# Experience Prospective Life-Tables for the Algerian Retirees

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## Abstract

**:**

## 1. Introduction

## 2. Retirees Experience Mortality

#### 2.1. Data

#### 2.2. Estimation of the Experience Death Rates

#### 2.3. Interpolating and Fitting the Experience Age-Specific Death Rates

## 3. External Reference Mortality

#### 3.1. Historical Mortality Surface of the Global Population

#### 3.2. The Product Ratio Method

#### 3.3. Reference Mortality Coherent Forecasting

#### 3.3.1. Model Estimation

#### 3.3.2. Time Indexes Forecasting

#### 3.3.3. Old Age Mortality Extrapolation

#### 3.4. Reference Mortality Extended and Forecasted Surface

## 4. Adjustment to an External Reference

#### 4.1. Logit-Linear Regression Model

#### 4.2. The Logit-Quadratic Regression Model

#### 4.3. Retired Population Dynamic Life Tables

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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1 | Caisse Nationale des Retraites: www.cnr.dz. |

2 | Caisse Nationale de Sécurité Sociales des Non-Salariés: www.casnos.com.dz. |

3 | Moudjahidine are the former combatants of the Algerian liberation war (1954–1962). |

4 | The Multiple Indicators Cluster Survey is a UNICEF program conducted in collaboration with national health ministries of member countries. The 4th wave was organized in 2012–2013 and dedicated a part for general mortality in Algeria. The report of the survey can be accessed on: https://www.unicef.org/algeria/Rapport_MICS4_(2012-2013).pdf. |

**Figure 1.**Deaths and population at risk by age and sex: (

**a**,

**b**) the observed number of deaths and its evolution over age for males and females, respectively; and (

**c**,

**d**) the population at risk by age for males and females, respectively. Data Source: CNR.

**Figure 2.**Crude mortality surfaces (${M}_{x,x+5}^{t}$): the five ages’ death rates in logarithm for males (

**a**); and the five ages’ death rates in logarithm for females (

**b**).

**Figure 3.**Annual life-tables fitting. Each subplot represents the death rates for the five age intervals observed during each year from 2004 to 2013 for: males (

**a**); and females (

**b**). The continuous lines represent the quadratic fits.

**Figure 4.**Experience crude mortality surface (ASDRs) issued from the retired population mortality data for: males (

**a**); and females (

**b**).

**Figure 6.**ln(${m}_{x,\text{}t}^{B}$) and ${R}_{x,t}$ observed during 1977–2014: (

**a**) the annual mortality curves in log scale; and (

**b**) the age pattern of the male–female mortality ratio for the different years. Even if some differences can be easily identified when comparing ${R}_{x,t}$ in different years, relative stability is observed for recent years (1998–2014) and an overall decrease can be observed regularly at all ages.

**Figure 7.**Coherent model parameters estimation: (

**top**) the alpha, beta and kappa parameters, respectively, of the LC model for the joint mortality surface; and (

**bottom**) the same parameters issued from the differential mortality function. Alpha and beta were smoothed using two-order polynomial functions to improve the regularity of the projected surfaces.

**Figure 8.**Time components forecast: (

**a**) the observed, smoothed and extrapolated ${\kappa}_{t}$; and (

**b**) the results obtained with ${K}_{t}$.

**Figure 10.**Projected life expectancy at age 50 for the global population by sex: (

**a**) the historical and the expected evolution of the residual life expectancy at age 50 for males and females of the global population (reference population) from 1977 to 2100; and (

**b**) the expected evolution of the male–female gap in life expectancy at age 50.

**Figure 11.**Linear regression of $Logit\left({m}_{x,t}^{exp}\right)$ in function of $Logit\left({m}_{x,t}^{ref}\right)$.

**Figure 12.**Confidence bounds of the numbers of deaths predicted by the linear regression model, for males and females.

**Figure 14.**Confidence bounds of the number of deaths predicted by the quadratic regression for males and females.

**Figure 15.**Experience mortality surface (ASMRs) projected till 2100 for males and females and extended to the ages beyond 80 until 120 years old.

**Figure 16.**Projected life expectancy at age 50 for the retired population: (

**a**) the time evolution of the life expectancy at age 50 for retired males and females; and (

**b**) the sex gap in life expectancy and its expected time evolution.

**Figure 17.**Remaining life expectancy at age 50—a comparison by sex: (

**a**) the remaining life expectancy at age 50 between retirees and global population for males; and (

**b**) the same indicator for females.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Flici, F.; Planchet, F.
Experience Prospective Life-Tables for the Algerian Retirees. *Risks* **2019**, *7*, 38.
https://doi.org/10.3390/risks7020038

**AMA Style**

Flici F, Planchet F.
Experience Prospective Life-Tables for the Algerian Retirees. *Risks*. 2019; 7(2):38.
https://doi.org/10.3390/risks7020038

**Chicago/Turabian Style**

Flici, Farid, and Frédéric Planchet.
2019. "Experience Prospective Life-Tables for the Algerian Retirees" *Risks* 7, no. 2: 38.
https://doi.org/10.3390/risks7020038