Package {DepDoubleTruncKS}

Type:	Package
Title:	Kolmogorov-Smirnov Test for Dependently Double-Truncated Durations
Version:	0.1.0
Description:	Performs the Kolmogorov-Smirnov-type goodness-of-fit test for exponential duration models under independent or dependently double-truncated sampling scheme using Farlie-Gumbel-Morgenstern ('FGM') copulas, as proposed by Toparkus and Weissbach (2026) <doi:10.1007/s10985-026-09722-0>. Provides functions for profile maximum likelihood estimation / score equation solving, computation of the two-dimensional Kolmogorov-Smirnov test statistic over the double-truncation parallelogram, simulation of the asymptotic Gaussian process limit distribution for critical values and p-value calculation, and synthetic dataset generation.
License:	GPL (≥ 3)
Depends:	R (≥ 3.5.0)
Encoding:	UTF-8
LazyData:	true
RoxygenNote:	7.3.3
Imports:	stats, graphics
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
URL:	https://doi.org/10.1007/s10985-026-09722-0
NeedsCompilation:	no
Packaged:	2026-07-31 04:03:55 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-07 20:10:03 UTC

Region Integral E_theta(g_x,t,D) for FGM-Dependent Model

Description

Computes the expectation E_theta(g_x,t,D) = P_theta((X,T) in [0,x] x [0,t] intersect D) and its derivatives with respect to theta and vtheta under the FGM copula.

Usage

calc_E_fgm(x, t, s, G, theta, vtheta)

Arguments

Value

A list containing:

Region Integral E_theta(g_x,t,D) for Independent Model

Description

Computes the expectation E_theta(g_x,t,D) = P_theta((X,T) in [0,x] x [0,t] intersect D) and its derivative with respect to theta for independent truncation.

Usage

calc_E_ind(x, t, s, G, theta)

Arguments

Value

A list containing:

Calculate Observation Probability for FGM-Dependent Double Truncation

Description

Computes the observation probability alpha_theta and its gradient vector with respect to (theta, vtheta) for an exponentially distributed lifespan and uniformly distributed age under Farlie-Gumbel-Morgenstern (FGM) copula dependence.

Usage

calc_alpha_fgm(theta, vtheta, s, G)

Arguments

Value

A list containing:

Examples

calc_alpha_fgm(theta = 0.082, vtheta = 0.103, s = 3, G = 24)

Calculate Observation Probability for Independent Double Truncation

Description

Computes the observation probability alpha_theta and its derivative with respect to theta for an exponentially distributed lifespan and uniformly distributed age at study start under independent double truncation.

Usage

calc_alpha_ind(theta, s, G)

Arguments

Value

A list containing:

Examples

calc_alpha_ind(theta = 0.082, s = 3, G = 24)

Calculate Asymptotic Critical Values and P-Value

Description

Implements Algorithm 2 from Toparkus & Weissbach (2026) to compute critical values (90 on a 2D grid over the double-truncation region D.

Usage

calc_critical_values(
  ks_stat,
  theta,
  vtheta = 0,
  s,
  G,
  model = c("fgm", "ind"),
  grid_dim = 25,
  n_sim = 500
)

Arguments

Value

A list containing:

Examples

set.seed(123)
res <- calc_critical_values(ks_stat = 1.2, theta = 0.08, vtheta = 0,
                            s = 3, G = 24, model = "ind", grid_dim = 15, n_sim = 100)
res$crit_95

Compute 2D Kolmogorov-Smirnov Test Statistic for Truncated Data

Description

Implements Algorithm 1 from Toparkus & Weissbach (2026) to compute the 2D Kolmogorov-Smirnov test statistic comparing the empirical CDF and the parametric CDF over the double-truncation region D.

