This page illustrates diagnostic plots provided by the ExtremePlots.jl package. These plots help assess the fit of extreme value models and explore the distribution of extreme data.
Load the required packages:
using Distributions, ExtremePlots, GadflySimulate data from a Generalized Extreme Value (GEV) distribution:
pd = GeneralizedExtremeValue(0,1,0)
y = rand(pd, 300);Displays a histogram of the data with the distribution overlay.
histplot(pd, y)
Data
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h,j,k,l,arrows,drag to pan
i,o,+,-,scroll,shift-drag to zoom
r,dbl-click to reset
c for coordinates
? for help
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Model density
Compares empirical and model probabilities.
probplot(pd, y)
Empirical probability
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h,j,k,l,arrows,drag to pan
i,o,+,-,scroll,shift-drag to zoom
r,dbl-click to reset
c for coordinates
? for help
?
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1
Model probability
Compares empirical and model quantiles.
qqplot(pd, y)
Empirical quantile
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h,j,k,l,arrows,drag to pan
i,o,+,-,scroll,shift-drag to zoom
r,dbl-click to reset
c for coordinates
? for help
?
-2
0
2
4
6
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
-2.00
-1.95
-1.90
-1.85
-1.80
-1.75
-1.70
-1.65
-1.60
-1.55
-1.50
-1.45
-1.40
-1.35
-1.30
-1.25
-1.20
-1.15
-1.10
-1.05
-1.00
-0.95
-0.90
-0.85
-0.80
-0.75
-0.70
-0.65
-0.60
-0.55
-0.50
-0.45
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
4.45
4.50
4.55
4.60
4.65
4.70
4.75
4.80
4.85
4.90
4.95
5.00
5.05
5.10
5.15
5.20
5.25
5.30
5.35
5.40
5.45
5.50
5.55
5.60
5.65
5.70
5.75
5.80
5.85
5.90
5.95
6.00
-2
0
2
4
6
Model quantile
Displays empirical and model-predicted return levels as a function of the return period.
returnlevelplot(pd, y)
Return Period
100.0
100.5
101.0
101.5
102.0
102.5
100.0
100.1
100.2
100.3
100.4
100.5
100.6
100.7
100.8
100.9
101.0
101.1
101.2
101.3
101.4
101.5
101.6
101.7
101.8
101.9
102.0
102.1
102.2
102.3
102.4
102.5
100.00
100.01
100.02
100.03
100.04
100.05
100.06
100.07
100.08
100.09
100.10
100.11
100.12
100.13
100.14
100.15
100.16
100.17
100.18
100.19
100.20
100.21
100.22
100.23
100.24
100.25
100.26
100.27
100.28
100.29
100.30
100.31
100.32
100.33
100.34
100.35
100.36
100.37
100.38
100.39
100.40
100.41
100.42
100.43
100.44
100.45
100.46
100.47
100.48
100.49
100.50
100.51
100.52
100.53
100.54
100.55
100.56
100.57
100.58
100.59
100.60
100.61
100.62
100.63
100.64
100.65
100.66
100.67
100.68
100.69
100.70
100.71
100.72
100.73
100.74
100.75
100.76
100.77
100.78
100.79
100.80
100.81
100.82
100.83
100.84
100.85
100.86
100.87
100.88
100.89
100.90
100.91
100.92
100.93
100.94
100.95
100.96
100.97
100.98
100.99
101.00
101.01
101.02
101.03
101.04
101.05
101.06
101.07
101.08
101.09
101.10
101.11
101.12
101.13
101.14
101.15
101.16
101.17
101.18
101.19
101.20
101.21
101.22
101.23
101.24
101.25
101.26
101.27
101.28
101.29
101.30
101.31
101.32
101.33
101.34
101.35
101.36
101.37
101.38
101.39
101.40
101.41
101.42
101.43
101.44
101.45
101.46
101.47
101.48
101.49
101.50
101.51
101.52
101.53
101.54
101.55
101.56
101.57
101.58
101.59
101.60
101.61
101.62
101.63
101.64
101.65
101.66
101.67
101.68
101.69
101.70
101.71
101.72
101.73
101.74
101.75
101.76
101.77
101.78
101.79
101.80
101.81
101.82
101.83
101.84
101.85
101.86
101.87
101.88
101.89
101.90
101.91
101.92
101.93
101.94
101.95
101.96
101.97
101.98
101.99
102.00
102.01
102.02
102.03
102.04
102.05
102.06
102.07
102.08
102.09
102.10
102.11
102.12
102.13
102.14
102.15
102.16
102.17
102.18
102.19
102.20
102.21
102.22
102.23
102.24
102.25
102.26
102.27
102.28
102.29
102.30
102.31
102.32
102.33
102.34
102.35
102.36
102.37
102.38
102.39
102.40
102.41
102.42
102.43
102.44
102.45
102.46
102.47
102.48
102.49
102.50
100.0
102.5
2.47856649559384054.823715688164914
2.1775364999298594.402342346746901
2.00144524087418274.390116637162636
1.87650650426588174.21207619069694
1.77959649125782464.143871954130822
