An R package for testing goodness of fit: goft
Abstract
This R package implements three types of goodness-of-fit tests for some widely used probability distributions where there are unknown parameters, namely tests based on data transformations, on the ratio of two estimators of a dispersion parameter, and correlation tests. Most of the considered tests have been proved to be powerful against a wide range of alternatives and some new ones are proposed here. The package's functionality is illustrated with several examples by using some data sets from the areas of environmental studies, biology and finance, among others.
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The response variables anxiety and death follow an Inverse Gaussian distribution.
“For both anxiety and death, the test confirmed an Inverse Gaussian distribution (W = 0.339, p < .001 and W = 0.557, p < .001 respectively).”
From Understanding terror states of online users in the context of COVID-19: An application of Terror Management Theory (2021) · cites this paper as Gonzalez-Estrada & Villasenor-Alva, 2018
Cites
Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
Anderson, T. W., & Darling, D. A. (1952) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729437 · Cited by 3,542 · see citing works
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Cook, C., Mosqueiro, T., Brent, C., Ozturk, C., Gadau, J., Pinter-Wollman, N., & Smith, B. (2018) · Journal of Animal Ecology · doi:10.1111/1365-2656.12911 · Cited by 50
Accelerated degradation data analysis based on inverse Gaussian process with unit heterogeneity
Zheng, H., Yang, J., Kang, W., & Zhao, Y. (2023) · Applied Mathematical Modelling · doi:10.1016/j.apm.2023.11.003 · Cited by 33
de Oliveira-Junior, N. D., Heringer, G., Bueno, M., Pontara, V., & Meira-Neto, J. (2020) · Forest Ecology and Management · doi:10.1016/j.foreco.2020.118247 · Cited by 32 · see citing works
“3 version (R Development Core Team, 2017), where the Jaccard index was calculated with ‘vegdist’ function in ‘vegan’ package (Oksanen, 2016), the linearity of the models were tested with ‘cumres’ function in ‘gof’ package (González-Estrada and Villaseñor, 2018), the best model was assessed with ‘dredge’ function const…”
MethodBarnes, S. J. (2021) · Computers in Human Behavior · doi:10.1016/j.chb.2021.106967 · Cited by 23 · see citing works
Maitra, N., Anandhakumar, J., Blank, H., Kaplan, C., & Polymenis, M. (2018) · G3: Genes, Genomes, Genetics · doi:10.1534/g3.118.200854 · Cited by 13 · see citing works
Jana, N., & Gautam, M. (2022) · Communications in statistics. Simulation and computation · doi:10.1080/03610918.2022.2102652 · Cited by 10
Davila, C., Fiorenza, J. E., Gershenzon, J., Reichelt, M., Zavala, J. A., & Fernández, P. (2023) · Frontiers in Ecology and Evolution · doi:10.3389/fevo.2023.1084063 · Cited by 8
“Goodness of fit for gamma was previously tested with goft package (González-Estrada and Villaseñor, 2018).”
MethodOrdered classification rules for inverse gaussian populations with unknown parameters
Jana, N., & Kumar, S. (2019) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2019.1628233 · Cited by 8
Goodness-of-fit tests for inverse Gaussian distribution in the presence and absence of censoring
Xavier, T., Vaisakh, K. M., & Sreedevi, E. (2024) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2024.2443133 · Cited by 7
“Moreover, we compare the competitiveness of our test with the another three tests proposed specifically for testing IG distribution, given by Henze and Klar [9] and González-Estrada and Villaseñor [26].”
Yadav, A., Srivastava, S., & Pant, M. (2024) · Life Cycle Reliability and Safety Engineering · doi:10.1007/s41872-024-00265-7 · Cited by 5
Age-related effects on lexical, but not syntactic, processes during sentence production
Hardy, S., Segaert, K., & Wheeldon, L. (2021) · Language, Cognition and Neuroscience · doi:10.1080/23273798.2021.1948081 · Cited by 5 · see citing works
“We also performed a goodness-of-fi t test using the “ ig_test ” function in the goft package (González-Estrada & Villaseñor, 2018).”
MethodHigh-sugar diet leads to loss of beneficial probiotics in housefly larvae guts
Voulgari‐Kokota, A., Boatta, F., Rijkers, R., Wertheim, B., Beukeboom, L. W., Ellers, J., & Salles, J. F. (2024) · The ISME Journal · doi:10.1093/ismejo/wrae193 · Cited by 3 · see citing works
“The larval biomass measurements, pupation, and adult emergence counts were tested for distribution using the package goft [51] and they were subsequently compared with t-tests with the native stats package [38].”
MethodIdentifying priority connectivity in a tropical forest hotspot severely affected by land use changes
de Oliveira-Junior, N. D., Heringer, G., Bueno, M., Pontara, V., & Meira-Neto, J. (2020) · bioRxiv · doi:10.1101/2020.03.13.991372 · Cited by 4
“…was calculated with ‘vegdist’ function in ‘vegan’ package (Oksanen, 2016), the linearity of the models were tested with ‘cumres’ function in ‘gof’ package (González-Estrada and Villaseñor, 2018), the best model was assessed with ‘dredge’ function constraining the selection to models with only one…”
MethodSequential Estimation of an Inverse Gaussian Mean with Known Coefficient of Variation
Chaturvedi, A., Bapat, S. R., & Joshi, N. (2021) · Sankhya B · doi:10.1007/s13571-021-00266-x · Cited by 3
“One may refer to Mancera-Rico (2014) or Gonzalez-Estrada and Villasenor (2018) for more details.”
