Package 'Gofpt2'

Gofpt2: Generalized Goodness-of-Fit Test for Progressive Type-II Censored Data

Description

Implements a generalized goodness-of-fit test based on spacings for general progressive Type-II censored data. The test statistic is based on the work of Qin et al. (2022) and extends the methodology of Balakrishnan et al. (2003). Users can test data against any distribution by providing custom pdf, cdf, and survival functions. The package supports both normal approximation and Monte Carlo simulation approaches for computing p-values and critical values.

Author(s)

Maintainer: Shikhar Tyagi [email protected] (ORCID)

Authors:

• Arvind Pandey [email protected]

• Bhupendra Singh [email protected]

• Vrijesh Tripathi [email protected]

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 Huber-Carol, C., Balakrishnan, N., Nikulin, M.S., & Mesbah, M. (Eds.), Goodness-of-Fit Tests and Model Validity (pp. 89-111). Birkhäuser, Boston, MA. doi:10.1007/978-1-4612-0103-8_8

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.

---

Compute Spacings from Censored Data

Description

Computes the spacings $S_{r+1}, S_{r+2}, \dots, S_m$ from progressive Type-II censored data according to equation (5) in Qin et al. (2022).

Usage

compute_spacings(
  data,
  censoring_scheme,
  cdf_func = NULL,
  survival_func = NULL,
  parameters = list()
)

Arguments

data	Numeric vector of observed failure times (length $m - r$).
censoring_scheme	A list containing n (total sample size), m (number of observed failures), and r (removals vector or initial unobserved count).
cdf_func	Optional cumulative distribution function of hypothesized distribution.
survival_func	Optional survival function of hypothesized distribution.
parameters	List of distribution parameters.

Value

A numeric vector of computed spacings $S_{r+1}, \dots, S_m$ of length $m - r$.

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

Examples

scheme <- list(n = 19, m = 11, r = 2, R = c(0, 0, 2, 0, 0, 2, 0, 0, 4))
obs_data <- c(3.16, 4.15, 4.67, 7.35, 8.01, 8.27, 32.52, 33.91, 36.71)
compute_spacings(obs_data, scheme)

---

Compute Critical Values for Goodness-of-Fit Test

Description

Computes lower and upper critical values of the test statistic $T$ for a specified significance level $\alpha$ using either normal approximation or Monte Carlo simulation.

Usage

critical_values(
  censoring_scheme,
  alpha = 0.05,
  method = c("normal", "simulation"),
  n_sim = 10000
)

Arguments

censoring_scheme	A list containing n (total sample size), m (number of observed failures), and r (removals vector or initial unobserved count).
alpha	Numeric, significance level (default: 0.05).
method	Character string, either "normal" for normal approximation or "simulation" for Monte Carlo simulation.
n_sim	Integer, number of simulations for Monte Carlo method (default: 10000).

Value

A named numeric vector of length 2 containing lower and upper critical bounds.

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

Examples

scheme <- list(n = 19, m = 11, r = 2, R = c(0, 0, 2, 0, 0, 2, 0, 0, 4))
critical_values(scheme, alpha = 0.05, method = "normal")

---

Compute Expected Spacings under Null Hypothesis

Description

Calculates the expected values of spacings $E(S_i)$ under the standard exponential null distribution for a given censoring scheme.

Usage

expected_spacings(censoring_scheme)

Arguments

censoring_scheme

A list containing n (total sample size), m (number of observed failures), and r (removals vector or initial unobserved count).

Value

A numeric vector of expected spacings $E(S_{r+1}), \dots, E(S_m)$.

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.

Examples

scheme <- list(n = 19, m = 11, r = 2, R = c(0, 0, 2, 0, 0, 2, 0, 0, 4))
expected_spacings(scheme)

---

Generate General Progressive Type-II Censored Data

Description

Generates progressive Type-II censored samples from a specified probability distribution.

Usage

generate_progressive_censored(
  censoring_scheme,
  pdf_func = NULL,
  cdf_func = NULL,
  survival_func = NULL,
  quantile_func = NULL,
  parameters = list()
)

Arguments

censoring_scheme	A list containing n (total sample size), m (number of observed failures), and r (removals vector or initial unobserved count).
pdf_func	Optional probability density function of target distribution.
cdf_func	Optional cumulative distribution function of target distribution.
survival_func	Optional survival function of target distribution.
quantile_func	Optional quantile function (inverse CDF) of target distribution.
parameters	List of distribution parameters.

Value

A numeric vector of length m - r containing ordered failure times.

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.

Balakrishnan, N., & Sandhu, R.A. (1995). A simple simulational algorithm for generating progressive type-II censored samples. The American Statistician, 49(2), 229-230.

Examples

scheme <- list(n = 19, m = 11, r = 2, R = c(0, 0, 2, 0, 0, 2, 0, 0, 1))
generate_progressive_censored(scheme)

---

Generalized Goodness-of-Fit Test for Progressive Type-II Censored Data

Description

Performs a generalized goodness-of-fit test based on spacings for general progressive Type-II censored data as proposed by Qin et al. (2022).

Usage

gof_test_censored(
  data,
  censoring_scheme,
  pdf_func = NULL,
  cdf_func = NULL,
  survival_func = NULL,
  method = c("normal", "simulation"),
  n_sim = 10000,
  alpha = 0.05,
  parameters = list()
)

Arguments

data	Numeric vector of observed failure times (ordered).
censoring_scheme	A list containing n (total sample size), m (number of observed failures), and r (removals vector or initial unobserved count).
pdf_func	Optional probability density function of hypothesized distribution.
cdf_func	Optional cumulative distribution function of hypothesized distribution.
survival_func	Optional survival function of hypothesized distribution.
method	Character string, either "normal" for normal approximation or "simulation" for Monte Carlo simulation.
n_sim	Integer, number of simulations for Monte Carlo method (default: 10000).
alpha	Numeric, significance level for critical values (default: 0.05).
parameters	List of distribution parameters.

Value

An object of class "gof_censored" containing:

test_statistic	Value of the test statistic $T$.
p_value	Computed p-value.
critical_value	Named vector of lower and upper critical values at significance level $\alpha$.
method	Method used for computation ("normal" or "simulation").
mu	Expected mean of test statistic $T$ under null distribution.
sigma	Standard deviation of test statistic $T$ under null distribution.
censoring_scheme	Parsed input censoring scheme.
data	Validated input failure data.
spacings	Computed spacings vector.
alpha	Significance level.
parameters	Distribution parameters.
distribution	Name of hypothesized distribution.

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.

Examples

scheme <- list(n = 19, m = 11, r = 2, R = c(0, 0, 2, 0, 0, 2, 0, 0, 4))
obs_data <- c(3.16, 4.15, 4.67, 7.35, 8.01, 8.27, 32.52, 33.91, 36.71)

# Test for Exponential distribution using Normal approximation
fit <- gof_test_censored(obs_data, scheme, method = "normal")
print(fit)
summary(fit)

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