# Statistical Distributions - Inverted Gamma Distribution - Example

Graphical Representation 1

Summary 1

 Distribution Parameters Population Statistics # r a n s2 s Exp. Val. Mode Variance St.Dev. 1 5.0 50 10 10 3.1623 3.4270 3.0151 0.7555 0.8692 2 10.0 100 20 10 3.1623 3.2874 3.0861 0.3042 0.5516 3 12.5 125 25 10 3.1623 3.2613 3.1009 0.2337 0.4834 4 15.0 150 30 10 3.1623 3.2442 3.1109 0.1896 0.4354 5 20.0 200 40 10 3.1623 3.2232 3.1235 0.1376 0.3709 6 25.0 250 50 10 3.1623 3.2107 3.1311 0.1079 0.3285 7 30.0 300 60 10 3.1623 3.2025 3.1363 0.0888 0.2980 8 37.5 375 75 10 3.1623 3.1943 3.1414 0.0701 0.2648 9 50.0 500 100 10 3.1623 3.1862 3.1466 0.0519 0.2279 10 100.0 1000 200 10 3.1623 3.1742 3.1544 0.0255 0.1596 11 150.0 1500 300 10 3.1623 3.1702 3.1570 0.0169 0.1299

Graphical Representation 2

Summary 2

 Distribution Parameters Population Statistics # r a n s2 s Exp. Val. Mode Variance St.Dev. 1 15 1.50 30 0.10 0.3162 0.3244 0.3111 0.0019 0.0435 2 15 3.00 30 0.20 0.4474 0.4588 0.4399 0.0038 0.0616 3 15 3.75 30 0.25 0.5000 0.5130 0.4919 0.0047 0.0688 4 15 7.50 30 0.50 0.7071 0.7254 0.6956 0.0095 0.0974 5 15 11.25 30 0.75 0.8660 0.8885 0.8519 0.0142 0.1192 6 15 15.00 30 1.00 1.0000 1.0259 0.9837 0.0190 0.1377

Parameters :

#### Output

```+-----------------------------+
¦ INVERTED GAMMA DISTRIBUTION ¦
+-----------------------------+

MOMENTS - UNCENTERED                    STATISTICS

1st :  3.42703084e+00              Expected Value     :      3.427031
2nd :  1.25000000e+01              Variance           :       .755460
3rd :  4.89575835e+01              Standard Deviation :       .869172
4th :  2.08333333e+02              Skewness           :      1.434201
Kurtosis           :      7.454771
MOMENTS - CENTERED                      Mode               :      3.015113

1st :  0.00000000e+00
2nd :  7.55459593e-01
3rd :  9.41731284e-01
4th :  4.25458104e+00```

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