Table 1 Observed and expected frequencies of trips made by Dutch households owning at least one car during a particular survey week in 1989(van Ophem, 2000)
From: Mittag - Leffler function distribution - a new generalization of hyper-Poisson distribution
x | Observed | Expected Frequencies | |||
|---|---|---|---|---|---|
HP (λ, β) | MLFD (λ, α, 1) | MLFD (λ, α, β) | COMNB (λ, α, β) | ||
0 | 75 | 93.208 | 99.150 | 74.175 | 89.965 |
1 | 312 | 269.133 | 273.608 | 308.769 | 284.076 |
2 | 384 | 403.029 | 399.3458 | 420.586 | 411.107 |
3 | 421 | 407.420 | 399.724 | 389.683 | 397.963 |
4 | 307 | 310.848 | 305.795 | 286.233 | 296.794 |
5 | 183 | 190.456 | 189.821 | 178.113 | 183.213 |
6 | 77 | 97.491 | 99.311 | 97.428 | 97.687 |
7 | 47 | 42.853 | 44.958 | 47.962 | 46.258 |
8 | 15 | 16.504 | 17.9533 | 21.598 | 19.836 |
9 | 9 | 5.656 | 6.4181 | 9.003 | 7.813 |
10 | 5 | 1.746 | 2.078 | 3.506 | 2.858 |
11 | 0 | 0.490 | 0.615 | 1.285 | 0.979 |
12 | 0 | 0.126 | 0.166 | 0.445 | 0.316 |
13 | 1 | 0.030 | 0.042 | 0.147 | 0.097 |
14 | 2 | 0.007 | 0.010 | 0.046 | 0.028 |
15 | 0 | 0.001 | 0.002 | 0.014 | 0.008 |
16 | 0 | 0.000 | 0.000 | 0.004 | 0.002 |
17 | 1 | 0.000 | 0.000 | 0.002 | 0.001 |
Total | 1839 | 1839 | 1839 | 1839 | 1839 |
\( \widehat{\lambda} \) | 3.110 (0.121) | 2.697 (0.182) | 1.000 (0.130) | 3.288 (4.25) | |
\( \widehat{\alpha} \) | ---- | 0.943 (0.032) | 0.576 (0.063) | 0.960 (1.22) | |
\( \widehat{\beta} \) | 1.080(0.121) | ---- | 0.183 (0.058) | 1.509 (0.40) | |
χ 2, df | 37.034, 7 | 32.564, 8 | 17.716, 8 | 20.676, 8 | |
p-val | <0.01 | <0.01 | 0.023 | <0.01 | |
AIC | 7234.620 | 7231.970 | 7213.917 | 7218.610 | |