Package 'emplikCS' reference manual

Title:	Empirical Likelihood with Current Status Data for Mean, Probability, Hazard
Description:	Compute the empirical likelihood ratio, -2LogLikRatio (Wilks) statistics, based on current status data for the hypotheses about the parameters of mean or probability or weighted cumulative hazard.
Authors:	Mai Zhou [aut, cre]
Maintainer:	Mai Zhou <[email protected]>
License:	GPL (>= 2)
Version:	0.3
Built:	2026-06-03 09:50:13 UTC
Source:	https://github.com/cran/emplikCS

Current Status Data Buckley-James Estimator For Linear Regression Models

Description

In an AFT regression model, when the reponses are current status censored (observe yi either > ti or <= ti), we may still estimate the regression coefficients by the Buckley-James (extension from right censored case). We assume the inspection time ti have a larger support to cover the support of error epsilon, which is assumed iid.

Usage

CSbj(x, delta, Itime, maxiter = 99, error = 0.0001) 
CSbj(x, delta, Itime, maxiter = 99, error = 0.0001)

Arguments

x

Design matrix. N rows p columns.

delta

Either 0 or 1. I[yi <= Itimei]. Length N. yi = beta xi + ei

Itime

The inspection times. Length N.

maxiter

Default to 99. Control the iteration.

error

Default to 0.0001. Control the iteration.

Details

This function is an implementation of the Buckley-James estimator for the regression parameter beta in the AFT regression model when the responses, yi, are current status censored. Similar to the Binary Choice model in econometrics where all the inspection times are fixed at zero. I wrote an S-plus function for the binary choice model (name bibj). It is easily adapted to the current status situation, and this is the function. The AFT model we considered here has an intercept term. But we try to estimate the regression parameter beta, without the intercept term first. The estimator of the intercept can be obtained (if needed) as the mean of the iid errors/residuals after we got the estimator of the slope parameter beta.

This function depends on the functions monotone from package monotone and lsfit from the basic stats package.

At this point, we do not have a good estimate for the variance for the Buckley-James estimators. Bootstrap is one method one can try.

Value

It returns a list containing

est

The Buckley-James estimator of the regression coefficients.

iterN

Number of iterations done.

distFx

Locations of the jumps of final estimator of the error distribution.

distFy

Probabilities of the final estimator of the error distribution at jump locations. Mean of this error distribution is the intercept term estimator of the regression model.

Author(s)

Mai Zhou <[email protected]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Wang, W., and Zhou, M. (1995). Iterative least squares estimator of binary choice models: a semi-parametric approach. Tech. Report, University of Kentucky. https://www.ms.uky.edu/~mai/research/eco5wz.pdf

Buckley, J. J., and James, I. R. (1979). Linear regression with censored data. Biometrika 66, 429–436.

Examples

 
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)

Order the Given Current Status Data and Output with Some Additional Information

Description

Given N current status data, order according to inspection times, and find the positions (in the ordered data) of the first 1 and last 0 of the delta.

Usage

CSdataclean(itime, delta) 
CSdataclean(itime, delta)

Arguments

itime

The inspection times. Length N.

delta

Either 0 or 1. I[yi <= itimei]. Length N.

Details

When calculate NPMLE of the CDF F(t) from current status data, it is obvious that F(t) = 0 before the location (in itime) of first delta=1 occurance in the delta list, and similarly, F(t) = 1 after the last delta=0 occurance. So in the calculation of NPMLE we need only to consider estimating F(.) when time t is from itime[first] to itime[last].

We take the definition of NPMLE $\hat F_n(t)$ as right continuous.

Usually, the current status data are stored in either long format or short format. The short format is often used when there are many tied inspection times. This function, CSdataclean, takes input of current status data in the long format: itime=(t1, t2, ... tN) and delta=(0,1,... 1). The only values in the delta are 0 or 1. If needed you can convert the short format to long format using function L2S.

Value

It returns a list containing

itime

The ordered inspection times.

delta

The delta, ordered according to itime.

