = -0.0183303885809
RMSE for S_n = 0.512219921401
RMSE for S_n-1 = 0.56852949897
2500 iterations:
Mean error for S_n = -0.156491700952
Mean error for S_n-1 = -0.0159069844446
RMSE for S_n = 0.511924874599
RMSE for S_n-1 = 0.568878110629
2600 iterations:
Mean error for S_n = -0.156493139513
Mean error for S_n-1 = -0.0159086627657
RMSE for S_n = 0.5102149031
RMSE for S_n-1 = 0.566782810811
2700 iterations:
Mean error for S_n = -0.158453468611
Mean error for S_n-1 = -0.0181957133798
RMSE for S_n = 0.50873050645
RMSE for S_n-1 = 0.564288665315
2800 iterations:
Mean error for S_n = -0.158979698275
Mean error for S_n-1 = -0.018809647987
RMSE for S_n = 0.507912087084
RMSE for S_n-1 = 0.56310261415
2900 iterations:
Mean error for S_n = -0.158716710216
Mean error for S_n-1 = -0.0185028285853
RMSE for S_n = 0.507641431417
RMSE for S_n-1 = 0.562861177345
3000 iterations:
Mean error for S_n = -0.157363609131
Mean error for S_n-1 = -0.0169242106529
RMSE for S_n = 0.507486771804
RMSE for S_n-1 = 0.5631387195
3100 iterations:
Mean error for S_n = -0.156695053382
Mean error for S_n-1 = -0.016144228946
RMSE for S_n = 0.506612518307
RMSE for S_n-1 = 0.56229749921
3200 iterations:
Mean error for S_n = -0.153538472316
Mean error for S_n-1 = -0.0124615510351
RMSE for S_n = 0.504774619331
RMSE for S_n-1 = 0.561138099146
3300 iterations:
Mean error for S_n = -0.152967184408
Mean error for S_n-1 = -0.0117950484766
RMSE for S_n = 0.503778931531
RMSE for S_n-1 = 0.560117219854
3400 iterations:
Mean error for S_n = -0.151702330573
Mean error for S_n-1 = -0.0103193856687
RMSE for S_n = 0.50411559675
RMSE for S_n-1 = 0.560967952675
3500 iterations:
Mean error for S_n = -0.154117793324
Mean error for S_n-1 = -0.0131374255444
RMSE for S_n = 0.503294015449
RMSE for S_n-1 = 0.559123553401
3600 iterations:
Mean error for S_n = -0.153860264632
Mean error for S_n-1 = -0.0128369754044
RMSE for S_n = 0.503949251413
RMSE for S_n-1 = 0.560015720195
3700 iterations:
Mean error for S_n = -0.153517393605
Mean error for S_n-1 = -0.0124369592057
RMSE for S_n = 0.505461000105
RMSE for S_n-1 = 0.561985735244
3800 iterations:
Mean error for S_n = -0.153477536328
Mean error for S_n-1 = -0.0123904590498
RMSE for S_n = 0.506187686484
RMSE for S_n-1 = 0.562889055945
3900 iterations:
Mean error for S_n = -0.154479628211
Mean error for S_n-1 = -0.0135595662461
RMSE for S_n = 0.505419017584
RMSE for S_n-1 = 0.561601281765
4000 iterations:
Mean error for S_n = -0.154235098692
Mean error for S_n-1 = -0.0132742818068
RMSE for S_n = 0.505161057569
RMSE for S_n-1 = 0.561369991589
4100 iterations:
Mean error for S_n = -0.153049108896
Mean error for S_n-1 = -0.0118906270458
RMSE for S_n = 0.509193190057
RMSE for S_n-1 = 0.566713723798
4200 iterations:
Mean error for S_n = -0.152213946508
Mean error for S_n-1 = -0.0109162709257
RMSE for S_n = 0.51053591002
RMSE for S_n-1 = 0.568641255892
4300 iterations:
Mean error for S_n = -0.151859915415
Mean error for S_n-1 = -0.0105032346507
RMSE for S_n = 0.510099107014
RMSE for S_n-1 = 0.568228607997
4400 iterations:
Mean error for S_n = -0.150950051945
Mean error for S_n-1 = -0.0094417272686
RMSE for S_n = 0.509887969015
RMSE for S_n-1 = 0.568282025522
4500 iterations:
Mean error for S_n = -0.150470664026
Mean error for S_n-1 = -0.00888244136401
RMSE for S_n = 0.51060417386
RMSE for S_n-1 = 0.569320384304
4600 iterations:
Mean error for S_n = -0.149534448057
Mean error for S_n-1 = -0.00779018939968
RMSE for S_n = 0.51130821523
