Multivariate zero-truncated/adjusted Charlier series distributions with applications

Journal of Statistical Distributions and Applications

Table 10 Finding the value of K by maximizing the log-likelihood function for fitting the data of Table 9 by the multivariate ZTCS distribution

K	\(\hat {\pi }\)	\(\hat {\lambda }_{1}\)	\(\hat {\lambda }_{2}\)	\(\hat {\lambda }_{3}\)	\(\hat {\lambda }_{4}\)	\(\hat {\lambda }_{5}\)	Log-likelihood
2	0.396	8.405	13.520	16.667	14.513	5.262	−498.992
3	0.383	8.046	13.161	16.308	14.154	4.903	−492.749
4	0.372	7.707	12.822	15.969	13.815	4.564	−487.185
5	0.349	7.452	12.567	15.714	13.559	4.309	−482.820
8	0.292	6.858	11.973	15.120	12.966	3.715	−473.529
9	0.276	6.710	11.825	14.972	12.818	3.567	−471.336
10	0.261	6.585	11.700	14.847	12.693	3.442	−469.490
14	0.209	6.271	11.387	14.533	12.379	3.128	−464.604
15	0.198	6.226	11.341	14.488	12.333	3.083	−463.810
20	0.155	6.092	11.207	14.354	12.200	2.949	−461.170
30	0.106	5.997	11.112	14.259	12.105	2.854	−458.806
50	0.065	5.944	11.059	14.206	12.051	2.800	−457.125
51	0.064	5.942	11.057	14.204	12.050	2.799	−457.078
52	0.062	5.941	11.056	14.203	12.049	2.798	−457.033
53	0.061	5.940	11.055	14.202	12.047	2.797	−456.990
54	0.060	5.939	11.054	14.201	12.046	2.795	−456.949
75	0.043	5.923	11.038	14.185	12.030	2.779	−456.350
100	0.032	5.913	11.028	14.175	12.021	2.770	−455.978
150	0.021	5.905	11.020	14.167	12.012	2.762	−455.617
250	0.013	5.898	11.014	14.160	12.006	2.755	−455.334
350	0.009	5.896	11.011	14.158	12.003	2.753	−455.215