1.70041524521019934.056300086235662
1.63346845557958583.7818910864853246
1.57547650860190073.764297874067387
1.52432398615451883.7617131776945687
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1.3993852495462183.420000007595399
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1.06359314762302542.7830434992022703
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1.01616849769488752.5175437971016965
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0.1481527222446525-0.3008920208321207
0.146128035678238-0.30564634636654997
0.14411274444291242-0.3127020283579354
0.1421067617453139-0.3192304090405993
0.14011000198923848-0.34327593733985784
0.13812238075372504-0.36685577457107066
0.13614381477163712-0.36788208091851693
0.1341742219087326-0.36992363641381304
0.13221352114320478-0.37592499478446656
0.13026163254568265-0.3786280578804837
0.12831847725968054-0.40035905954901707
0.12638397748248087-0.4029511605204874
0.12445805644644242-0.4124311113021034
0.12254063840072067-0.4444036263104824
0.12063164859338957-0.4449678290179241
0.11873101325395538-0.4452100043662837
0.11683865957625048-0.4775225132189956
0.11495451570169904-0.5088268015294467
0.11307851070294372-0.5089877853665498
0.11121057456782443-0.5190380672441316
0.10935063818370055-0.5281211745671426
0.10749863332210707-0.5393122699737346
0.10565449262373676-0.5415390011021232
0.1038181495837395-0.5484866575099854
0.10198953853733146-0.5518752632055772
0.10016859464570571-0.5776001797651237
0.09835525388223733-0.5840224621481309
0.09654945301897497-0.5869869196133348
0.09475112961341214-0.5902784291999603
0.09296022199553118-0.5905851091065971
0.09117666925511393-0.6038653697037683
0.08940041122931092-0.6063967107244509
0.08763138849046424-0.6305596731316452
0.08586954233417765-0.6518962559769996
0.08411481476762707-0.6781321122741698
0.08236714849810699-0.7010681553900757
0.08062648692180573-0.7014209262232383
0.07889277411280524-0.7043497574519876
0.07716595481229933-0.7061212923826949
0.07544597441802545-0.7069534249644744
0.07373277897390534-0.7069785773334737
0.0720263151598882-0.7073754112614781
0.0703265302819938-0.7080258925211749
0.06863337226254884-0.7107478754045806
0.06694678963061314-0.7371179222255723
0.06526673151259157-0.7623929199764721
0.06359314762302543-0.762984944899893
0.06192598825556238-0.7677584210491585
0.06026520427409785-0.7766229930428669
0.05861074710408545-0.7984304422696986
0.056962568724012286-0.8079825857962738
0.055320621657035496-0.8200481067755364
0.053684858962776354-0.8338200912241834
0.05205523422926808-0.8393264494443283
0.05043170156505452-0.8454492954988968
0.04881421559143535-0.8779796831901051
0.047202731434856086-0.9111552207172593
0.04559720471943765-0.9506632515013067
0.04399759155964467-0.9568214182883361
0.042403848553087264-0.9575040240844639
0.04081593277345537-0.9753002197012779
0.039233801763580683-0.9828993256187232
0.03765741352862564-0.9860077979583394
0.036086726529394764-0.9907207394172979
0.034521699675767056-0.995625630503178
0.032962292320245834-1.0055873590419604
0.03140846425162412-1.0108300998601019
0.029860175688763462-1.0354011971189334
0.02831738727448223-1.0483325338530571
0.026780060069553125-1.055147031120399
0.025248155546805692-1.0635450286289463
0.023721635585333134-1.0687048134379802
0.022200462464800376-1.0692134073022588
0.02068459885985105-1.0958018103638316
0.019174007834612487-1.1318049413797755
0.017668652837295486-1.1332282905503412
0.016168497694887256-1.1347989068478186
0.01467350660793611-1.1673043986103704
0.01318364414542507-1.2286006138881551
0.011698875239733885-1.2798138358632163
0.010219165181686122-1.2949705430212854
0.008744479615680414-1.3212691561255183
0.007274784534904772-1.3235519685797568
0.005810046276630978-1.3702913736154658
0.0043502315175880935-1.3745804156574397
0.0028953072694137072-1.6918474464973483
0.001445240874180953-1.7029145625853002
h,j,k,l,arrows,drag to pan
i,o,+,-,scroll,shift-drag to zoom
r,dbl-click to reset
c for coordinates
? for help
?
