| Type: | Package |
| Title: | Maximum Likelihood Estimation under Censoring Schemes |
| Version: | 0.1.0 |
| Description: | Provides generalized functions to compute Maximum Likelihood Estimation (MLE) for any univariate distribution under various censoring and truncation schemes. Users supply the probability density function (PDF), cumulative distribution function (CDF), survival function, support bounds, and initial parameter values; the package constructs and maximizes the appropriate log-likelihood automatically. Supported schemes include right and left truncation, random, right, left, interval, and middle censoring, block random censoring, balanced joint progressive Type-II (BJPT-II), progressive first failure, joint Type-I, Type-I, Type-II, progressive Type-II, Type-II progressively hybrid, joint Type-II, hybrid, hybrid Type-I, doubly Type-II, Type-I hybrid, and hybrid Type-II censoring. Optimization methods include Newton-Raphson (NR), Broyden-Fletcher-Goldfarb-Shanno (BFGS), the BFGS algorithm implemented in R (BFGSR), Berndt-Hall-Hall-Hausman (BHHH), Simulated Annealing (SANN), Conjugate Gradients (CG), and Nelder-Mead (NM). Inference summaries provide the Akaike Information Criterion (AIC), estimated coefficients, log-likelihood, iteration count, standard errors, z-values, p-values, and the variance-covariance matrix. Methods are described in Nagar, Kumar, and Krishna (2026) <doi:10.59467/IJASS.2026.22.1>, Goel, Kumar, and Krishna (2026, "Estimation in power Lindley distributions using balanced joint progressively Type-II censored data"), Wu and Kus (2009) <doi:10.1016/j.csda.2009.03.010>, Goel and Krishna (2026) <doi:10.1007/s13198-026-03208-w>, Balakrishnan and Aggarwala (2000, ISBN:978-1-4612-1334-5), Mondal and Kundu (2020) <doi:10.1080/03610926.2018.1554128>, Ding and Gui (2023) <doi:10.3390/math11092003>, Prajapati, Mitra, and Kundu (2019) <doi:10.1007/s13571-018-0167-0>, Yadav, Jaiswal, and Yadav (2026) <doi:10.1007/s11135-026-02647-8>, Iyer, Jammalamadaka, and Kundu (2008) <doi:10.1016/j.jspi.2007.03.062>, Banerjee and Kundu (2008) <doi:10.1109/TR.2008.916890>, Kundu and Joarder (2006) <doi:10.1016/j.csda.2005.05.002>, Berndt, Hall, Hall, and Hausman (1974) "Estimation and Inference in Nonlinear Structural Models" <doi:10.3386/t0003>, Fletcher (1987, "Practical Methods of Optimization", ISBN:978-0-471-91547-8), Nelder and Mead (1965) <doi:10.1093/comjnl/7.4.308>, McKinnon (1999) "Convergence of the Nelder-Mead simplex method to a non-stationary point" <doi:10.1137/S1052623496303482>, Kirkpatrick, Gelatt, and Vecchi (1983) <doi:10.1126/science.220.4598.671>, Fletcher and Reeves (1964) <doi:10.1093/comjnl/7.2.149>, and Nocedal and Wright (2006, "Numerical Optimization", ISBN:978-0-387-30303-1). |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.3 |
| Imports: | stats |
| Suggests: | testthat (≥ 3.0.0) |
| NeedsCompilation: | no |
| Packaged: | 2026-07-16 15:12:18 UTC; 30017827 |
| Author: | Shikhar Tyagi 
[aut, cre],
Vrijesh Tripathi [aut] |
| Maintainer: | Shikhar Tyagi <shikhar1093tyagi@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2026-07-23 14:10:09 UTC |
Extract Akaike Information Criterion (AIC)
Description
Extract Akaike Information Criterion (AIC)
Usage
## S3 method for class 'mle_fit'
AIC(object, ..., k = 2)
Arguments
object |
an object of class 'mle_fit' |
... |
further arguments |
k |
numeric, penalty per parameter (default is 2) |
Value
numeric value of AIC
Check if parameters are in their specified range
Description
Check if parameters are in their specified range
Usage
check_param_range(theta, param_range)
Arguments
theta |
numeric vector of parameters |
param_range |
list of ranges or a function |
Value
logical value indicating if parameters are in range
Extract Parameter Estimates
Description
Extract Parameter Estimates
Usage
## S3 method for class 'mle_fit'
coef(object, ...)
Arguments
object |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
numeric vector of estimated parameters
Inequality constraint handling via Logarithmic Barrier
Description
Inequality constraint handling via Logarithmic Barrier
Usage
constrOptim2(
fn,
grad_fn,
hess_fn,
start,
method,
ineqA,
ineqB,
param_range,
control,
...
