fitype1: Computing the Fisher information matrix under progressive...
In bccp: Bias Correction under Censoring Plan

Description Usage Arguments Details Value Author(s) References Examples

Computes the Fisher information matrix under progressive type-I interval censoring scheme. The Fisher information matrix is given by

I_{rs}=-E\Bigl(\frac{\partial^2 l(Θ)}{\partial θ_r \partial θ_s}\Bigr),

where

l(Θ)=\log L(Θ) \propto ∑_{i=1}^{m}X_i \log \bigl[F(t_{i}{{;}}Θ)-F(t_{i-1}{{;}}Θ)\bigr]+∑_{i=1}^{m}R_i\bigl[1-F(t_{i}{{;}}Θ)\bigr],

in which F(.;Θ) is the family cumulative distribution function for Θ=(θ_1,…,θ_k)^T and r,s=1,…,k.

1 2	fitype1(plan, param, mle, cdf.expression = FALSE, pdf.expression = TRUE, cdf, pdf , lb = 0)

`plan`	Censoring plan for progressive type-I interval censoring scheme. It must be given as a `data.frame` that includes vector of upper bounds of the censoring times `T`, vector of number of failed subjects `X`, vector of removed subjects in each interval `R`, and percentage of the removed alive items in each interval `P`.
`param`	Vector of the of the family parameter's names.
`mle`	Vector of the maximum likelihood estimators.
`cdf.expression`	Logical. That is `TRUE`, if there is a closed form expression for the cumulative distribution function.
`pdf.expression`	Logical. That is `TRUE`, if there is a closed form expression for the probability density function.
`cdf`	Expression of the cumulative distribution function.
`pdf`	Expression of the probability density function.
`lb`	Lower bound of the family support. That is zero by default.

For some families of distributions whose support is the positive semi-axis, i.e., x>0, the cumulative distribution function (cdf) may not be differentiable. In this case, the lower bound of the support of random variable, i.e., lb that is zero by default, must be chosen some positive small value to ensure the differentiability of the cdf.

Matrices that represent the expected and observed Fisher information matrices.

Mahdi Teimouri

N. Balakrishnan and E. Cramer. 2014. The art of progressive censoring. New York: Springer.

D. G. Chen and Y. L. Lio 2010. Parameter estimations for generalized exponential distribution under progressive type-I interval censoring, Computational Statistics and Data Analysis, 54, 1581-1591.

M. Teimouri 2020. Bias corrected maximum likelihood estimators under progressive type-I interval censoring scheme, Communications in Statistics-Simulation and Computation, doi.org/10.1080/036 10918.2020.1819320

  data(plasma)
      n <- 20
  param <- c("alpha","beta")
    mle <- c(0.4, 0.05)
    cdf <- quote( 1-exp( beta*(1-exp( x^alpha )) ) )
       pdf <- quote( exp( beta*(1-exp( x^alpha )) )*( beta*(exp( x^alpha )*(x^(alpha-1)*alpha) )) )
     lb <- 0
     plan <- rtype1(n = n, P = plasma$P, T = plasma$upper, param = param, mle = mle, cdf.expression
                  = FALSE, pdf.expression = TRUE, cdf = cdf, pdf = pdf, lb = lb)
fitype1(plan = plan, param = param, mle = mle, cdf.expression = FALSE, pdf.expression = TRUE, cdf =
        cdf, pdf = pdf, lb = lb)