Table 5 Parameter estimates for the annual flow of the Nile River data
From: The generalized Cauchy family of distributions with applications
Distribution | Cauchy | Gamma-Pareto | Beta-Cauchy | Gamma-Cauchy{exponential} |
|---|---|---|---|---|
Parameter Estimates | ĉ = 879.3679 (17.3969)a \( \widehat{\theta} \) = 103.8804 (13.44841) | \( \widehat{\alpha} \) = 5.0437 (0.6902) ĉ = 0.1357 (0.0195) \( \widehat{\theta} \) = 456 | \( \widehat{\alpha} \) = 50.9201 (66.0939) \( \widehat{\beta} \) = 25.1275 (29.7478) ĉ = 712.2062 (445.6252) \( \widehat{\theta} \) = 482.3092 (361.7110) | \( \widehat{\alpha} \) = 322.5715 (6.4901) \( \widehat{\beta} \) = 0.0103 (0.0003) \( \widehat{\theta} \) = 103.5797 (76.1343) |
Log-likelihood | -674.4637 | -696.7975 | -653.4892 | -654.3825 |
AIC | 1352.9270 | 1397.5950 | 1314.9780 | 1314.7650 |
K-S | 0.1311 | 0.1705 | 0.0736 | 0.0637 |
K-S p-value | 0.0642 | 0.0060 | 0.6515 | 0.8120 |