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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

From: Multivariate zero-truncated/adjusted Charlier series distributions with applications

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