BackgroundKraiem, Z., Ouerghi, S., Elcheikh, R., & Achour, H. (2025) · Ain Shams Engineering Journal · doi:10.1016/j.asej.2025.103775 · Cited by 2
Computationally Efficient Tests for Multivariate Skew Normality
González-Estrada, E. (2025) · Journal of Statistical Theory and Practice · doi:10.1007/s42519-025-00457-z · Cited by 2
Self-citationHolistic pedestrian safety assessment for average males and females
Leo, C., Fredriksson, A., Grumert, E. F., Linder, A., Schachner, M., Tidborg, F., & Klug, C. (2023) · Frontiers in Public Health · doi:10.3389/fpubh.2023.1199949 · Cited by 2
cvmgof: an R package for Cramér–von Mises goodness-of-fit tests in regression models
Azaïs, R., Ferrigno, S., & Martinez, M.-J. (2021) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2021.1991346 · Cited by 2
“Another recent package is goft [13] which performs several goodness-of-fit tests for probability distributions with unknown parameters that are used in statistical modelling , such as the multivariate and univariate Gaussian distributions.”
MethodChakraborty, A., & Jana, N. (2024) · Computational statistics (Zeitschrift) · doi:10.1007/s00180-024-01554-6 · Cited by 1
“We use goft package (González-Estrada and Villaseñor 2017) in R programming language to fit the IG distribution to the data.”
Long-read sequencing identifies a common transposition haplotype predisposing for CLCNKB deletions
Tschernoster, N., Erger, F., Kohl, S., Reusch, B., Wenzel, A., Walsh, S., Thiele, H., Becker, C., Franitza, M., Bartram, M. P., et al. (2023) · Genome Medicine · doi:10.1186/s13073-023-01215-1 · Cited by 1 · see citing works
“1-2), and goft [36] (v1.”
INVERSE GAUSSIAN REGRESSION MODELING AND ITS APPLICATION IN NEONATAL MORTALITY CASES IN INDONESIA
Fathurahman, M. (2022) · BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN · doi:10.30598/barekengvol16iss4pp1197-1206 · Cited by 1
“Adopting [5], [6], and [7], the hypotheses used for this test are: H0: Y1 = Y2 = ⋯ = Yn~IG(μ, ζ) (Yi does follow an IG distribution) H1: Yi does not follow an IG distribution, for i = 1,2,.”
MethodThe PYSATL Experiment Framework
Mironov, A., Golofastov, L., & Gorikhovskii, V. (2025) · Conference of the Open Innovations Association · doi:10.23919/fruct65909.2025.11008066
“[5] [6] Their main problem is the lack of flexibility in testing and the lack of functionality for comparing criteria.”
Jana, N., & Gautam, M. (2025) · Journal of Statistical Computation and Simulation · doi:10.1080/00949655.2025.2453857
“Table 4 presents criteria information, including p -values obtained using goft package [30], RMSE, and different ICs.”
Voulgari-Kokota, A., Slijfer, R., Beukeboom, L., Salles, J., & Wertheim, B. (2024) · Journal of Insects as Food and Feed · doi:10.1163/23524588-20230094
Li, B. (2018) · doi:10.25236/ajcis.010011
“The general steps are as follows [7]: (1) Enter data first, using scan () function; (2) Group data, calculate frequency of each group, and call cut () function and table () function to group and count; (3) Calculate the theoretical probability values of the original hypothesis (hypothesis distribution) in each cell.”
MethodScale-free networks: improved inference
Jerez-Lillo, N., Rodrigues, F. A., & Ramos, P. (2023) · arXiv.org · doi:10.48550/arxiv.2311.11200
“For continuous distributions, many tests have already been implemented in different statistical software for general families of distributions [20].”
- Authors
- González-Estrada, E., & Villaseñor, J. A.
- Affiliations
- Colegio de Postgraduados
- Venue
- Journal of Statistical Computation and Simulation
- Publisher
- Informa UK Limited
- Published
- 2017-11-23
- Volume
- 88
- Issue
- 4
- Pages
- 726-751
- ISSN
- 0094-9655 (ISSN-L)
- 1563-5163
- OpenAlex
- W2771058404
- Cited by
- 29
- References
- 0
- Citations by year
- 2025: 4 · 2024: 8 · 2023: 4 · 2022: 3 · 2021: 4 · 2020: 2 · 2019: 1 · 2018: 3
- FWCI
- 1.15
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Statistical Computation and Simulation (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Computer Science › Artificial Intelligence › Data Analysis with R
- Keywords
- goodness-of-fit tests, probability distributions, unknown parameters, data transformation, dispersion parameter, correlation test, R package, statistical software
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