Istart

delta[Istart] is the first 1 in the ordered delta output.

Iend

delta[Iend] is the last 0 in the ordered delta output.

Author(s)

Mai Zhou <[email protected]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Examples

 
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)

Current Status Data Empirical Likellihood Test for Two Parameters: $F(t_1)$ and $F(t_2)$ Jointly

Description

Given n current status data, we may estimate the CDF F(t) by NPMLE (e.g. by isotNEW2() function in this package). This function, el.CS.2prob, uses empirical likelihood to test the hypothesis that F(t) at two given locations(t01 and t02) equal to two given values (Ft01 and Ft02): i.e. H0: F(t01) = Ft01 and F(t02) = Ft02 jointly.

Empirical likelihood ratio test returns the Wilks statistics, -2LLR. By our working conjecture, the -2 log likelihood ratio times (5/3) under H0 is approximately chi square DF=2 distributed. See reference below.

Usage

 
el.CS.2prob(ti, di, t01, Ft01, t02, Ft02) 
el.CS.2prob(ti, di, t01, Ft01, t02, Ft02)

Arguments

ti

The inspection times, a vector of length n.

di

Either 0 or 1. I[yi <= ti]. length n.

t01

The given time where F() value is tested.

Ft01

The hypothesized value of F(t01). Must be within (0, 1).

t02

The given time where F() value is tested.

Ft02

The hypothesized value of F(t02). Must be within (0, 1).

Details

This function tests the null hypothesis that F(t01) = Ft01 and F(t02) = Ft02 versus at least one not equal. We assume the data given is current status censored data.

We require t01 (and also t02) be equal to one of the inspection times. If not, you have to do something using the right continuity of the NPMLE (change t01 to the closest ti on the left, etc.).

The NPMLE F(t) is convergent at cubic root n speed and the -2LLR times (5/3) has chi square DF=2 null distribution, according to the working conjecture.

It goes without saying that we assume the NPMLE has finite asymptotic variance (when normalized by cubic root n).

Value

It returns a list containing

"-2LLR"

The Wilks statistics of the EL test, after multiply by (5/3) has approximate chi SQ DF=2 distribution under null hypothesis.

LogLik0

The log lik value achieved by the un-constrained NPMLE.

LogLik1

The log lik value achieved by the constrained NPMLE.

Author(s)

Mai Zhou <[email protected]>.

References

Banerjee, M., and Wellner, J. (2001). Likelihood ratio tests for monotone functions. Annals of Statistics 29, 1699-1731.

Banerjee, M., and Wellner, J. (2005). Score statistics for current sta- tus data: Comparisons with likelihood ratio and Wald statistics. The International Journal of Biostatistics 1, 1-29.

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC.

Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data Springer, New York.

Examples

N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-2), 0.3, 0.6) )       #### inspection times      
Stime <- rexp(N)                         #### survival times
delta <- as.numeric(Stime <= itime)      ####  current status censoring
N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-2), 0.3, 0.6) )       #### inspection times      
Stime <- rexp(N)                         #### survival times
delta <- as.numeric(Stime <= itime)      ####  current status censoring

Current Status Data Empirical Likellihood Test for a Parameter Defined by Weighted Cumulative Hazard

Description

Given n current status data, we may estimate the CDF F(t) by NPMLE (e.g. by isotNEW2 in this package). By the 1 to 1 correspondence, $\Lambda (t)= - \log [1-F(t)]$ , we can also calculate the NPMLE of the cumulative hazard function $\Lambda(t)$ . We are interested in a parameter defined by weighted average of cumulative hazard function (or integrated cumulative hazard) defined below. Empirical likelihood ratio test is performed and return a Wilks statistics. The Wilks statistics, -2 log likelihood ratio, under H0 is approximately chi square DF=1 distributed.

Usage

 
el.CS.Hz(ti, di, Pfun, thetaMU, error=1e-11, maxit=25) 
el.CS.Hz(ti, di, Pfun, thetaMU, error=1e-11, maxit=25)

Arguments

ti

The inspection times, a vector of length n.

di

Either 0 or 1. I[yi <= ti]. length n.