RMSE for S_n-1 = 0.570498957647
4700 iterations:
Mean error for S_n = -0.148242723545
Mean error for S_n-1 = -0.00628317746891
RMSE for S_n = 0.511913080773
RMSE for S_n-1 = 0.571676311421
4800 iterations:
Mean error for S_n = -0.148145506796
Mean error for S_n-1 = -0.00616975792827
RMSE for S_n = 0.511683085742
RMSE for S_n-1 = 0.571429064723
4900 iterations:
Mean error for S_n = -0.1468705737
Mean error for S_n-1 = -0.00468233598284
RMSE for S_n = 0.512925402796
RMSE for S_n-1 = 0.573375554188
5000 iterations:
Mean error for S_n = -0.147055803459
Mean error for S_n-1 = -0.00489843736933
RMSE for S_n = 0.512403675736
RMSE for S_n-1 = 0.572677375968
5100 iterations:
Mean error for S_n = -0.147281647474
Mean error for S_n-1 = -0.00516192205289
RMSE for S_n = 0.511489616287
RMSE for S_n-1 = 0.571487257714
5200 iterations:
Mean error for S_n = -0.149746747689
Mean error for S_n-1 = -0.00803787230335
RMSE for S_n = 0.510892769921
RMSE for S_n-1 = 0.569919712374
5300 iterations:
Mean error for S_n = -0.149060746267
Mean error for S_n-1 = -0.00723753731096
RMSE for S_n = 0.510891975364
RMSE for S_n-1 = 0.570152744309
5400 iterations:
Mean error for S_n = -0.148448264209
Mean error for S_n-1 = -0.00652297491049
RMSE for S_n = 0.511020204525
RMSE for S_n-1 = 0.570517920725
5500 iterations:
Mean error for S_n = -0.149834870784
Mean error for S_n-1 = -0.0081406825816
RMSE for S_n = 0.509761760604
RMSE for S_n-1 = 0.568509439606
5600 iterations:
Mean error for S_n = -0.150020757446
Mean error for S_n-1 = -0.00835755035366
RMSE for S_n = 0.511198413765
RMSE for S_n-1 = 0.570199197389
5700 iterations:
Mean error for S_n = -0.150889953931
Mean error for S_n-1 = -0.00937161291927
RMSE for S_n = 0.511653353052
RMSE for S_n-1 = 0.570458129141
5800 iterations:
Mean error for S_n = -0.150297408534
Mean error for S_n-1 = -0.00868030995649
RMSE for S_n = 0.511557070846
RMSE for S_n-1 = 0.570542565371
5900 iterations:
Mean error for S_n = -0.150793500289
Mean error for S_n-1 = -0.00925908367062
RMSE for S_n = 0.511116188426
RMSE for S_n-1 = 0.569835237918
6000 iterations:
Mean error for S_n = -0.148134775307
Mean error for S_n-1 = -0.00615723785816
RMSE for S_n = 0.513352802062
RMSE for S_n-1 = 0.573467450775
6100 iterations:
Mean error for S_n = -0.148275618745
Mean error for S_n-1 = -0.00632155520259
RMSE for S_n = 0.513658276024
RMSE for S_n-1 = 0.573791913003
6200 iterations:
Mean error for S_n = -0.147810371834
Mean error for S_n-1 = -0.00577876713939
RMSE for S_n = 0.514099928026
RMSE for S_n-1 = 0.57448752182
6300 iterations:
Mean error for S_n = -0.147025721942
Mean error for S_n-1 = -0.0048633422656
RMSE for S_n = 0.513679829507
RMSE for S_n-1 = 0.574241559888
6400 iterations:
Mean error for S_n = -0.149866937988
Mean error for S_n-1 = -0.0081780943194
RMSE for S_n = 0.513617943266
RMSE for S_n-1 = 0.573203208556
6500 iterations:
Mean error for S_n = -0.150927606137
Mean error for S_n-1 = -0.00941554049343
RMSE for S_n = 0.513530702284
RMSE for S_n-1 = 0.572736822471
6600 iterations:
Mean error for S_n = -0.149281470691
Mean error for S_n-1 = -0.00749504913923
RMSE for S_n = 0.514703619935
RMSE for S_n-1 = 0.574725306673
6700 iterations:
Mean error for S_n = -0.148908882831
Mean error for S_n-1 = -0.00706036330321
RMSE for S_n = 0.514580899973
RMSE for S_n-1 = 0.574701789061
6800 iterations:
Mean error for S_n = -0.149302375209
Mean error for S_n-1 = -0.00751943774378
RMSE for S_n = 0.514126942133
RMSE for S_n-1 = 0.574015240453
6900 iterations:
