excans:6c038ef0a5: Difference between revisions
From Stochiki
No edit summary Tag: Reverted |
No edit summary Tag: Reverted |
||
| Line 13: | Line 13: | ||
The contribution to the log-likelihood is <math>\ln (0.01426)=-4.25</math>. | The contribution to the log-likelihood is <math>\ln (0.01426)=-4.25</math>. | ||
{{soacopyright|2024}} | |||
{{soacopyright|2024}} | {{soacopyright|2024}} | ||
{{soacopyright|2024}} | {{soacopyright|2024}} | ||
Revision as of 02:34, 18 January 2024
Answer: D
The contribution from Life 1 is [math]{ }_{14.5} p_{60}[/math]. With Gompertz and the selected parameters, the contribution is
[[math]]{ }_{14.5} p_{60}=\exp \left[-\frac{B}{\ln c} c^{60}\left(c^{14.5}-1\right)\right]=\exp \left[-\frac{0.000004}{\ln 1.12} 1.12^{60}\left(1.12^{14.5}-1\right)\right]=0.87619.[[/math]]
The contribution from Life 2 is [math]{ }_{14.5} p_{60} \times \mu_{74.5}[/math]. The contribution is
[[math]]
{ }_{14.5} p_{60} \times \mu_{74.5}=0.87619 \times 0.000004 \times 1.12^{74.5}=0.01627
[[/math]]
The contribution to the likelihood is [math]0.87619(0.01627)=0.01426[/math].
The contribution to the log-likelihood is [math]\ln (0.01426)=-4.25[/math].
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.