Gofpt2: Generalized Goodness-of-Fit Test for Censored Data

Implements a generalized goodness-of-fit test based on spacings for general progressive Type-II censored data. The test statistic is based on the methodology proposed by Qin et al. (2022) and extends the foundational work of Balakrishnan et al. (2003).

Users can test whether their observed censored lifetime data follows any specified continuous distribution by providing custom probability density function (pdf_func), cumulative distribution function (cdf_func), and survival function (survival_func). The package supports both normal approximation and Monte Carlo simulation approaches for computing \(p\)-values and critical values.

Features

• Generalized Goodness-of-Fit Test: Perform goodness-of-fit hypothesis testing on general progressive Type-II censored datasets.
• Custom Distribution Testing: Test against standard distributions (Exponential, Weibull, Gamma, Lognormal, etc.) or custom user-defined continuous probability distributions.
• Dual Inference Approaches: Compute \(p\)-values and critical bounds using either the analytical normal approximation (Theorem 4.1, Qin et al. 2022) or Monte Carlo simulation.
• Data Generation: Function generate_progressive_censored() enables generation of general progressive Type-II censored samples from arbitrary continuous distributions.
• Rich S3 Interface: Comprehensive print(), summary(), and plot() visualization methods.

Installation

You can install the development version of Gofpt2 from GitHub with:

# install.packages("devtools")
devtools::install_github("shikhartyagi/Gofpt2")

Quick Example

library(Gofpt2)

# Define censoring scheme: n = 19, m = 11, r = 2
scheme <- list(
  n = 19,
  m = 11,
  r = 2,
  R = c(0, 0, 2, 0, 0, 2, 0, 0, 1)
)

# Insulating fluid failure data from Example 6.1 (Qin et al., 2022)
obs_data <- c(0.96, 1.31, 3.16, 4.15, 4.67, 7.35, 8.01, 8.27, 32.52, 33.91, 36.71)

# Run goodness-of-fit test against exponential distribution
res <- gof_test_censored(
  data = obs_data,
  censoring_scheme = scheme,
  method = "normal"
)

# Display results
print(res)
summary(res)
plot(res)

References

• Qin, X., Gui, W., & Balakrishnan, N. (2022). A goodness-of-fit test for exponential distribution based on spacings for general progressive Type-II censored data. Journal of Applied Statistics, 49(8), 1821-1636. doi:10.1080/02664763.2020.1821613
• Balakrishnan, N., Ng, H.K.T., & Kannan, N. (2003). A test of exponentiality based on spacings for progressively type-II censored data. In Goodness-of-Fit Tests and Model Validity (pp. 89-111). Birkhäuser, Boston, MA.
• Balakrishnan, N., & Aggarwala, R. (2000). Progressive Censoring: Theory, Methods, and Applications. Birkhäuser, Boston.
• Lawless, J.F. (2003). Statistical Models and Methods for Lifetime Data (2nd ed.). John Wiley & Sons, New York.