-2
0
2
4
6
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
-2.00
-1.95
-1.90
-1.85
-1.80
-1.75
-1.70
-1.65
-1.60
-1.55
-1.50
-1.45
-1.40
-1.35
-1.30
-1.25
-1.20
-1.15
-1.10
-1.05
-1.00
-0.95
-0.90
-0.85
-0.80
-0.75
-0.70
-0.65
-0.60
-0.55
-0.50
-0.45
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
4.45
4.50
4.55
4.60
4.65
4.70
4.75
4.80
4.85
4.90
4.95
5.00
5.05
5.10
5.15
5.20
5.25
5.30
5.35
5.40
5.45
5.50
5.55
5.60
5.65
5.70
5.75
5.80
5.85
5.90
5.95
6.00
-2
0
2
4
6
Return Level
Used to assess the suitability of a threshold for Peaks-Over-Threshold (POT) modeling.
mrlplot(y)
Threshold
-2
0
2
4
6
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
-2.00
-1.95
-1.90
-1.85
-1.80
-1.75
-1.70
-1.65
-1.60
-1.55
-1.50
-1.45
-1.40
-1.35
-1.30
-1.25
-1.20
-1.15
-1.10
-1.05
-1.00
-0.95
-0.90
-0.85
-0.80
-0.75
-0.70
-0.65
-0.60
-0.55
-0.50
-0.45
-0.40
-0.35
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
1.85
1.90
1.95
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
2.80
2.85
2.90
2.95
3.00
3.05
3.10
3.15
3.20
3.25
3.30
3.35
3.40
3.45
3.50
3.55
3.60
3.65
3.70
3.75
3.80
3.85
3.90
3.95
4.00
4.05
4.10
4.15
4.20
4.25
4.30
4.35
4.40
4.45
4.50
4.55
4.60
4.65
4.70
4.75
4.80
4.85
4.90
4.95
5.00
5.05
5.10
5.15
5.20
5.25
5.30
5.35
5.40
5.45
5.50
5.55
5.60
5.65
5.70
5.75
5.80
5.85
5.90
5.95
6.00
-2
0
2
4
6
h,j,k,l,arrows,drag to pan
i,o,+,-,scroll,shift-drag to zoom
r,dbl-click to reset
c for coordinates
? for help
?
-1
0
1
2
3
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
-1.00
-0.98
-0.96
-0.94
-0.92
-0.90
-0.88
-0.86
-0.84
-0.82
-0.80
-0.78
-0.76
-0.74
-0.72
-0.70
-0.68
-0.66
-0.64
-0.62
-0.60
-0.58
-0.56
-0.54
-0.52
-0.50
-0.48
-0.46
-0.44
-0.42
-0.40
-0.38
-0.36
-0.34
-0.32
-0.30
-0.28
-0.26
-0.24
-0.22
-0.20
-0.18
-0.16
-0.14
-0.12
-0.10
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
0.42
0.44
0.46
0.48
0.50
0.52
0.54
0.56
0.58
0.60
0.62
0.64
0.66
0.68
0.70
0.72
0.74
0.76
0.78
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
1.32
1.34
1.36
1.38
1.40
1.42
1.44
1.46
1.48
1.50
1.52
1.54
1.56
1.58
1.60
1.62
1.64
1.66
1.68
1.70
1.72
1.74
1.76
1.78
1.80
1.82
1.84
1.86
1.88
1.90
1.92
1.94
1.96
1.98
2.00
2.02
2.04
2.06
2.08
2.10
2.12
2.14
2.16
2.18
2.20
2.22
2.24
2.26
2.28
2.30
2.32
2.34
2.36
2.38
2.40
2.42
2.44
2.46
2.48
2.50
2.52
2.54
2.56
2.58
2.60
2.62
2.64
2.66
2.68
2.70
2.72
2.74
2.76
2.78
2.80
2.82
2.84
2.86
2.88
2.90
2.92
2.94
2.96
2.98
3.00
-1
0
1
2
3
Mean Residual Life