# 统计代写|生存模型代写survival model代考|Actual Age Summary

#### Doug I. Jones

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## 统计代写|生存模型代写survival model代考|Actual Age Summary

Here we recapitulate the steps involved in processing basic data for the purpose of estimating $q_x$ (or a constant force of mortality) over the estimation interval $(x, x+1]$. We assume that the basic data for each person consists of the date of birth, date of joining the group under study (e.g., date of insurance policy issue), and date of death or withdrawal, if applicable. In addition, the opening and closing dates of the observation period (O.P.) must be specified. Actual ages are used.
(1) Any person whose death or withdrawal occurs before the O.P. opens, or whose date of joining the group occurs after the O.P. closes, is not part of the study sample.
(2) Dates of birth, joining the group, and death or withdrawal are converted to decimal years.
(3) Age at entry to study, $y_i$, is found as age when O.P. opens, or age when person $i$ joins group, whichever is later.
(4) Scheduled age at exit from study, $z_i$, is found as age on closing date of O.P.
(5) Age at death or withdrawal, $\theta_i$ or $\phi_i$, is found from date of event and date of birth; steps (3), (4) and (5) produce the age vector $\mathbf{v}i^{\prime}=\left[y_i, z_i, \theta_i, \phi_i\right]$. (6) The duration vector $u{i, x}^{\prime}=\left[r_i, s_i, \iota_i \kappa_i\right]$ is obtained from $\mathbf{v}i^{\prime}$ with respect to the estimation interval $(x, x+1]$. (7) The estimators presented in Chapters 6, 7 and 8 can then be evaluated from the $\mathbf{u}{i, x}$ vectors for all persons in the study.

## 统计代写|生存模型代写survival model代考|INSURING AGES

Since most people do not purchase individual insurance policies on their actual birthdays, it follows that they are various fractional attained ages when their policies are issued. The insurance company, on the other hand, will not calculate a premium for the policy that depends on the insured’s actual fractional age at issue. Instead an integral insuring age is substituted for the insured’s actual age as of the policy issue date. Most commonly this insuring age will be the insured’s actual age on the birthday nearest the policy issue date. In other words,
$$I A=\text { Actual Age Nearest Birthday, }$$
where $I A$ is the insuring age.
Less commonly, the insuring age could be taken as the actual age on the birthday preceding the policy issue date, in which case we say that $I A$ is the actual age last birthday. Note that the examples and exercises in this chapter all use the age nearest birthday basis.

Assigning an integral insuring age to the insured as of the policy issue date implies that a hypothetical date of birth, called the insuring date of birth, has been substituted for the actual date of birth. Clearly the month and day of this insuring date of birth are the same as the policy issue date. The hypothetical year of birth, called the valuation year of birth (VYB), is then found as
$$V Y B=C Y I-I A$$

where $C Y I$ is the calendar year of policy issue. It should be recognized that $V Y B$ will frequently be the same as $C Y B$, but it can also be one year earlier or one year later than $C Y B$.

# 生存模型代考

## 统计代写|生存模型代写survival model代考|Actual Age Summary

(1)任何在op开放之前死亡或退出，或在op关闭之后加入小组的人，不属于研究样本的一部分。
(2)出生、加入团体、死亡或退出的日期转换为十进制年。
(3)入学年龄$y_i$为op开放时的年龄，或$i$入组时的年龄，以较晚者为准。
(4)退出学习时的预定年龄$z_i$以op截止日期的年龄为准
(5)死亡或退出时的年龄，$\theta_i$或$\phi_i$，从事件发生之日和出生之日算起;步骤(3)、(4)、(5)生成年龄向量$\mathbf{v}i^{\prime}=\left[y_i, z_i, \theta_i, \phi_i\right]$。(6)由$\mathbf{v}i^{\prime}$相对于估计区间$(x, x+1]$得到持续时间向量$u{i, x}^{\prime}=\left[r_i, s_i, \iota_i \kappa_i\right]$。(7)然后可以从研究中所有人的$\mathbf{u}{i, x}$向量中评估第6,7和8章中给出的估计量。

## 统计代写|生存模型代写survival model代考|INSURING AGES

$$I A=\text { Actual Age Nearest Birthday, }$$
$I A$是保险年龄。

$$V Y B=C Y I-I A$$

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