Table 4 Goodness of fit test results for temperature and rainfall distributions.

From: A systematic approach to modeling monthly maximum temperature and total rainfall in Kenya

Distribution

KS tests

AD tests

CvM tests

Chi square test

Information criterion

 

Statistic

p value

Statistic

p value

Statistic

p value

Statistic

p value

AIC

BIC

RMSE

(a) Temperature distributions

   Normal

0.0401

0.1202

1.4212

0.1965

0.2031

0.2617

16.3101

0.0911

2910.44

2919.99

1.3321

   LogNormal

0.0342

0.2559

1.2911

0.2353

0.1898

0.2882

16.5991

0.0837

2907.32

2916.87

1.3335

   Gamma

0.0362

0.2006

1.2962

0.2336

0.1883

0.2913

16.2235

0.0934

2907.81

2917.36

1.3324

   Weibull

0.0626

0.0021

7.7696

0.0001

1.0687

0.0017

51.381

0.0000

3012.31

3021.86

1.4798

   Uniform

0.0457

0.0517

Inf

0.0000

12.1632

0.0000

389.4772

0.0000

2954.14

2963.69

1.819

   Logistic

0.1993

0.0000

2.745

0.037

0.3695

0.0871

36.0075

0.0001

3365.02

3374.57

1.3876

   GEV

0.0297

0.4206

0.889

0.4211

0.1335

0.4442

3.5969

0.9637

2898.30

2912.63

1.5694

   GPD

1.000

0.000

Inf

0.000

237.66

0.000

Inf

0.0000

1965.84

1974.98

25.0933

(b) Rainfall distributions

   LogNormal

0.0491

0.0292

2.2209

0.0697

0.3347

0.1083

12.34

0.2628

8731.72

8741.27

69.72

   Exponential

0.2020

0.0000

58.9464

0.0000

10.6643

0.0000

198.86

0.0001

9039.54

9044.31

81.22

   Gamma

0.0594

0.0041

3.4029

0.0172

0.6878

0.0136

36.40

0.0000

8717.89

8727.44

62.96

   Weibull

0.0765

0.0001

7.6860

0.0002

1.3937

0.0003

70.78

0.0000

8762.53

8772.08

63.38

   GEV

0.0315

0.3487

1.1799

0.2753

0.1891

0.2897

17.13

0.0716

8713.87

8728.20

58.86

   GPD

0.6694

0.0000

341.7810

0.0000

68.2021

0.0000

273.02

0.0000

4286.20

4294.42

77.84

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