Mean error for S_n = -0.147159952739
Mean error for S_n-1 = -0.00501994486171
RMSE for S_n = 0.515731376171
RMSE for S_n-1 = 0.576693747621
7000 iterations:
Mean error for S_n = -0.146945978226
Mean error for S_n-1 = -0.00477030793013
RMSE for S_n = 0.515425249097
RMSE for S_n-1 = 0.576393299555
7100 iterations:
Mean error for S_n = -0.147631956407
Mean error for S_n-1 = -0.0055706158086
RMSE for S_n = 0.514902982018
RMSE for S_n-1 = 0.575525884493
7200 iterations:
Mean error for S_n = -0.148074633779
Mean error for S_n-1 = -0.00608707274273
RMSE for S_n = 0.515460705825
RMSE for S_n-1 = 0.576055609544
7300 iterations:
Mean error for S_n = -0.147571091863
Mean error for S_n-1 = -0.00549960717293
RMSE for S_n = 0.515790747545
RMSE for S_n-1 = 0.57662739224
7400 iterations:
Mean error for S_n = -0.148056622205
Mean error for S_n-1 = -0.00606605923918
RMSE for S_n = 0.515060838776
RMSE for S_n-1 = 0.575574664611
7500 iterations:
Mean error for S_n = -0.148878206078
Mean error for S_n-1 = -0.0070245737582
RMSE for S_n = 0.514710225803
RMSE for S_n-1 = 0.574869775728
7600 iterations:
Mean error for S_n = -0.148352231035
Mean error for S_n-1 = -0.00641093620694
RMSE for S_n = 0.514860795087
RMSE for S_n-1 = 0.57523108987
7700 iterations:
Mean error for S_n = -0.146861618577
Mean error for S_n-1 = -0.00467188834014
RMSE for S_n = 0.514500551392
RMSE for S_n-1 = 0.575296237499
7800 iterations:
Mean error for S_n = -0.146942308371
Mean error for S_n-1 = -0.00476602643324
RMSE for S_n = 0.514013901944
RMSE for S_n-1 = 0.574676526428
7900 iterations:
Mean error for S_n = -0.146228926069
Mean error for S_n-1 = -0.00393374708067
RMSE for S_n = 0.514105866115
RMSE for S_n-1 = 0.575029764257
8000 iterations:
Mean error for S_n = -0.145732282038
Mean error for S_n-1 = -0.00335432904379
RMSE for S_n = 0.514209162285
RMSE for S_n-1 = 0.575323341884
8100 iterations:
Mean error for S_n = -0.145726344738
Mean error for S_n-1 = -0.00334740219476
RMSE for S_n = 0.514529359066
RMSE for S_n-1 = 0.575714864306
8200 iterations:
Mean error for S_n = -0.145518891675
Mean error for S_n-1 = -0.00310537362088
RMSE for S_n = 0.514347864585
RMSE for S_n-1 = 0.575564169627
8300 iterations:
Mean error for S_n = -0.146730701387
Mean error for S_n-1 = -0.00451915161866
RMSE for S_n = 0.514403311441
RMSE for S_n-1 = 0.575222125087
8400 iterations:
Mean error for S_n = -0.146555567677
Mean error for S_n-1 = -0.00431482895632
RMSE for S_n = 0.514285910557
RMSE for S_n-1 = 0.575138436103
8500 iterations:
Mean error for S_n = -0.14665129142
Mean error for S_n-1 = -0.00442650665651
RMSE for S_n = 0.514208130107
RMSE for S_n-1 = 0.575011400188
8600 iterations:
Mean error for S_n = -0.144867816155
Mean error for S_n-1 = -0.00234578551414
RMSE for S_n = 0.514406193079
RMSE for S_n-1 = 0.575855002396
8700 iterations:
Mean error for S_n = -0.145062593088
Mean error for S_n-1 = -0.00257302526912
RMSE for S_n = 0.514459514416
RMSE for S_n-1 = 0.575854068692
8800 iterations:
Mean error for S_n = -0.144723277161
Mean error for S_n-1 = -0.00217715668842
RMSE for S_n = 0.514748467809
RMSE for S_n-1 = 0.576319919601
8900 iterations:
Mean error for S_n = -0.145116641368
Mean error for S_n-1 = -0.00263608159632
RMSE for S_n = 0.514340290812
RMSE for S_n-1 = 0.575690836776
9000 iterations:
Mean error for S_n = -0.144720969071
Mean error for S_n-1 = -0.00217446391561
RMSE for S_n = 0.515086048676
RMSE for S_n-1 = 0.576731081963
9100 iterations:
Mean error for S_n = -0.145092604981