Pfun

The function used in calculate the weighted cumulative hazard. See an example below.

thetaMU

The null hypothesis value of the weighted cumulative hazard to be tested.

error

Default to 1e-11. Control the SQP iteration.

maxit

Default to 25. Control the SQP iteration.

Details

This function tests the null hypothesis that the parameter of weighted (or integrated) cumulative hazard function equal to the given value (thetaMU). We assume the data given is current status censored data.

The (unknown) true value of the parameter of interest is defined by

$\theta(\Lambda_0) = \int_0^M \Lambda_0(s) d \Psi(s)$

where $\Lambda_0(s)$ is the true cumulative hazard function. And $\Psi(s)$ is the weight function given(Pfun, used to generate weights). The function $\Psi (s)$ is assumed to be continuous and at least piecewise differtiable.

The NPMLE of cumulative hazard, $\hat \Lambda_n(t)$ , is obtained via the NPMLE of CDF $\hat F_n(t)$ :

$\hat \Lambda_n(t) = - \log [ 1- \hat F_n(t)] ~.$

It goes without saying that we assume the parameter is well defined (not equal to infinity) and its NPMLE has finite asymptotic variance.

Value

It returns a list containing

"-2LLR"

The Wilks statistics of the EL test, has approximate chi SQ DF=1 distribution under null hypothesis.

location

The locations of jumps of the NPMLE of cumulative hazard function (also of CDF).

Haz

The constrained NPMLE of cumulative hazard function.

iter

Number of iterations done.

error

The error at final iteration, = sum(abs(difference))

Loglik1

The log lik value achieved by the constrained NPMLE.

Check

The weighted cumulative hazard by the constrained NPMLE. This should equal to thetaMU (of input). A check of convergence.

thetaMLE

The NPMLE of the (non-constrained) weighted cumulative hazard. The input value thetaMU should not deviate from this value by too much.

Author(s)

Mai Zhou <[email protected]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Examples

#### An example of the Pfun (or Psi(s) or weight function) and calculation ####
mydgfun2 <- function(t){0.3*t*(10-t)*as.numeric(t<=10)}

N <- 3000
set.seed(12345)
itime <- sort(rexp(N, rate=0.1))       #### inspection times      
Stime <- rexp(N, rate=0.1)             #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

el.CS.Hz(ti=itime, di=delta, Pfun=mydgfun2, thetaMU= -5) ## -5 is the true value of parameter.

#### You should get 
## $`-2LLR`
## [1] 1.04782          #### and more.
#### An example of the Pfun (or Psi(s) or weight function) and calculation ####
mydgfun2 <- function(t){0.3*t*(10-t)*as.numeric(t<=10)}

N <- 3000
set.seed(12345)
itime <- sort(rexp(N, rate=0.1))       #### inspection times      
Stime <- rexp(N, rate=0.1)             #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

el.CS.Hz(ti=itime, di=delta, Pfun=mydgfun2, thetaMU= -5) ## -5 is the true value of parameter.

#### You should get 
## $`-2LLR`
## [1] 1.04782          #### and more.

Current Status Data Empirical Likellihood Test for the Parameter of Mean: mu(F)

Description

Given n current status data, we may estimate the CDF F(t) by NPMLE (e.g. by the isotNEW2() function in this package). Based on the NPMLE $\hat F_n(t)$ we can estimate the mean mu(F).

This function, el.CS.mean, uses empirical likelihood to test the hypothesis that mu(F) equal to a given value(mu): i.e. H0: mu(F) = mu.

Empirical likelihood ratio test returns the Wilks statistics, -2LLR. The -2 log likelihood ratio under H0 is asymptotically chi square DF=1 distributed. See reference below.

Usage

 
el.CS.mean(mu, Itime, delta, Pfun) 
el.CS.mean(mu, Itime, delta, Pfun)

Arguments

mu

The hypothesized mean value.

