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

Journal of Statistical Distributions and Applications

Table 9 Table for goodness of fit

Total number of carious teeth (x)	0	1	2	≥3	Total	p-value
Observed Frequency (O_i)	64	17	10	9	100
Poisson(0.67)
E_i	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)
E_i	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)
E_i	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)
E_i	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)
E_i	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)
E_i	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