coxbctype2 {bccp}

Computing the bias corrected maximum likelihood estimator.

Description

Computing the bias corrected maximum likelihood estimator (MLE) for the parameters of the general family of distributions under progressive type-II censoring scheme.

Usage

coxbctype2(plan, param, mle, cdf, pdf, lb = 0, ub = Inf, N = 100)

Arguments

plan

Censoring plan for progressive type-II censoring scheme. It must be given as a data.frame that includes number of failed items X, and vector of removed items R.

param

Vector of the of the family parameter's names.

mle

Vector of the maximum likelihood estimators.

cdf

Expression for the cumulative distribution function.

pdf

Expression for the probability density function.

lb

Lower bound of the family's support. That is zero by default.

ub

Upper bound of the family support. That is Inf by default.

N

An even integer value indicating the number of subdivisions for applying Simpson's integration method.

Details

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.

Value

A list of the outputs including: a matric that represents the variance-covariance matrix of the MLE, a matrix that represents the variance-covariance matrix of the bias corrected MLE, a list of three outputs including MLE, bias of MLE, and bias corrected MLE, a list of godness-of-fit measures consists of Anderson-Darling (AD), Cramer-von Misses (CVM), and Kolmogorov-Smirnov (KS), statistics.

Author(s)

Mahdi Teimouri

References

D. R. Cox and E. J. Snell 1968. A general definition of residuals. Journal of the Royal Statistical Society: Series B (Methodological), 30(2), 248-265.

M. Teimouri and S. Nadarajah 2016. Bias corrected MLEs under progressive type-II censoring scheme, Journal of Statistical Computation and Simulation, 86 (14), 2714-2726.

Examples

     n <- 10
     R <- c(5, rep(0, n-6) )
 param <- c("alpha","beta")
   mle <- c(2,6)
   pdf <- quote( alpha/beta*(x/beta)^(alpha-1)*exp( -(x/beta)^alpha ) )
   cdf <- quote( 1-exp( -(x/beta)^alpha ) )
    lb <- 0
    ub <- Inf
     N <- 100
  plan <- rtype2(n = n, R = R, param = param, mle = mle, cdf = cdf, lb = lb, ub = ub)
  coxbctype2(plan = plan, param = param, mle = mle, cdf = cdf, pdf = pdf, lb = lb, ub = ub, N = N)