)
Extract Log-Likelihood
Description
Extract Log-Likelihood
Usage
## S3 method for class 'mle_fit'
logLik(object, ...)
Arguments
object |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
an object of class 'logLik' with attributes "df" and "nobs"
MLE under Balanced Joint Progressive Type-II (BJPT-II) Censoring
Description
MLE under Balanced Joint Progressive Type-II (BJPT-II) Censoring
Usage
mle_bjpt2(
w,
z,
D_A,
D_B,
pdf_A = NULL,
cdf_A = NULL,
surv_A = NULL,
pdf_B = NULL,
cdf_B = NULL,
surv_B = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
w |
numeric vector of failure times (ordered). |
z |
numeric vector indicating group membership (1 for population A, 0 for population B). |
D_A |
numeric vector of removals from population A at each failure time. |
D_B |
numeric vector of removals from population B at each failure time. |
pdf_A |
density function of population A. |
cdf_A |
cumulative distribution function of population A. |
surv_A |
survival function of population A (optional). |
pdf_B |
density function of population B (optional, defaults to pdf_A). |
cdf_B |
cumulative distribution function of population B (optional, defaults to cdf_A). |
surv_B |
survival function of population B (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Block Random Censoring
Description
MLE under Block Random Censoring
Usage
mle_block_random(
x,
status,
block,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
status |
numeric vector indicating censoring status (1 = failure, 0 = censored). |
block |
vector indicating block/group membership for each observation. |
pdf |
density function of the distribution, potentially accepting a 'block' argument. |
cdf |
cumulative distribution function of the distribution, potentially accepting a 'block' argument. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Doubly Type-II Censoring
Description
MLE under Doubly Type-II Censoring
Usage
mle_doubly_type2(
x,
r,
s,
n,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
r |
integer, index of the first observed failure (1-based). |
s |
integer, index of the last observed failure (1-based). |
n |
integer, total initial units. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Hybrid Censoring (Type-I Hybrid)
Description
MLE under Hybrid Censoring (Type-I Hybrid)
Usage
mle_hybrid(
x,
r,
tc,
n,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
r |
integer, target number of failures. |
tc |
numeric, fixed censoring time. |
n |
integer, total initial units. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Hybrid Type-I Censoring
Description
Alias for mle_hybrid. The experiment terminates at
T^* = \min(x_{(r)}, T_c).
Usage
mle_hybrid_type1(
x,
r,
tc,
n,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
r |
integer, target number of failures. |
tc |
numeric, fixed censoring time. |
n |
integer, total initial units. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Hybrid Type-II Censoring
Description
MLE under Hybrid Type-II Censoring
Usage
mle_hybrid_type2(
x,
r,
tc,
n,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
r |
integer, target number of failures. |
tc |
numeric, fixed censoring time. |
n |
integer, total initial units. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Interval Censoring
Description
MLE under Interval Censoring
Usage
mle_interval(
l,
r,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
l |
numeric vector of lower bounds of the censoring intervals. |
r |
numeric vector of upper bounds of the censoring intervals. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Joint Type-I Censoring
Description
MLE under Joint Type-I Censoring
Usage
mle_joint_type1(
x,
z,
tc,
n_A,
n_B,
pdf_A = NULL,
cdf_A = NULL,
surv_A = NULL,
pdf_B = NULL,
cdf_B = NULL,
surv_B = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (<= tc) for both groups. |
z |
numeric vector indicating group membership (1 for population A, 0 for population B). |
tc |
numeric, fixed censoring time. |
n_A |
integer, total number of initial units in population A. |
n_B |
integer, total number of initial units in population B. |
pdf_A |
density function of population A. |
cdf_A |
cumulative distribution function of population A. |
surv_A |
survival function of population A (optional). |
pdf_B |
density function of population B (optional, defaults to pdf_A). |
cdf_B |
cumulative distribution function of population B (optional, defaults to cdf_A). |
surv_B |
survival function of population B (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Joint Type-II Censoring
Description
MLE under Joint Type-II Censoring
Usage
mle_joint_type2(
w,
z,
n_A,
n_B,
pdf_A = NULL,
cdf_A = NULL,
surv_A = NULL,
pdf_B = NULL,
cdf_B = NULL,
surv_B = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
w |
numeric vector of observed failure times (ordered). |
z |
numeric vector indicating group membership (1 for population A, 0 for population B). |
n_A |
integer, total initial units in population A. |
n_B |
integer, total initial units in population B. |
pdf_A |
density function of population A. |
cdf_A |
cumulative distribution function of population A. |
surv_A |
survival function of population A (optional). |
pdf_B |
density function of population B (optional, defaults to pdf_A). |
cdf_B |
cumulative distribution function of population B (optional, defaults to cdf_A). |
surv_B |
survival function of population B (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Left Censoring
Description
MLE under Left Censoring
Usage
mle_left(
x,
status,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
status |
numeric vector indicating censoring status (1 = failure, 0 = censored). |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Left Truncation
Description
MLE under Left Truncation
Usage
mle_left_truncation(
x,
tl,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
tl |
numeric vector or scalar of left truncation limits. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Middle Censoring
Description
MLE under Middle Censoring
Usage
mle_middle(
x,
u,
v,
status,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed times (or NA if censored). |
u |
numeric vector of lower bounds of the censoring intervals. |
v |
numeric vector of upper bounds of the censoring intervals. |
status |
numeric vector indicating censoring status (1 = exact, 0 = censored). |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
Unified optimization engine
Description
Unified optimization engine
Usage
mle_optimizer(
loglik_fn,
grad_fn,
hess_fn,
start,
method,
constraints,
param_range,
...
