Denny {fmsb}

Denny's model mortality for lx and its fitting

Description

Implementing Denny's model mortality function of lx and fitting the model to actual lx of given lifetable.

Usage

 Denny(a, b, c, t)
 fitDenny(initialpar=rep(0.1, 3), data, mode=3, Method="Nelder-Mead", ...)

Arguments

a

The parameter a of the Denny model, l(t)=1/(1+a*(t/(105-t))^3+b*sqrt(exp(t/(105-t))-1)+c*(1-exp(-2*t))).

b

The parameter b of the Denny model, l(t)=1/(1+a*(t/(105-t))^3+b*sqrt(exp(t/(105-t))-1)+c*(1-exp(-2*t))).

c

The parameter c of the Denny model, l(t)=1/(1+a*(t/(105-t))^3+b*sqrt(exp(t/(105-t))-1)+c*(1-exp(-2*t))).

t

Age (vector OK) in years. The t must be less than 105, otherwise the value by Denny() become 0.

initialpar

Initial value for the parameters to be estimated. If not given, rep(0.1, 3) is used.

data

Actual vector of qx in the lifetable to be used to obtain the best-fit parameters of the Denny's model. If the ages for qx are equal or elder than 105 years old, those will be ignored in fitting.

mode

Which of lifetable functions should be used to calculate the RMSE: 1 qx, 2 dx, otherwise lx. Default is 3.

Method

The method to be used in optim() function. Default is "Nelder-Mead".

...

Other options to be passed to optim().

Value

Denny() returns model lx for the same length with t. fitDenny() returns the numeric vector of fitted parameters a, b, and c, RMSE for those values, and the flag of convergence.

Author(s)

Minato Nakazawa [e-mail] https://minato.sip21c.org/

References

Denny C (1997) A model of the probability of survival from birth. Mathematical and Computer Modelling, 26: 69-78. doi:10.1016/S0895-7177(97)00170-2

See Also

Jlife

Examples

 res <- fitDenny(,qxtolx(Jlife$qx2005M))
 FLAG <- res[5]
 while (FLAG>0) {
   res <- fitDenny(res[1:3], qxtolx(Jlife$qx2005M))
   FLAG <- res[5]
 }
 print(res)