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Advanced Statistics Assignment

3761 words - 16 pages

MGSC 372 Fall 2014
Assignment 1 Prof. B. Smith Due Oct 4,

QUESTION 1

The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a probability distribution that may be used to describe social, scientific, geophysical, actuarial, and many other types of observable phenomena.

Pareto originally used this distribution to describe the allocation of wealth among individuals since it seemed to show rather well the way that a larger portion of the wealth of any society is owned by a smaller percentage of the ...view middle of the document...

1. Use the spreadsheet to estimate the MLE for the sample of part (b) when x0=3. Obtain the graph of the likelihood function.
Theta | x1 | x2 | x3 | x4 | x5 | L | x0 |
| 3.0000 | 2.0000 | 3.0000 | 6.0000 | 5.0000 | | 3 |
1.0 | 0.3333 | 0.7500 | 0.3333 | 0.0833 | 0.1200 | 0.0008 | |
1.1 | 0.3667 | 0.8591 | 0.3667 | 0.0855 | 0.1254 | 0.0012 | |
1.2 | 0.4000 | 0.9760 | 0.4000 | 0.0871 | 0.1300 | 0.0018 | |
1.3 | 0.4333 | 1.1011 | 0.4333 | 0.0880 | 0.1338 | 0.0024 | |
1.4 | 0.4667 | 1.2349 | 0.4667 | 0.0884 | 0.1370 | 0.0033 | |
1.5 | 0.5000 | 1.3778 | 0.5000 | 0.0884 | 0.1394 | 0.0042 | |
1.6 | 0.5333 | 1.5305 | 0.5333 | 0.0880 | 0.1413 | 0.0054 | |
1.7 | 0.5667 | 1.6935 | 0.5667 | 0.0872 | 0.1427 | 0.0068 | |
1.8 | 0.6000 | 1.8673 | 0.6000 | 0.0862 | 0.1435 | 0.0083 | |
1.9 | 0.6333 | 2.0526 | 0.6333 | 0.0848 | 0.1440 | 0.0101 | |
2.0 | 0.6667 | 2.2500 | 0.6667 | 0.0833 | 0.1440 | 0.0120 | |
2.1 | 0.7000 | 2.4603 | 0.7000 | 0.0816 | 0.1437 | 0.0141 | |
2.2 | 0.7333 | 2.6841 | 0.7333 | 0.0798 | 0.1430 | 0.0165 | |
2.3 | 0.7667 | 2.9222 | 0.7667 | 0.0778 | 0.1421 | 0.0190 | |
2.4 | 0.8000 | 3.1754 | 0.8000 | 0.0758 | 0.1409 | 0.0217 | |
2.5 | 0.8333 | 3.4446 | 0.8333 | 0.0737 | 0.1394 | 0.0246 | |
2.6 | 0.8667 | 3.7306 | 0.8667 | 0.0715 | 0.1378 | 0.0276 | |
2.7 | 0.9000 | 4.0344 | 0.9000 | 0.0693 | 0.1360 | 0.0308 | |
2.8 | 0.9333 | 4.3570 | 0.9333 | 0.0670 | 0.1340 | 0.0341 | |
2.9 | 0.9667 | 4.6993 | 0.9667 | 0.0648 | 0.1318 | 0.0375 | |
3.0 | 1.0000 | 5.0625 | 1.0000 | 0.0625 | 0.1296 | 0.0410 | |
3.1 | 1.0333 | 5.4477 | 1.0333 | 0.0603 | 0.1273 | 0.0446 | |
3.2 | 1.0667 | 5.8561 | 1.0667 | 0.0580 | 0.1248 | 0.0483 | |
3.3 | 1.1000 | 6.2891 | 1.1000 | 0.0558 | 0.1223 | 0.0520 | |
3.4 | 1.1333 | 6.7478 | 1.1333 | 0.0537 | 0.1197 | 0.0557 | |
3.5 | 1.1667 | 7.2336 | 1.1667 | 0.0516 | 0.1171 | 0.0595 | |
3.6 | 1.2000 | 7.7482 | 1.2000 | 0.0495 | 0.1145 | 0.0632 | |
3.7 | 1.2333 | 8.2930 | 1.2333 | 0.0475 | 0.1118 | 0.0669 | |
3.8 | 1.2667 | 8.8695 | 1.2667 | 0.0455 | 0.1091 | 0.0706 | |
3.9 | 1.3000 | 9.4796 | 1.3000 | 0.0435 | 0.1064 | 0.0742 | |
4.0 | 1.3333 | 10.1250 | 1.3333 | 0.0417 | 0.1037 | 0.0778 | |
4.1 | 1.3667 | 10.8076 | 1.3667 | 0.0398 | 0.1010 | 0.0812 | |
4.2 | 1.4000 | 11.5293 | 1.4000 | 0.0381 | 0.0983 | 0.0846 | |
4.3 | 1.4333 | 12.2922 | 1.4333 | 0.0364 | 0.0956 | 0.0879 | |
4.4 | 1.4667 | 13.0986 | 1.4667 | 0.0347 | 0.0930 | 0.0910 | |
4.5 | 1.5000 | 13.9506 | 1.5000 | 0.0331 | 0.0903 | 0.0940 | |
4.6 | 1.5333 | 14.8507 | 1.5333 | 0.0316 | 0.0878 | 0.0969 | |
4.7 | 1.5667 | 15.8014 | 1.5667 | 0.0301 | 0.0852 | 0.0996 | |
4.8 | 1.6000 | 16.8054 | 1.6000 | 0.0287 | 0.0827 | 0.1021 | |
4.9 | 1.6333 | 17.8654 | 1.6333 | 0.0274 | 0.0802 | 0.1046 | |
5.0 | 1.6667 | 18.9844 | 1.6667 | 0.0260 | 0.0778 | 0.1068 | |
5.1 | 1.7000 | 20.1653 | 1.7000 | 0.0248 | 0.0754 | 0.1089 | |
5.2 | 1.7333 | 21.4115 |...

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