)
MLE under Progressive First Failure Censoring
Description
MLE under Progressive First Failure Censoring
Usage
mle_progressive_first_failure(
x,
r_removals,
k_group_size,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed first-failure times (ordered). |
r_removals |
numeric vector of group removals at each failure time. |
k_group_size |
integer, number of units per group. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Type-II Progressively Hybrid Censoring
Description
Computes the MLE for any univariate distribution under the Type-II
progressively hybrid censoring scheme (Kundu & Joarder, 2006). The experiment
terminates at T^* = \min(x_{(m)}, T_c), where
m is the planned number of failures and T_c is a
pre-specified time limit.
Usage
mle_progressive_hybrid_type2(
x,
r_removals,
tc,
n,
m,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered), only failures
observed before |
r_removals |
numeric vector of the full planned progressive
removal scheme |
tc |
numeric, pre-specified time limit |
n |
integer, total number of units initially placed on test. |
m |
integer, planned total number of failures (length of the full removal scheme). |
pdf |
density function of the distribution, accepting |
cdf |
cumulative distribution function of the distribution, accepting
|
surv |
survival function of the distribution (optional). If not
provided, computed as |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Details
The likelihood depends on whether the m-th failure occurs before or
after T_c:
Case I (D = m, i.e., all m failures observed before T_c):
L(\theta) \propto \prod_{i=1}^{m} f(x_i; \theta) \cdot S(x_i; \theta)^{R_i}
Case II (D = J < m, i.e., only J failures observed
before T_c):
L(\theta) \propto \left[\prod_{i=1}^{J} f(x_i; \theta) \cdot S(x_i;
\theta)^{R_i}\right] \cdot S(T_c; \theta)^{R_J^*}
where R_J^* = n - J - \sum_{i=1}^{J} R_i.
Value
An object of class mle_fit containing the optimization results.
References
Kundu, D., & Joarder, A. (2006). Analysis of Type-II progressively hybrid censored data. Computational Statistics & Data Analysis, 50(10), 2509-2528.
Examples
# Exponential distribution under Type-II progressively hybrid censoring
pdf_exp <- function(x, theta) dexp(x, rate = theta[1])
cdf_exp <- function(x, theta) pexp(x, rate = theta[1])
# Suppose n = 20, m = 10, tc = 2.0
# 7 failures observed before tc: Case II
x <- c(0.12, 0.35, 0.62, 0.89, 1.15, 1.48, 1.82)
r_removals <- c(1, 0, 1, 0, 1, 0, 0, 1, 0, 0) # full plan for m = 10
fit <- mle_progressive_hybrid_type2(
x = x, r_removals = r_removals, tc = 2.0, n = 20, m = 10,
pdf = pdf_exp, cdf = cdf_exp,
start = c(rate = 1.0)
)
summary(fit)
MLE under Progressive Type-II Censoring
Description
MLE under Progressive Type-II Censoring
Usage
mle_progressive_type2(
x,
r_removals,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
r_removals |
numeric vector of removals at each failure time. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Random Censoring
Description
MLE under Random Censoring
Usage
mle_random(
x,
status,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
status |
numeric vector indicating censoring status (1 = failure, 0 = censored). |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Right Censoring
Description
MLE under Right Censoring
Usage
mle_right(
x,
status,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
status |
numeric vector indicating censoring status (1 = failure, 0 = censored). |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Right Truncation
Description
MLE under Right Truncation
Usage
mle_right_truncation(
x,
tr,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
tr |
numeric vector or scalar of right truncation limits. |
pdf |
density function of the distribution, accepting '(x, theta, ...)'. |
cdf |
cumulative distribution function of the distribution, accepting '(x, theta, ...)'. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Type-I Censoring
Description
MLE under Type-I Censoring
Usage
mle_type1(
x,
tc,
status = NULL,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed values. |
tc |
numeric, fixed censoring time. |
status |
numeric vector indicating censoring status (optional, determined as x < tc if NULL). |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Type-I Hybrid Censoring
Description
Alias for mle_hybrid. The experiment terminates at
T^* = \min(x_{(r)}, T_c).
