Analisis Outlier, Hujan Rerata, Analisis Frekuensi, Hujan & Debit Rencana [PDF]

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Data Hujan Harian Maksimum No



Tahun



1 2 3 4 5 6 7 8 9 10



2002 2003 2004 2005 2006 2007 2008 2009 2010 2011



11 12 13 14 15



2012 2013 2014 2015 2016



Koefisien Skewness (Cs log)



Hujan Harian Maksimum (mm) Stasiun 1 Stasiun 2 Stasiun 3 Stasiun 4 Stasiun 5 55 62 57 49 52 187 160 110 101 165 134 130 108 90 133 150 155 105 88 145 157 152 100 83 155 133 140 98 90 138 140 144 95 93 135 138 131 99 97 130 129 125 93 86 120 117 113 95 89 119 110 105 99 101 231



102 100 94 140 240



100 105 110 125 200



95 100 108 119 187



107 106 89 187 191



�_𝑙𝑜𝑔=√(1/((𝑛−1)) ∑_(�=1)^�▒(����_�−(����)   )^3 )



〖��〗 _log 〖 = (�∑24_(�=1)^�▒(����_�− (����)   )^3 )/((�−1)(�−2) 〖 (�_���) 〗 ^3 ) 〗



Analisa Outlier Stasiun 1 Data (Seri X) 1 55 2 187 3 134 4 150 5 157 6 133 7 140 8 138 9 129 10 117 11 110 12 105 13 99 14 101 15 231 Ʃ 1986 Average 132.4 Rank



Data (Seri Y) Data (Y-Ȳ) (Y-Ȳ)² (Y-Ȳ)³ diurutkan Y = Log X 1.740 2.364 0.262 0.0686 0.0180 2.272 2.272 0.170 0.0289 0.0049 2.127 2.196 0.094 0.0089 0.0008 2.176 2.176 0.074 0.0055 0.0004 2.196 2.146 0.044 0.0020 0.0001 2.124 2.140 0.038 0.0015 0.0001 2.146 2.127 0.025 0.0006 0.0000 2.140 2.124 0.022 0.0005 0.0000 2.111 2.111 0.009 0.0001 0.0000 2.068 2.068 -0.034 0.0011 0.0000 2.041 2.041 -0.060 0.0036 -0.0002 2.021 2.021 -0.081 0.0065 -0.0005 1.996 2.004 -0.097 0.0095 -0.0009 2.004 1.996 -0.106 0.0113 -0.0012 2.364 1.740 -0.361 0.1306 -0.0472 31.526 0.279 -0.026 2.102 �_𝑙𝑜𝑔=√(1/((𝑛−1)) ∑_(�=1)^�▒(����_�−(����)   )^3 )



〖��〗 _ 〖 log 〗〖 = (�∑24_(�=1)^�▒(����_�−(����)   )^3 )/ ((�−1)(�−2) 〖 (�_���) 〗 ^3 ) 〗 �_𝑙𝑜𝑔= 〖��〗 _log -0.755125 〖 = 〗



0.141204



Jadi Cs log < -0.4 Uji Outlier rendah :



n=



log 〖�𝑙 = (𝑙𝑜𝑔�)  ̅ 〗−�𝑛 ∗ � _𝑙𝑜𝑔



15



�𝑛=(−3.62201)+( 〖 6.28446 𝑛 〗 ^(1/4) )−( 〖 2.49835 𝑛 〗 ^(1/2) )+( 〖 0.491436 𝑛 〗 ^(3/4) )-(0.037911 𝑛) kn = 2.247 log Xl = 1.784490 Xl = 60.88 Data di check terhadap Xl Data (Seri X)



Rank 1



Data (Seri X)



Rank



55



1



60.88



2 3 4 5 6 7 8 9 10 11 12 13 14



187 134 150 157 133 140 138 129 117 110 105 99 101



2 3 4 5 6 7 8 9 10 11 12 13 14



187 134 150 157 133 140 138 129 117 110 105 99 101



15



231



15



231



Analisis Parameter Statistik Data Terkoreksi Rendah Data Data (Seri Y) Data Rank (Y-Ȳ) diurutkan (Seri X) Y = Log X 1 60.882137 1.784 2.364 0.259 2 187 2.272 2.272 0.167 3 134 2.127 2.196 0.091 4 150 2.176 2.176 0.071 5 157 2.196 2.146 0.041 6 133 2.124 2.140 0.035 7 140 2.146 2.127 0.022 8 138 2.140 2.124 0.019 9 129 2.111 2.111 0.006 10 117 2.068 2.068 -0.036 11 110 2.041 2.041 -0.063 12 105 2.021 2.021 -0.083 13 99 1.996 2.004 -0.100 14 101 2.004 1.996 -0.109 15 231 2.364 1.784 -0.320 Ʃ 1991.8821 31.570 Average 132.79214 2.105 �_𝑙𝑜𝑔=



