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(Created page with "You are doing a mortality study of insureds between ages 60 and 90 . Two specific lives contributed this data to the study: {| class="table table-bordered" ! Life !! Age at Entry !! Age at Exit !! Cause of exit |- | 1 || 60.0 || 74.5 || Policy lapsed |- | 2 || 60.0 || 74.5 || Death |} You assume mortality follows Gompertz law <math>\mu_{x}=B \times c^{x}</math> and plan to use maximum likelihood estimation. <math>L</math> is the log-likelihood function (using natural...") |
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<ul class="mw-excansopts"><li>-4,67</li><li>-4.53</li><li>-4.39</li><li>-4.25</li><li> -4.11</li></ul> | <ul class="mw-excansopts"><li>-4,67</li><li>-4.53</li><li>-4.39</li><li>-4.25</li><li> -4.11</li></ul> | ||
{{soacopyright|2024}} | |||
Latest revision as of 02:40, 18 January 2024
You are doing a mortality study of insureds between ages 60 and 90 . Two specific lives contributed this data to the study:
| Life | Age at Entry | Age at Exit | Cause of exit |
|---|---|---|---|
| 1 | 60.0 | 74.5 | Policy lapsed |
| 2 | 60.0 | 74.5 | Death |
You assume mortality follows Gompertz law [math]\mu_{x}=B \times c^{x}[/math] and plan to use maximum likelihood estimation.
[math]L[/math] is the log-likelihood function (using natural logs) associated with these two lives.
[math]L^{*}[/math] denotes the value of [math]L[/math] if the Gompertz parameters are [math]B=0.000004[/math] and [math]c=1.12[/math].
Calculate [math]L^{*}[/math].
- -4,67
- -4.53
- -4.39
- -4.25
- -4.11
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.