mletype1 {bccp} R Documentation

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.

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)


[Package bccp version 0.5.0 Index]