0.13338



Uji Outlier Tinggi : log 〖�𝑙 = (𝑙𝑜𝑔�)  ̅ 〗 +�𝑛 ∗ �_𝑙𝑜𝑔



n= kn =



15 2.247



(Y-Ȳ)²



(Y-Ȳ)³



0.0670 0.0279 0.0083 0.0051 0.0017 0.0012 0.0005 0.0004 0.0000 0.0013 0.0040 0.0070 0.0101 0.0119 0.1025 0.249



0.0174 0.0047 0.0008 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0003 -0.0006 -0.0010 -0.0013 -0.0328 -0.013



log Xh = Xh =



2.404 253.72



Data di Check terhadap Xh : Data hasil Koreksi Outlier Rendah Data Rank (Seri X) 1 60.882137 2 187 3 134 4 150 5 157 6 133 7 140 8 138 9 129 10 117 11 110 12 105 13 99 14 101 15 231



Xh =



253.72 Data hasil Koreksi Outlier Tinggi Data Rank (Seri X) 1 60.882137 2 187 3 134 4 150 5 157 6 133 7 140 8 138 9 129 10 117 11 110 12 105 13 99 14 101 15 231



Hasil Koreksi Outlier tidak ada perubahan Data hasil koreksi outlier, yang akan digunakan dalam analisis selanjutnya No 1 2 3 4 5 6 7 8 9 10 11 12 13



Data 60.88 187 134 150 157 133 140 138 129 117 110 105 99



14 15



101 231



4) )-(0.037911 𝑛)



Analisa Outlier Stasiun 2 Data Data (Seri Y) Data (Y-Ȳ) (Y-Ȳ)² (Y-Ȳ)³ diurutkan (Seri X) Y = Log X 1 62 1.792 2.380 0.276 0.0762 0.0210 2 160 2.204 2.204 0.100 0.0100 0.0010 3 130 2.114 2.190 0.086 0.0074 0.0006 4 155 2.190 2.182 0.078 0.0060 0.0005 5 152 2.182 2.158 0.054 0.0029 0.0002 6 140 2.146 2.146 0.042 0.0018 0.0001 7 144 2.158 2.146 0.042 0.0018 0.0001 8 131 2.117 2.117 0.013 0.0002 0.0000 9 125 2.097 2.114 0.010 0.0001 0.0000 10 113 2.053 2.097 -0.007 0.0001 0.0000 11 102 2.009 2.053 -0.051 0.0026 -0.0001 12 100 2.000 2.009 -0.096 0.0091 -0.0009 13 94 1.973 2.000 -0.104 0.0108 -0.0011 14 140 2.146 1.973 -0.131 0.0172 -0.0022 15 240 2.380 1.792 -0.312 0.0972 -0.0303 Ʃ 1988 31.562 0.243 -0.011 Average 132.5333 2.104 �_𝑙𝑜𝑔=√(1/((𝑛−1)) ∑_(𝑖=1)^𝑛▒(𝐿𝑜𝑔�_𝑖−(𝐿𝑜𝑔�)  ̅ )^3 ) Rank



〖��〗 _ 〖 log 〗〖 = (𝑛∑_(𝑖=1)^𝑛▒(𝐿𝑜𝑔�_𝑖−(𝐿𝑜𝑔�)  ̅ ) ^3 )/((𝑛−1)(𝑛−2) 〖 (�_𝑙𝑜𝑔) 〗 ^3 ) 〗 �_𝑙𝑜𝑔= 〖��〗 _log ### 〖 = 〗



0.131854



Jadi Cs log < -0.4 Uji Outlier rendah :



n=



log 〖�𝑙 = (𝑙𝑜𝑔�)  ̅ 〗−�𝑛 ∗ � _𝑙𝑜𝑔



15



�𝑛=(−3.62201)+( 〖 6.28446 𝑛 〗 ^(1/4) )−( 〖 2.49835 𝑛 〗 ^(1/2) )+( 〖 0.491436 𝑛 〗 ^(3/4) )-(0.037911 𝑛) kn = 2.247 log Xl = 1.807921 Xl = 64.26 Data di check terhadap Xl Data (Seri X)



Rank 1



Data (Seri X)



