mletype1 {bccp} | R Documentation |
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
.
mletype1(plan, param, start, cdf.expression = FALSE, pdf.expression = TRUE, cdf, pdf,
method = "Nelder-Mead", lb = 0, ub = Inf, level = 0.05)
plan |
Censoring plan for progressive type-I interval censoring scheme. It must be given as a |
param |
Vector of the of the family parameter's names. |
start |
Vector of the initial values. |
cdf.expression |
Logical. That is |
pdf.expression |
Logical. That is |
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 |
lb |
Lower bound of the family's support. That is zero by default. |
ub |
Upper bound of the family's support. That is |
level |
Significance level for constructing asymptotic confidence interval That is |
MLE, standard error of MLE, and asymptotic confidence interval for MLE.
Mahdi Teimouri
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)