Negative inverse link function (for estimation with maxlogL object)

NegInv_link object provides a way to implement negative inverse link function that maxlogL needs to perform estimation. See documentation for maxlogL for further information on parameter estimation and implementation of link objects.

Usage

NegInv_link()

Value

A list with negative inverse link function, its inverse and its name.

Details

NegInv_link is part of a family of generic functions with no input arguments that defines and returns a list with details of the link function:

1. name: a character string with the name of the link function.

2. g: implementation of the link function as a generic function in R.

3. g_inv: implementation of the inverse link function as a generic function in R.

There is a way to add new mapping functions. The user must specify the details aforesaid.

See also

maxlogL

Other link functions: log_link(), logit_link()

Examples

# Estimation of rate parameter in exponential distribution
T <- rexp(n = 1000, rate = 3)
lambda <- maxlogL(x = T, dist = "dexp", start = 5,
                  link = list(over = "rate", fun = "NegInv_link"))
summary(lambda)
#> _______________________________________________________________
#> Optimization routine: nlminb 
#> Standard Error calculation: Hessian from optim 
#> _______________________________________________________________
#>         AIC       BIC
#>   -279.3799 -274.4721
#> _______________________________________________________________
#>      Estimate  Std. Error Z value Pr(>|z|)    
#> rate   3.12893    0.09895   31.62   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> _______________________________________________________________
#> Note: p-values valid under asymptotic normality of estimators 
#> ---

# Link function name
fun <- NegInv_link()$name
print(fun)
#> [1] "NegInv"

# Link function
g <- NegInv_link()$g
curve(g(x), from = 0.1, to = 1)


# Inverse link function
ginv <- NegInv_link()$g_inv
curve(ginv(x), from = 0.1, to = 1)