Mean error for S_n-1 = -0.0026080391444
RMSE for S_n = 0.515252983923
RMSE for S_n-1 = 0.576808743695
9200 iterations:
Mean error for S_n = -0.145199440131
Mean error for S_n-1 = -0.0027326801533
RMSE for S_n = 0.51552129256
RMSE for S_n-1 = 0.577098965834
9300 iterations:
Mean error for S_n = -0.145673776899
Mean error for S_n-1 = -0.00328607304867
RMSE for S_n = 0.5155261718
RMSE for S_n-1 = 0.576945057565
9400 iterations:
Mean error for S_n = -0.145359046945
Mean error for S_n-1 = -0.00291888810229
RMSE for S_n = 0.515781934233
RMSE for S_n-1 = 0.577362117333
9500 iterations:
Mean error for S_n = -0.145640599478
Mean error for S_n-1 = -0.00324736605723
RMSE for S_n = 0.515401562483
RMSE for S_n-1 = 0.576804688858
9600 iterations:
Mean error for S_n = -0.145778950212
Mean error for S_n-1 = -0.00340877524716
RMSE for S_n = 0.515271486333
RMSE for S_n-1 = 0.576599832924
9700 iterations:
Mean error for S_n = -0.144830406516
Mean error for S_n-1 = -0.00230214093584
RMSE for S_n = 0.515306579683
RMSE for S_n-1 = 0.576962279503
9800 iterations:
Mean error for S_n = -0.145681770682
Mean error for S_n-1 = -0.00329539912924
RMSE for S_n = 0.514863834912
RMSE for S_n-1 = 0.576136771642
9900 iterations:
Mean error for S_n = -0.145657790875
Mean error for S_n-1 = -0.00326742268732
RMSE for S_n = 0.514846750497
RMSE for S_n-1 = 0.576124084245
In [23]:
!python --version
Python 2.7.10 :: Anaconda 2.3.0 (x86_64)
In [57]:
def Estimate3(n=7, m=1000):
"""Evaluates L and Lm as estimators of the exponential parameter.
n: sample size
m: number of iterations
"""
lam = 2
means = []
medians = []
for _ in range(m):
xs = np.random.exponential(1.0/lam, n)
L = 1 / np.mean(xs)
Lm = math.log(2) / np.median(xs)
means.append(L)
medians.append(Lm)
return means
print('Experiment 3:', m, 'iterations')
print('rmse L', RMSE(means, lam))
print('rmse Lm', RMSE(medians, lam))
print('mean error L', MeanError(means, lam))
print('mean error Lm', MeanError(medians, lam))
In [58]:
L_dist = Estimate3(10, 1000)
In [50]:
%matplotlib inline
In [60]:
thinkplot.Plot(L_dist)
In [59]:
print(L_dist)
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1.1338474840862853, 1.3363575640588972, 1.3736103387353715, 2.4122623231377793, 1.2522224458130513, 1.6128943045311828, 2.1473003571789722, 1.5412699908324479, 2.2006777762710712, 1.7195950258668824, 1.7361595753906633, 2.872294594117311, 2.7035426651993419, 2.0516467075340974, 2.1644043958757528, 1.6178811732284393, 2.0904272221165705, 1.7471512979633415, 2.4618922165363144, 1.9990912074032416, 3.3934239912283157, 1.8742673224901238, 3.5311023320869075, 2.0257018283483914, 1.9071306797472811, 1.430893816065111, 2.7830089176731505, 2.5093474845933081, 1.7776616853271712, 2.1766551108121028, 1.4217152264875266, 1.6539015826027352, 2.0131044801263891, 1.7349579638179873, 2.0482481783100308, 2.1514035492587786, 3.2599971747040795, 2.3993622992087702, 2.589120927703437, 2.3944299327282184, 4.4717121542523195, 1.8151258874444249, 3.6671630701646327, 1.4710250761608377, 4.5533518036457314, 2.9176290001818459, 2.033202580717119, 2.4104667879658548, 4.6459939096267027, 2.2805520584697012, 1.8990462343982912, 1.8415355468866135, 2.0554065643452817, 2.29733687134026, 1.6806685285554861, 2.4818952043887936, 2.0618979031412898, 2.1561563888830304, 1.2501537821626929, 2.4585433730528221, 2.9882577958278982, 1.9130227409509268, 1.8341739302148687, 2.0119488228528315, 3.0585560732266295, 2.2356532990296647, 0.9992068825962388, 