Itime

The inspection times, a vector of length n.

delta

Either 0 or 1. I[yi <= ti]. length n.

Pfun

A given function, $\Psi(s)$ , used to define the (weighted) mean.

Details

This function tests the null hypothesis that mu(F) = mu versus not equal. We assume the data given is current status censored data.

The definition of the mean, mu(F) is

$\mu(F) = \int_0^M [1- F(t)] d \Psi(t)$

and its estimator based on $(\delta_i, t_i)$ or $\hat F_n$ is (assume $\min(t_i) =0$ or $t_{(1)} =0$ )

${\mu(\hat F_n )} = \sum_{i=1}^n [1-\hat F_n(t_{(i)})] \Delta \Psi(t_{(i)})~,$

where $\Psi (t)$ is a given function and $\Delta \Psi(t_{(i)})= \Psi (t_{(i+1)}) - \Psi(t_{(i)})$ . If $\Psi(t) =t$ in the above, then this is the ordinary mean (assuming F(t) has support (0, M) ).

The NPMLE $\hat F_n(t)$ is convergent at cubic root n speed, but the mean estimator is convergent at ordinary root n speed. The -2LLR has chi square DF=1 null distribution asymptotically.

It goes without saying that we assume the NPMLE mu(hat F) has finite asymptotic variance (when normalized by root n).

Value

It returns a list containing

"-2LLR"

The Wilks statistics of the EL test, has approximate chi SQ DF=1 distribution under null hypothesis.

Author(s)

Mai Zhou <[email protected]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Huang, J. and Wellner, J. (1995). Asymptotic normality of the NPMLE of linear functionals for interval censored data, case 1 Statistica Neerlandica 49, 2, 153–163.

Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data Springer, New York.

Examples

N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-1), 0.5) )       #### inspection times      
Stime <- rexp(N)                       #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring
N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-1), 0.5) )       #### inspection times      
Stime <- rexp(N)                       #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

Current Status Data Empirical Likellihood Test for the Probability $F(t_0)$ .

Description

Given n current status data, we may estimate the CDF F(t) by NPMLE (e.g. by isotNEW2() function in this package). This function, el.CS.prob, uses empirical likelihood to test the hypothesis that F(t) at a given location (t0) equal to a given value (Ft0): i.e. H0: F(t0) = Ft0.

Empirical likelihood ratio test returns the Wilks statistics, -2LLR. According to our working conjecture, the -2 log likelihood ratio times (5/3) under H0 is approximately chi square DF=1 distributed. See references below.

Usage

 
el.CS.prob(ti, di, t0=0.5, Ft0=0.5) 
el.CS.prob(ti, di, t0=0.5, Ft0=0.5)

Arguments

ti

The inspection times, a vector of length n.

di

Either 0 or 1. I[yi <= ti]. length n.

t0

The given time where F() value is tested.

Ft0

The hypothesized value of F(t0). Must be within (0, 1).

Details

This function tests the null hypothesis that F(t0) = Ft0 versus not equal. We assume the data given is current status censored data.

We require t0 equals to one of the inspection times. If not, you have to do something by the right continuity of the NPMLE (change t0 to the closest ti on the left).

The NPMLE F(t) is convergent at cubic root speed and the -2LLR times (5/3) has chi square DF=1 null distribution, according to our working conjecture.

It goes without saying that we assume the NPMLE has finite asymptotic variance (when normalized by cubic root n).

Value

It returns a list containing

"-2LLR"

The Wilks statistics of the EL test, when multiply by (5/3) has approximate chi SQ DF=1 distribution under null hypothesis.

LogLik0

The log lik value achieved by the un-constrained NPMLE.

LogLik1

The log lik value achieved by the constrained NPMLE.

Author(s)

Mai Zhou <[email protected]>.

References

Banerjee, M., and Wellner, J. (2001). Likelihood ratio tests for monotone functions. Annals of Statistics 29, 1699-1731.

