Table 7 The result of comparison between our new distribution \(NBS({\alpha }_{N},{\beta }_{N})\) and \(BS\left(\alpha ,\beta \right)\).
Application | Distribution | MLE | − 2LL | AIC | BIC |
|---|---|---|---|---|---|
Application 1 | \(NBS({\alpha }_{N},{\beta }_{N})\) | \({\alpha }_{N}=\left(\mathrm{0.0019,0.0020}\right)\) \({\beta }_{N}=(\mathrm{0.0044,0.0047})\) | (2929.146,2999.523) | (5860.827,5897.769) | (5864.169,5904.826) |
\(BS\left(\alpha ,\beta \right)\) | \(\alpha =0.0019\) \(\beta =0.0503\) | 11,939.523 | 23,855.62 | 23,887.02 | |
Application 2 | \(NBS({\alpha }_{N},{\beta }_{N})\) | \({\alpha }_{N}=\left(\mathrm{0.0626,0.0456}\right)\) \({\beta }_{N}=(\mathrm{0.7583,7546})\) | (4403.694,4599.646) | (4407.694,4503) | (4409.474,4505.427) |
\(BS\left(\alpha ,\beta \right)\) | \(\alpha =0.0528\) \(\beta =0.7562\) | 4671.254 | 4675.254 | 4677.035 |
