Fitting life probabilities to Weibull

Fitting the January 2016 life table for an Italian individual with age 50 to the Weibull function.
Data source http://demo.istat.it/tvm2016/index.php?lingua=ita

## 4.711926 :  70  4
## 1.064565 :  90.955947  4.195393
## 0.1892839 :  90.042928  7.307404
## 0.01893533 :  87.962986  9.328979
## 0.01140994 :  88.147920  9.936885
## 0.01135915 :  88.146239  9.999379
## 0.01135898 :  88.14776 10.00178
## 0.01135898 :  88.14777 10.00199
## 0.01135898 :  88.14778 10.00200

## 
## Formula: y ~ prob_fun(50, t, c1, c2)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## c1 88.14778    0.07984 1104.09   <2e-16 ***
## c2 10.00200    0.11854   84.38   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01292 on 68 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.044e-07

## The expected residual life time at x = 50:

## [1] 33.93908

## Standard error:

## [1] 0.009721619

## 95% confidence interval:

## [1] 33.92003 33.95813