Banerjee, M., and Wellner, J. (2005). Score statistics for current sta- tus data: Comparisons with likelihood ratio and Wald statistics. The International Journal of Biostatistics 1, 1-29.

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data Springer, New York.

Examples

N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-1), 0.5) )       #### inspection times      
Stime <- rexp(N)             #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

el.CS.prob( ti=itime, di=delta, t0=0.5, Ft0=pexp(0.5) ) 

#### You should get 
## $`-2LLR`
## [1] 1.867655     #### and more.
N <- 300
set.seed(12345)
itime <- sort(c(rexp(N-1), 0.5) )       #### inspection times      
Stime <- rexp(N)             #### survival times
delta <- as.numeric(Stime <= itime)    ####  current status censoring

el.CS.prob( ti=itime, di=delta, t0=0.5, Ft0=pexp(0.5) ) 

#### You should get 
## $`-2LLR`
## [1] 1.867655     #### and more.

Given Current Status Data, Calculate the NPMLE of CDF F(t) by Calling the monotone Function from monotone Package

Description

Using improved PAVA algorithm to calculate the NPMLE of CDF F(t). Input inspection times (x) can have ties. We require two extra inputs a and b to make sure the output is a proper CDF: $F(t_{(1)}-a) =0$ , and $F(t_{(n)}+b) =1$ always, and the rest are increase from 0 to 1.

Usage

isotNEW2(x, y, a, b, LONG=TRUE) 
isotNEW2(x, y, a, b, LONG=TRUE)

Arguments

x

Inspection time of the current status data.

y

Equivalent to delta in the current status data. Either 0 or 1 as in I[survTi <= xi]. length N.

a

To make sure the output F(.) is a proper CDF: F(x[1]-a) = 0 always.

b

To make sure the output F(.) is a proper CDF: F(x[n]+b) = 1 always.

LONG

Should the output in the LONG format or not? Default is TRUE.

Details

Usually, the current status data are stored in either long format or short format. The short format is often used when there are many tied inspection times. This function, isotNEW2, takes in the current status data in the long form: x=(t1, t2, ... tN) and y=(0, 1, ... 1). The only values of the y are 0 or 1.

For more details please refer to monotone package.

May be we should put a=1, b=1 as default?

Since the NPMLE of F(t) has very few number of jumps (for sample size N, the number of positive jumps are about cubic root N), a short format output can same space. For current status data of sample size 1000, usually the NPMLE F(t) has about 10 jumps. So the short format has length about 10 and the long format has length 1000.

Value

It returns a list in either the long format or short format containing

x

The ordered inspection times, including x[1]-a, and x[n]+b.

y

The NPMLE of F(x) at the x time, F(x[1]-a)=0 always; F(x[n]+b)=1 always.

Author(s)

Mai Zhou <[email protected]>.

References

Busing, F. (2022). Monotone regression: A simple and fast O(n) PAVA implementation. Journal of Statistical Software, Code Snippets 102, 1, 1–25. doi:10.18637/jss.v102.c01

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Examples

 
itime <- c(1,  2,  3,  4,  5,  6,  7,  8)
delta <- c(0,  1,  0,  1,  1,  1,  0,  1)

isotNEW2(x=itime, y=delta, a=0.5, b=0.5)
## $x
##  [1] 0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 8.5
## 
## $y
##  [1] 0.00 0.00 0.50 0.50 0.75 0.75 0.75 0.75 1.00 1.00
####  the correct answer is  F(t) =  0,  .5, .5, .75, .75, .75, .75,  1
####  at the ordered itime, augumented by a and b.
isotNEW2(x=itime, y=delta, a=0.5, b=0.5, LONG=FALSE)
## $x
## [1] 2 4 8
## 
## $y
## [1] 0.50 0.75 1.00  #### for time t < 2, F(t) = 0 by right cont.
itime <- c(1,  2,  3,  4,  5,  6,  7,  8)
delta <- c(0,  1,  0,  1,  1,  1,  0,  1)

