Description Usage Arguments Value Author(s) References Examples
Computes the MLE of for the parameters of the model fitted to a progressive type-II censoring scheme with likelihood function
l(Θ)=\log L(Θ) \propto C ∑_{i=1}^{m} \log f(x_{i:m:n}{{;}}Θ) + ∑_{i=1}^{m} R_i \log \bigl[1-F(x_{i:m:n}{{;}}Θ)\bigr],
in which F(.;Θ) is the family cumulative distribution function for Θ=(θ_1,…,θ_k)^T and r,s=1,…,k, and C=n(n-R_1-1)(n-R_1-R_2-2)… (n-R_1-R_2-…-R_{m-1}-m+1).
1 2 |
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 | 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)
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