2.1084076290801286, 2.8324349588113429, 2.7116617306886295, 1.9568221889884183, 2.4519527302208348, 3.2265355412541643, 2.836909862584037, 2.8216462392599873, 1.7509352812006631, 2.3378176124049697, 1.812641363425775, 1.8509710816426934, 1.4182260971433724, 3.1558725981542368, 2.5018421949265663, 1.6938384089674943, 1.4778870767888335, 1.6846088803778574, 1.886820286058811, 2.185721812983199, 1.7814937543720695, 2.4013264702004689, 1.7815308125484024, 3.3108325018684188, 2.1652307705651603, 2.0496930324808997, 2.0277313418698264, 1.4602296590350479, 1.0113945575569581, 1.703628846437508, 2.3692793947585709, 1.7750836204258247, 1.9843563571769924, 1.5371186386884803, 1.1065154437366269, 1.4826802170300384, 3.2079770489046138, 2.2963361075909421, 2.1440269143286566, 2.4747812669844627, 1.7401357505459192, 1.1450234047425238, 2.1949456542390644, 1.3057102452052523, 4.3135618946991023, 1.2480880208285685, 1.8358193639475473, 2.1055996822185343, 2.2960226639333507, 1.68197280394209, 2.0216594022942491, 3.1729666206613971, 1.6872801160947679, 1.4673931405479557, 1.9347969840202037, 2.1672058317727134, 1.7865161236330518, 2.0950363275564294, 2.2638967615373207, 3.004235572442687, 1.2767363357065609, 1.1971531222932925, 5.4357559692300015, 2.7247772942141268, 1.9916773447028198, 1.9487986267018702, 2.5137071977174159, 2.0728789772870893, 1.9868448006142996, 1.6926464723028281, 1.813903553369967, 1.5647808758568007, 2.0297824916889877, 3.4818098398170654, 1.7457154925253313, 2.2690237338899317, 1.5170210337259791, 1.9917107345318574, 0.98877047085004854, 3.0889480248500205, 4.1642864446674839, 1.416670670495277, 2.383081364297583, 2.0229707529971894, 1.7781295931366563, 1.8570756894600324, 1.9941716846024384, 2.7530911965599691, 2.5082037206328338, 1.6335495158909235, 2.4105857749917181, 1.7426141220918929, 1.9486543202662276, 1.0742712683929656, 2.3904350306478634, 2.3622563817506141, 1.6090434378778753, 2.6874863847354349, 5.7400246023064305, 2.2566477908862064, 1.5734823384364365, 1.6199723947354476, 1.7540489909776684, 3.230679198320654, 1.2543488367917162, 1.9182172153992274, 2.3084903717554393, 2.8761730147431352, 1.700034760869662, 3.4456278590089364, 2.3057128732970837, 1.3103258810687795, 2.5849698821945739, 1.585243921420467, 1.9733790817602366, 3.0417397150476599, 2.1677271164042087, 2.2978351215421142, 3.320558880027026, 5.52204889867666, 1.7711695647249428, 2.2386440820338276, 2.3910319247315335, 1.7552688774646332, 2.3591338701841051, 2.2717823303823739, 2.2071943167599373, 3.2787299994718611, 1.8444158546148792, 2.7398324045008411, 1.3604106299019549, 1.7992957132887331, 2.3043430861457188, 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In [61]:
L_cdf = thinkstats2.Cdf(L_dist)
thinkplot.Cdf(L_cdf)
Out[61]:
{'xscale': 'linear', 'yscale': 'linear'}
In [62]:
L_cdf.Percentile(5)
Out[62]:
1.2631468729214126
In [63]:
L_cdf.Percentile(95)
Out[63]:
3.5808095664573094
In [68]:
st_errs = []
conf_ints = []
for i in xrange(5, 100, 5):
L_dist = Estimate3(i, 1000)
st_err = RMSE(L_dist, 2)
L_cdf = thinkstats2.Cdf(L_dist)
conf_int = L_cdf.Percentile(95) - L_cdf.Percentile(5)
st_errs.append(st_err)
conf_ints.append(conf_int)
thinkplot.Plot(xrange(5, 100, 5), st_errs, label='Standard Error')
thinkplot.Plot(xrange(5, 100, 5), conf_ints, label='Confidence Interval')
thinkplot.Show()
<matplotlib.figure.Figure at 0x108cee8d0>
In [ ]:
Content source: Nathx/think_stats
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