Usage
mle_type1_hybrid(
x,
r,
tc,
n,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
r |
integer, target number of failures. |
tc |
numeric, fixed censoring time. |
n |
integer, total initial units. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
MLE under Type-II Censoring
Description
MLE under Type-II Censoring
Usage
mle_type2(
x,
n,
pdf = NULL,
cdf = NULL,
surv = NULL,
start,
method = NULL,
constraints = NULL,
grad = NULL,
hess = NULL,
param_range = NULL,
logLik = NULL,
...
)
Arguments
x |
numeric vector of observed failure times (ordered). |
n |
integer, total number of units in the experiment. |
pdf |
density function of the distribution. |
cdf |
cumulative distribution function of the distribution. |
surv |
survival function of the distribution (optional). |
start |
numeric vector of initial parameter values. |
method |
character string, optimization method. |
constraints |
list, optimization constraints. |
grad |
gradient function. |
hess |
Hessian function. |
param_range |
list, parameter ranges. |
logLik |
custom log-likelihood function. |
... |
further arguments passed to optimization or user-defined functions. |
Value
An object of class 'mle_fit' containing the optimization results.
Extract Number of Iterations
Description
Extract Number of Iterations
Usage
nIter(x, ...)
Arguments
x |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
integer representing number of iterations
Numerical gradient using central difference
Description
Numerical gradient using central difference
Usage
num_grad(fn, theta, eps = 1e-05, ...)
Arguments
fn |
function returning scalar log-likelihood |
theta |
numeric vector of parameters |
eps |
step size |
... |
extra arguments passed to fn |
Value
gradient vector
Numerical observation-wise gradient
Description
Numerical observation-wise gradient
Usage
num_grad_obs(fn, theta, eps = 1e-05, ...)
Arguments
fn |
function returning observation-specific log-likelihood |
theta |
numeric vector of parameters |
eps |
step size |
... |
extra arguments passed to fn |
Value
matrix of gradients where rows correspond to observations and columns to parameters
Numerical Hessian
Description
Numerical Hessian
Usage
num_hess(grad_fn, theta, eps = 1e-05, ...)
Arguments
grad_fn |
function returning gradient vector |
theta |
numeric vector of parameters |
eps |
step size |
... |
extra arguments passed to grad_fn |
Value
Hessian matrix
BFGS Optimization in pure R (BFGSR method)
Description
BFGS Optimization in pure R (BFGSR method)
Usage
opt_BFGSR(fn, grad_fn, start, control, param_range, ...)
Newton-Raphson Optimization in pure R
Description
Newton-Raphson Optimization in pure R
Usage
opt_NR(fn, grad_fn, hess_fn, start, control, param_range, ...)
Print MLE Fit
Description
Print MLE Fit
Usage
## S3 method for class 'mle_fit'
print(x, ...)
Arguments
x |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
The input object x is returned invisibly. Called for its
side effect of printing estimated parameters and the log-likelihood
value to the console.
Print Summary Table
Description
Print Summary Table
Usage
## S3 method for class 'summary.mle_fit'
print(x, ...)
Arguments
x |
an object of class 'summary.mle_fit' |
... |
further arguments (currently ignored) |
Value
The input object x is returned invisibly. Called for its
side effect of printing a formatted summary table to the console.
Helper to resolve pdf, cdf, and surv functions
Description
Helper to resolve pdf, cdf, and surv functions
Usage
resolve_funcs(pdf, cdf, surv)
Safe logarithm to handle zero or negative values
Description
Safe logarithm to handle zero or negative values
Usage
safe_log(v)
Arguments
v |
numeric vector |
Value
numeric vector with log values, -Inf where v <= 0
Extract Standard Errors
Description
Extract Standard Errors
Usage
stdEr(x, ...)
Arguments
x |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
numeric vector of standard errors
Summarize MLE Fit
Description
Summarize MLE Fit
Usage
## S3 method for class 'mle_fit'
summary(object, ...)
Arguments
object |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
summary.mle_fit object
Equality constraint handling via SUMT (Sequential Unconstrained Minimization Technique)
Description
Equality constraint handling via SUMT (Sequential Unconstrained Minimization Technique)
Usage
sumt(fn, grad_fn, hess_fn, start, method, eqA, eqB, param_range, control, ...)
Extract Variance-Covariance Matrix
Description
Extract Variance-Covariance Matrix
Usage
## S3 method for class 'mle_fit'
vcov(object, ...)
Arguments
object |
an object of class 'mle_fit' |
... |
further arguments (currently ignored) |
Value
variance-covariance matrix