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&[DATE] &[TIME] - &[FILENAME]

RAIN FALL ANALYSIS - Standardized Precipitation Index (SPI)

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SAMPLE with First 10 Elements of Original DATA

X 30.4 278.7 63.9 387.1 330 187.3 495.9 18 163.3 128.8 101 mat :

X min 18

X max 495.9

n X rows : 10

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3. Dealing with zero values

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Program 2: To deal 
with ln(0) n.zero 0 : j 1 X rows range X j el 0 ≤ LNX j el 0 : n.zero n.zero 1 + : pos n.zero el j : 31 line LNX j el X j el ln : if for n.zero 0 ≡ pos Undefined : pos pos : if 31 line

ln(x) values LNX 3.414 5.63 4.157 5.959 5.799 5.233 6.206 2.89 5.096 4.858 101 mat

X 30.4 278.7 63.9 387.1 330 187.3 495.9 18 163.3 128.8 101 mat

Index of the LNX 
array where LNX = 0 pos Undefined

Clear j from memory j Clear 1

X.mean X sum n / : 208.34

LNX.mean LNX sum n / : 4.924298109

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4. Gamma PDF and CDF

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Number of 
zero values n.zero 0

Prob of zero values Pr.zero n.zero n / : 0

A X.mean ln LNX.mean - : 0.414873251

0.5 Gamma 1.772456367

α 14 A * / 114 A 3 / * + sqrt + (* : 1.353582167

β X.mean α / : 153.91751239

α Gamma 0.890795288

1 Gamma 1.000001604

Eqn for Gamma function PDF x g 1 β α^α Gamma * / x α 1 -^* e x β / -^* :

α Gamma 0.8908

5 Gamma 24

Eqn. 1

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12 / Gamma 1.7725

π sqrt 1.7725

Eqn for Gamma function CDF x_val G 1 β α^α Gamma * / x α 1 -^e x β / -^* x 0 x_val int * :

0 G 0

Eqn. 2

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0 g 0

PDF using Eqn 1 g1 X g vectorize : 0.0034 0.0015 0.0035 0.0008 0.0011 0.0023 0.0004 0.003 0.0026 0.003 101 mat

CDF using Eqn 2 G1 X G vectorize : 0.0923 1.8516 0.2522 2.8884 2.3286 1.0822 4.0407 0.0454 0.8983 0.6513 101 mat

X 4 el G 2.8884

X 4 el g 0.0008

X 4 el 387.1

Substitute g(x) in Eqn 2 x_val Q x g x 0 x_val int :

CDF using Eqn 3 G2 X Q vectorize : 0.0815 1.6353 0.2227 2.5509 2.0565 0.9557 3.5686 0.0401 0.7933 0.5752 101 mat

Eqn. 3

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X 4 el Q 2.5509

3 appVersion 0.99.7251

Both Eqns 2 & 3 are same, but the results

of Integration (G1 & G2) are slightly different.

Note: Mathcad results are totally different

from SS, but identical.

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