exercise:9952b47d39: Difference between revisions
From Stochiki
(Created page with "You are doing a mortality study of insureds between ages 70 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 || 70.0 || 90.0 || End of study |- | 2 || 70.0 || Between 89.0 and 90.0 || 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 likelihood function ass...") |
No edit summary |
||
| Line 18: | Line 18: | ||
<ul class="mw-excansopts"><li> 0.0115</li><li> 0.0131</li><li> 0.0147</li><li> 0.0163</li><li> 0.0179</li></ul> | <ul class="mw-excansopts"><li> 0.0115</li><li> 0.0131</li><li> 0.0147</li><li> 0.0163</li><li> 0.0179</li></ul> | ||
{{soacopyright|2024}} | |||
Latest revision as of 02:40, 18 January 2024
You are doing a mortality study of insureds between ages 70 and 90 . Two specific lives contributed this data to the study:
| Life | Age at Entry | Age at Exit | Cause of exit |
|---|---|---|---|
| 1 | 70.0 | 90.0 | End of study |
| 2 | 70.0 | Between 89.0 and 90.0 | 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 likelihood function associated with these two lives.
[math]L^{*}[/math] denotes the value of [math]L[/math] if the Gompertz parameters are [math]B=0.000003[/math] and [math]c=1.1[/math].
Calculate [math]L^{*}[/math].
- 0.0115
- 0.0131
- 0.0147
- 0.0163
- 0.0179
Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.