# Japanese Centenarians Data

### Description

The number of deaths at each year (1963-1980) for Japanese male centenarians (Table 2 of Emura and Murotani (2015)). See also the original reference Sibuya & Hanayama (2004).

### Usage

1 | ```
data("centenarian")
``` |

### Format

A data frame with 21 observations on the following 19 variables.

`X`

:the age at death

`X1963`

:the number of deaths between 1963 and 1964

`X1964`

:the number of deaths between 1964 and 1965

`X1965`

:the number of deaths between 1965 and 1966

`X1966`

:the number of deaths between 1966 and 1967

`X1967`

:the number of deaths between 1967 and 1968

`X1968`

:the number of deaths between 1968 and 1969

`X1969`

:the number of deaths between 1969 and 1970

`X1970`

:the number of deaths between 1970 and 1971

`X1971`

:the number of deaths between 1971 and 1972

`X1972`

:the number of deaths between 1972 and 1973

`X1973`

:the number of deaths between 1973 and 1974

`X1974`

:the number of deaths between 1974 and 1975

`X1975`

:the number of deaths between 1975 and 1976

`X1976`

:the number of deaths between 1976 and 1977

`X1977`

:the number of deaths between 1977 and 1978

`X1978`

:the number of deaths between 1978 and 1979

`X1979`

:the number of deaths between 1979 and 1980

`X1980`

:the number of deaths between 1980 and 1981

### References

Sibuya M, Hanayama N (2004), Estimation of Human Longevity Distribution Based on Tabulated Statistics. Proceeding of ISM 52: 117-34

Emura T, Murotani K (2015), An Algorithm for Estimating Survival Under a Copula-based Dependent Truncation Model, TEST 24 (No.4): 734-751.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
## Below is the centenarians data analysis of Emura & Murotani (2015) ##
data(centenarian)
Death=centenarian[,1]
Year=1963:1980
data.mat=centenarian[,-1]
X=T=NULL
for(i in 1:length(Death)){
for(j in 1:length(Year)){
X=c( X,rep(Death[i],data.mat[i,j]) )
T=c( T,rep(Year[j]-i+1,data.mat[i,j]) ) ### T= Year at age 100.5 ###
}
}
x.trunc=X
z.trunc=max(Year)+0.5-T+100
m=length(x.trunc)
d=rep(1,m)
set.seed(1)
x.trunc=x.trunc+runif(length(x.trunc),min=-0.01,max=0)
z.trunc=z.trunc+runif(length(z.trunc),min=0,max=0.01)
### Copula-based estimator ####
## CHAIEB.Frank(x.trunc, z.trunc, d, a = 1/10)
``` |