isotNEW2(x=itime, y=delta, a=0.5, b=0.5)
## $x
##  [1] 0.5 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 8.5
## 
## $y
##  [1] 0.00 0.00 0.50 0.50 0.75 0.75 0.75 0.75 1.00 1.00
####  the correct answer is  F(t) =  0,  .5, .5, .75, .75, .75, .75,  1
####  at the ordered itime, augumented by a and b.
isotNEW2(x=itime, y=delta, a=0.5, b=0.5, LONG=FALSE)
## $x
## [1] 2 4 8
## 
## $y
## [1] 0.50 0.75 1.00  #### for time t < 2, F(t) = 0 by right cont.

Convert the Current Status Data from Long Format to Short Format

Description

Given current status data (two vectors of length n): one vector of inspection times, the other vector = I[Yi <= ti]. We assume the input is ordered according to itime. Convert the same data into short format. Useful when there are a lot of tied inspection times. (saves space).

Usage

L2S(itime, delta) 
L2S(itime, delta)

Arguments

itime

The inspection times. Length n.

delta

Either 0 or 1. I[yi <= itimei]. Length n.

Details

Same data set of 850 cases Hepatitis A tests from Bulgaria recorded in long format hepABulg in the R package csci compare to the short format hepatitisA in the R package curstatCI.

This function (and the sister function S2L) can be used to convert between the short and long format.

Value

It returns a list containing

Sitime

The ordered inspection times. Short format. Tied itimes removed.

fi

Number of delta's=1, with identical itime ti.

ni

Number of itimes tied at ti.

Author(s)

Mai Zhou <[email protected]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Examples

 
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)

Convert the Current Status Data from Short Format to Long Format

Description

Given current status data in short format (three vectors), convert it to the long format (one vector of inspection times, another vector=I[Yi <= ti]). We assume the input is ordered according to inspection times itime.

Usage

S2L(itime, fi, ni, OneFirst=TRUE) 
S2L(itime, fi, ni, OneFirst=TRUE)

Arguments

itime

The unique inspection times. Tie removed. Length k.

fi

Frequency of 1's in the delta. Definition is I[yi <= itimei]. Length k.

ni

Frequency of inspection times ti tied at this value. Length k.

OneFirst

In the output of long format data, within the same inspection times, delta=1's comes before 0's. Default to TRUE.

Details

Same data set of 850 cases Hepatitis A tests from Bulgaria recorded in long format hepABulg in the R package csci compare to the short format hepatitisA in the R package curstatCI.

This function (and the sister function S2L) can be used to convert between the short and long format.

Value

It returns a list containing

Litime

The ordered inspection times. Long format.

delta

This is I[Yi <= ti].

Author(s)

Mai Zhou <[email protected]>.

References

Zhou, M. (2026). Empirical Likelihood Method in Survival Analysis 2nd Edition Chapman & Hall/CRC

Examples

 
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)
y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)

Package 'emplikCS'

Help Index

Current Status Data Buckley-James Estimator For Linear Regression Models

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Order the Given Current Status Data and Output with Some Additional Information

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Current Status Data Empirical Likellihood Test for Two Parameters: F(t1)F(t_1)F(t1​) and F(t2)F(t_2)F(t2​) Jointly

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Current Status Data Empirical Likellihood Test for a Parameter Defined by Weighted Cumulative Hazard

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Current Status Data Empirical Likellihood Test for the Parameter of Mean: mu(F)

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Current Status Data Empirical Likellihood Test for the Probability F(t0)F(t_0)F(t0​).

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Given Current Status Data, Calculate the NPMLE of CDF F(t) by Calling the monotone Function from monotone Package

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Convert the Current Status Data from Long Format to Short Format

Description

Usage

Arguments

Details

Value

Author(s)

References

Examples

Convert the Current Status Data from Short Format to Long Format

Description

Usage

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Current Status Data Empirical Likellihood Test for Two Parameters: $F(t_1)$ and $F(t_2)$ Jointly

Current Status Data Empirical Likellihood Test for the Probability $F(t_0)$ .