Rank



62



1



64.26



2 3 4 5 6 7 8 9 10 11 12 13 14



160 130 155 152 140 144 131 125 113 102 100 94 140



2 3 4 5 6 7 8 9 10 11 12 13 14



160 130 155 152 140 144 131 125 113 102 100 94 140



15



240



15



240



Analisis Parameter Statistik Data Terkoreksi Rendah Data Data (Seri Y) Data Rank (Y-Ȳ) diurutkan (Seri X) Y = Log X 1 64.25707 1.808 2.380 0.275 2 160 2.204 2.204 0.099 3 130 2.114 2.190 0.085 4 155 2.190 2.182 0.077 5 152 2.182 2.158 0.053 6 140 2.146 2.146 0.041 7 144 2.158 2.146 0.041 8 131 2.117 2.117 0.012 9 125 2.097 2.114 0.009 10 113 2.053 2.097 -0.008 11 102 2.009 2.053 -0.052 12 100 2.000 2.009 -0.097 13 94 1.973 2.000 -0.105 14 140 2.146 1.973 -0.132 15 240 2.380 1.808 -0.297 Ʃ 1990.257 31.578 Average 132.6838 2.105 �_𝑙𝑜𝑔=



0.12927



Uji Outlier Tinggi : log 〖�𝑙 = (𝑙𝑜𝑔�)  ̅ 〗 +�𝑛 ∗ �_𝑙𝑜𝑔



n= kn =



15 2.247



(Y-Ȳ)²



(Y-Ȳ)³



0.0756 0.0098 0.0072 0.0059 0.0028 0.0017 0.0017 0.0001 0.0001 0.0001 0.0027 0.0093 0.0111 0.0174 0.0884 0.234



0.0208 0.0010 0.0006 0.0005 0.0002 0.0001 0.0001 0.0000 0.0000 0.0000 -0.0001 -0.0009 -0.0012 -0.0023 -0.0263 -0.008



log Xh = Xh =



2.396 248.67



Data di Check terhadap Xh : Data hasil Koreksi Outlier Rendah Data Rank (Seri X) 1 64.25707 2 160 3 130 4 155 5 152 6 140 7 144 8 131 9 125 10 113 11 102 12 100 13 94 14 140 15 240



Xh =



248.67 Data hasil Koreksi Outlier Tinggi Data Rank (Seri X) 1 64.25707 2 160 3 130 4 155 5 152 6 140 7 144 8 131 9 125 10 113 11 102 12 100 13 94 14 140 15 240



Hasil Koreksi Outlier tidak ada perubahan Data hasil koreksi outlier, yang akan digunakan dalam analisis selanjutnya No 1 2 3 4 5 6 7 8 9 10 11 12 13



Data 64.26 160 130 155 152 140 144 131 125 113 102 100 94



14 15



140 240



) )-(0.037911 𝑛)



Analisa Outlier Stasiun 3 Data Data (Seri Y) Data (Y-Ȳ) (Y-Ȳ)² (Y-Ȳ)³ diurutkan (Seri X) Y = Log X 1 57 1.756 2.301 0.286 0.0819 0.0234 2 110 2.041 2.097 0.082 0.0067 0.0006 3 108 2.033 2.041 0.027 0.0007 0.0000 4 105 2.021 2.041 0.027 0.0007 0.0000 5 100 2.000 2.033 0.019 0.0003 0.0000 6 98 1.991 2.021 0.006 0.0000 0.0000 7 95 1.978 2.021 0.006 0.0000 0.0000 8 99 1.996 2.000 -0.015 0.0002 0.0000 9 93 1.968 2.000 -0.015 0.0002 0.0000 10 95 1.978 1.996 -0.019 0.0004 0.0000 11 100 2.000 1.991 -0.024 0.0006 0.0000 12 105 2.021 1.978 -0.037 0.0014 -0.0001 13 110 2.041 1.978 -0.037 0.0014 -0.0001 14 125 2.097 1.968 -0.046 0.0022 -0.0001 15 200 2.301 1.756 -0.259 0.0671 -0.0174 Ʃ 1600 30.223 0.164 0.006 Average 106.6667 2.015 �_𝑙𝑜𝑔=√(1/((𝑛−1)) ∑_(𝑖=1)^𝑛▒(𝐿𝑜𝑔�_𝑖−(𝐿𝑜𝑔�)  ̅ )^3 ) Rank



〖��〗 _ 〖 log 〗〖 = (𝑛∑_(𝑖=1)^𝑛▒(𝐿𝑜𝑔�_𝑖−(𝐿𝑜𝑔�)  ̅ ) ^3 )/((𝑛−1)(𝑛−2) 〖 (�_𝑙𝑜𝑔) 〗 ^3 ) 〗 �_𝑙𝑜𝑔= 〖��〗 _log 0.418211 〖 = 〗



0.108170



Jadi Cs log > 0.4 Uji Outlier Tinggi :



n=



log 〖�𝑙 = (𝑙𝑜𝑔�)  ̅ 〗 +�𝑛 ∗ �_𝑙𝑜𝑔



15



�𝑛=(−3.62201)+( 〖 6.28446 𝑛 〗 ^(1/4) )−( 〖 2.49835 𝑛 〗 ^(1/2) )+( 〖 0.491436 𝑛 〗 ^(3/4) )-(0.037911 𝑛) kn = 2.247 log Xh = 2.257910 Xh = 181.10 Data di check terhadap Xl Data (Seri X)



