mletype1 {bccp}

Computing the maximum likelihood estimator (MLE) for the parameters of the statistical model fitted to a progressive type-I interval censoring scheme.

Description

Computes the MLE of for the parameters of the model fitted to a progressive type-I interval censoring scheme with likelihood function

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

in which F(.;\Theta) is the family cumulative distribution function for \Theta=(\theta_1,\dots,\theta_k)^T provided that F(t_{0};\Theta)=0.

Usage

mletype1(plan, param, start, cdf.expression = FALSE, pdf.expression = TRUE, cdf, pdf,
         method = "Nelder-Mead", lb = 0, ub = Inf, level = 0.05)

Arguments

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 items X, and vector of removed items in each interval R.

param

Vector of the of the family parameter's names.

start

Vector of the initial values.

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.

method

The method for the numerically optimization that includes one of CG, Nelder-Mead, BFGS, L-BFGS-B, SANN.

lb

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

ub

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

level

Significance level for constructing asymptotic confidence interval That is 0.05 by default for constructing a 95% confidence interval.

Value

MLE, standard error of MLE, and asymptotic confidence interval for MLE.

Author(s)

Mahdi Teimouri

Examples

 data(plasma, package="bccp")
   plan <- data.frame(T = plasma$upper, X = plasma$X, P = plasma$P, R = plasma$R)
  param <- c("lambda","beta")
    mle <- c(1.4, 0.05)
    pdf <- quote( lambda*(1-exp( -(x*beta)))^(lambda-1)*beta*exp( -(x*beta)) )
    cdf <- quote( (1-exp( -(x*beta)))^lambda )
     lb <- 0
     ub <- Inf
  level <- 0.05
mletype1(plan = plan, param = param, start = mle, cdf.expression = FALSE, pdf.expression = TRUE,
         cdf = cdf, pdf = pdf, method = "Nelder-Mead", lb = lb, ub = ub, level = level)