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Table 9 Table for goodness of fit

From: A new discrete pareto type (IV) model: theory, properties and applications

Total number of carious teeth (x) 0 1 2 ≥3 Total p-value
Observed Frequency (Oi) 64 17 10 9 100  
Poisson(0.67)       
Ei 51.2 34.3 11.5 3 100  
\(\frac {\left (O_{i}-E_{i}\right)^{2}}{E_{i}}\) 3.2 8.7 0.2 12 24.1 0.000024
Geometric(0.5988)       
Ei 59.9 24 9.6 6.5 100  
\(\frac {\left (O_{i}-E_{i}\right)^{2}}{E_{i}}\) 0.28 2.74 0.02 0.96 4.0 0.2614
DBD (1.292,0.2108)       
Ei 66 19.4 6.7 7.9 100  
\(\frac {\left (O_{i}-E_{i}\right)^{2}}{E_{i}}\) 0.05 0.3 1.61 0.15 2.14 0.5438
DPareto (0.1935)       
Ei 68 15.6 6.2 10.2 100  
\(\frac {\left (O_{i}-E_{i}\right)^{2}}{E_{i}}\) 0.24 0.13 2.33 0.14 2.84 0.4169
GBPareto (1.2742, 1.5783, 2.0132)       
Ei 61 18 6 15 100  
\(\frac {\left (O_{i}-E_{i}\right)^{2}}{E_{i}}\) 0.1525 0.0609 0.9756 4.3902 5.5793 0.1339
DPIV(0.735, 1.282, 0.679)       
Ei 59 16.4 16.4 8.2 100  
\(\frac {\left (O_{i}-E_{i}\right)^{2}}{E_{i}}\) 0.4237 0.0219 2.4975 0.0780 3.02129 0.3884