Rank 1



Data (Seri X)



Rank 57



1



57



2 3 4 5 6 7 8 9 10 11 12 13 14



110 108 105 100 98 95 99 93 95 100 105 110 125



2 3 4 5 6 7 8 9 10 11 12 13 14



110 108 105 100 98 95 99 93 95 100 105 110 125



15



200



15



181.10



Analisis Parameter Statistik Data Terkoreksi Rendah Data Data (Seri Y) Data Rank (Y-Ȳ) diurutkan (Seri X) Y = Log X 1 57 1.756 2.258 0.246 2 110 2.041 2.097 0.085 3 108 2.033 2.041 0.029 4 105 2.021 2.041 0.029 5 100 2.000 2.033 0.021 6 98 1.991 2.021 0.009 7 95 1.978 2.021 0.009 8 99 1.996 2.000 -0.012 9 93 1.968 2.000 -0.012 10 95 1.978 1.996 -0.016 11 100 2.000 1.991 -0.021 12 105 2.021 1.978 -0.034 13 110 2.041 1.978 -0.034 14 125 2.097 1.968 -0.044 15 181.0964 2.258 1.756 -0.256 Ʃ 1581.096 30.180 Average 105.4064 2.012 �_𝑙𝑜𝑔=



0.10031



Uji Outlier Rendah : log 〖�𝑙 = (𝑙𝑜𝑔�)  ̅ 〗−�𝑛 ∗ � _𝑙𝑜𝑔



n= kn =



15 2.247



(Y-Ȳ)²



(Y-Ȳ)³



0.0605 0.0072 0.0009 0.0009 0.0005 0.0001 0.0001 0.0001 0.0001 0.0003 0.0004 0.0012 0.0012 0.0019 0.0656 0.141



0.0149 0.0006 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0001 -0.0168 -0.001



log Xl = Xl =



1.787 61.18



Data di Check terhadap Xh : Data hasil Koreksi Outlier Rendah Data Rank (Seri X) 1 57 2 110 3 108 4 105 5 100 6 98 7 95 8 99 9 93 10 95 11 100 12 105 13 110 14 125 15 181.0964



Xh =



61.18 Data hasil Koreksi Outlier Tinggi Data Rank (Seri X) 1 61.18 2 110 3 108 4 105 5 100 6 98 7 95 8 99 9 93 10 95 11 100 12 105 13 110 14 125 15 181.0964



Data hasil koreksi outlier, yang akan digunakan dalam analisis selanjutnya No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15



Data 61.18359 110 108 105 100 98 95 99 93 95 100 105 110 125 181.0964



)-(0.037911 𝑛)



Analisa Outlier Stasiun 4 Data Data (Seri Data (Y-Ȳ) (Y-Ȳ)² (Y-Ȳ)³ (Seri X) Y = Log X diurutkan 1 49 1.690 2.272 0.294 0.0866 0.0255 2 101 2.004 2.076 0.098 0.0096 0.0009 3 90 1.954 2.033 0.056 0.0031 0.0002 4 88 1.944 2.004 0.027 0.0007 0.0000 5 83 1.919 2.000 0.022 0.0005 0.0000 6 90 1.954 1.987 0.009 0.0001 0.0000 7 93 1.968 1.978 0.000 0.0000 0.0000 8 97 1.987 1.968 -0.009 0.0001 0.0000 9 86 1.934 1.954 -0.023 0.0005 0.0000 10 89 1.949 1.954 -0.023 0.0005 0.0000 11 95 1.978 1.949 -0.028 0.0008 0.0000 12 100 2.000 1.944 -0.033 0.0011 0.0000 13 108 2.033 1.934 -0.043 0.0019 -0.0001 14 119 2.076 1.919 -0.059 0.0034 -0.0002 15 187 2.272 1.690 -0.287 0.0826 -0.0237 Ʃ 1475 29.664 0.192 0.003 Average 98.33333 1.978 �_𝑙𝑜𝑔=√(1/((𝑛−1)) ∑_(𝑖=1)^𝑛▒(𝐿𝑜𝑔�_𝑖−(𝐿𝑜𝑔�)  ̅ )^3 ) Rank



〖��〗 _ 〖 log 〗〖 = (𝑛∑_(𝑖=1)^𝑛▒(𝐿𝑜𝑔�_𝑖−(𝐿𝑜𝑔�)  ̅ ) ^3 )/((𝑛−1)(𝑛−2) 〖 (�_𝑙𝑜𝑔) 〗 ^3 ) 〗 �_𝑙𝑜𝑔= 〖��〗 _log 0.129011 〖 = 〗 Jadi -0.4