Probability Distributions - Oxford University Press
Probability Distributions - Oxford University Press
Probability Distributions - Oxford University Press
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(b) To check how well the Poisson probability distribution fits the data set we note that<br />
the observed frequencies are given in the original table and that the expected frequencies<br />
can be calculated from the Poisson probability fit using the equation EF =<br />
∑ f P(X r)<br />
Table 5.13 illustrates the calculation of the Poisson probability values for λ = 1.4 by applying<br />
equation (5.17) as follows:<br />
r Poisson Value Excel<br />
( )<br />
0 −1.4<br />
1.4 e<br />
0 P X= 0 = = 0.2466<br />
0!<br />
( )<br />
1 −1.4<br />
1.4e<br />
1 P X=<br />
1 = = 0.3452<br />
1!<br />
( )<br />
2 −1.4<br />
1.4 e<br />
2 P X= 2 = = 0.2417<br />
2!<br />
( )<br />
3 −1.4<br />
1.4 e<br />
3 P X=<br />
3 = = 0.1128<br />
3!<br />
( )<br />
4 −1.4<br />
1.4 e<br />
4 P X= 4 = = 0.1128<br />
4!<br />
5 −1.4<br />
1.4 e<br />
5 P X= 5 = = 0.0111<br />
5!<br />
Table 5.13<br />
( ) × = . The manual solution is now presented in Table 5.12 as follows:<br />
r P(X = r) Observed frequency Expected frequency<br />
0 0.2466 24 24.66<br />
1 0.3452 35 34.52<br />
2 0.2417 24 24.17<br />
3 0.1128 12 11.28<br />
4 0.0395 4 3.95<br />
5 0.0111 1 1.11<br />
Table 5.12<br />
Totals = 100 99.68<br />
We note that the expected frequencies are approximately equal to the observed frequency<br />
values.<br />
( )<br />
=POISSON(J7,$C$16,FALSE)<br />
=POISSON(J8,$C$16,FALSE)<br />
=POISSON(J9,$C$16,FALSE)<br />
=POISSON(J10,$C$16,FALSE)<br />
=POISSON(J11,$C$16,FALSE)<br />
=POISSON(J12,$C$16,FALSE)<br />
<strong>Probability</strong> <strong>Distributions</strong><br />
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