mletype2 {bccp} | R Documentation |
Computes the MLE of for the parameters of the model fitted to a progressive type-II censoring scheme with likelihood function
l(\Theta)=\log L(\Theta) \propto C \sum_{i=1}^{m} \log f(x_{i:m:n}{{;}}\Theta) + \sum_{i=1}^{m} R_i \log \bigl[1-F(x_{i:m:n}{{;}}\Theta)\bigr],
in which F(.;\Theta)
is the family cumulative distribution function for \Theta=(\theta_1,\dots,\theta_k)^T
and r,s=1,\dots,k
, and C=n(n-R_1-1)(n-R_1-R_2-2)\dots (n-R_1-R_2-\dots-R_{m-1}-m+1)
.
mletype2(plan, param, start, cdf, pdf, method = "Nelder-Mead", lb = 0, ub = Inf, N = 100,
level = 0.05)
plan |
Censoring plan for progressive type-II censoring scheme. It must be given as a |
param |
Vector of the of the family parameter's names. |
start |
Vector of the initial values. |
pdf |
Expression of the probability density function. |
cdf |
Expression of the cumulative distribution 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 |
N |
An even integer number indicating the number of subdivisions for applying Simpson's integration method. |
level |
Significance level for constructing asymptotic confidence interval That is |
MLE, standard error of MLE, and asymptotic confidence interval for MLE.
Mahdi Teimouri
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.
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
level <- 0.05
plan <- rtype2(n = n, R = R, param = param, mle = mle, cdf = cdf, lb = lb, ub = ub)
mletype2(plan = plan, param = param, start = mle, cdf = cdf, pdf = pdf, method = "Nelder-Mead",
lb = lb, ub = ub, N = N, level = level)