Usage

calc_ks_stat(x, t, s, G, theta, vtheta = 0, model = c("fgm", "ind"))

Arguments

Value

A list containing:

Examples

set.seed(123)
dat <- sim_double_trunc(n = 300, theta = 0.08, G = 24, s = 3, model = "ind")
fit <- fit_double_trunc(dat$x, dat$t, s = 3, G = 24, model = "ind")
ks_res <- calc_ks_stat(dat$x, dat$t, s = 3, G = 24, theta = fit$theta, model = "ind")
ks_res$ks_stat

Synthetic Enterprise Lifespans under Double Truncation

Description

A synthetic dataset containing 500 observed enterprise durations and age at study start under double truncation, constructed to mimic German enterprise lifespan data described in Toparkus & Weissbach (2026).

Usage

enterprise_data

Format

A data frame with 500 rows and 2 variables:

x

Observed enterprise duration (lifespan in years).

t

Observed age at study start (truncation age in years, between 0 and G=24).

Source

Simulated based on parameters from Toparkus & Weissbach (2026).

References

Toparkus, A.-M. and Weissbach, R. (2026). Kolmogorov-Smirnov-type test for dependently double-truncated durations: A copula approach. *Lifetime Data Analysis*, 32, 41. doi:10.1007/s10985-026-09722-0.

Examples

data(enterprise_data)
head(enterprise_data)

Fit Double-Truncated Exponential Duration Model

Description

Estimates the parameters of an exponential duration model under independent or dependently double-truncated sampling using Z-estimation / maximum likelihood.

Usage

fit_double_trunc(x, t, s, G, model = c("fgm", "ind"))

Arguments

Value

A list of class '"fit_double_trunc"' containing:

Examples

set.seed(123)
sim_dat <- sim_double_trunc(n = 500, theta = 0.08, G = 24, s = 3, model = "ind")
fit <- fit_double_trunc(sim_dat$x, sim_dat$t, s = 3, G = 24, model = "ind")
fit$theta

Kolmogorov-Smirnov-type Test for Dependently Double-Truncated Data

Description

Performs the 2D Kolmogorov-Smirnov goodness-of-fit test for exponential lifespan distributions under independent or Farlie-Gumbel-Morgenstern (FGM) copula dependent double truncation, as proposed by Toparkus & Weissbach (2026).

Usage

ks_dep_trunc(x, t, s, G, model = c("fgm", "ind"), grid_dim = 25, n_sim = 500)

Arguments

Value

An object of class "ks_dep_trunc" containing:

References

Toparkus, A.-M. and Weissbach, R. (2026). Kolmogorov-Smirnov-type test for dependently double-truncated durations: A copula approach. *Lifetime Data Analysis*, 32, 41. doi:10.1007/s10985-026-09722-0.

Examples

set.seed(42)
dat <- sim_double_trunc(n = 300, theta = 0.082, G = 24, s = 3, model = "ind")
res <- ks_dep_trunc(dat$x, dat$t, s = 3, G = 24, model = "ind", grid_dim = 15, n_sim = 100)
print(res)

Plot S3 Method for ks_dep_trunc

Description

Scatter plot of observed durations and truncation ages inside the truncation parallelogram D, along with theoretical boundaries.

Usage

## S3 method for class 'ks_dep_trunc'
plot(x, ...)

Arguments

Value

No return value, called for side effects.

Print S3 Method for ks_dep_trunc

Description

Print S3 Method for ks_dep_trunc

Usage

## S3 method for class 'ks_dep_trunc'
print(x, ...)

Arguments

Value

Invisibly returns the input object x.

Simulate Double-Truncated Duration Data

Description

Generates double-truncated duration data (X, T) under independent or Farlie-Gumbel-Morgenstern (FGM) copula dependence according to Algorithms 4 & 5 from Toparkus & Weissbach (2026).

Usage

sim_double_trunc(n, theta, G, s, vtheta = 0, model = c("fgm", "ind"))

Arguments

Value

A list containing:

Examples

set.seed(123)
dat <- sim_double_trunc(n = 1000, theta = 0.082, G = 24, s = 3, model = "ind")
head(dat$x)
dat$mn

Summary S3 Method for ks_dep_trunc

Description

Summary S3 Method for ks_dep_trunc

Usage

## S3 method for class 'ks_dep_trunc'
summary(object, ...)

Arguments

Value

Invisibly returns the input object object.