Goodness-of-Fit Tests Based on<i>P</i>-<i>P</i>Probability Plots

Gan, F. F.; Koehler, Kenneth J.

doi:10.1080/00401706.1990.10484682

Cited by 21 publications

(9 citation statements)

References 19 publications

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“…For the selection of the tests included in the comparison the properties of tests for exponentiality can be used, which can be found in the studies of Stephens (1978), D'Agostino & Stephens (1986) and Gan & Koehler (1990). Gan & Koehler (1990) which use EDF based tests included the alternative hypothesis of a truncated exponential, finding only very low powers. With the stabilising transformation Kimber (1985) finds a larger power for the KS test, but did not include the truncated alternative.…”

Section: Description Of the Goodness-of-fit Test Statisticsmentioning

confidence: 99%

“…The most prominent goodness-of-fit test is the Kolmogorov-Smirnov (KS) statistic (Stephens 1978;D'Agostino & Stephens 1986;Gan & Koehler 1990),…”

Section: Edf Statistics Based On Distance Measuresmentioning

confidence: 99%

“…Another "measure of discrepancy" is the sum of the squared distances from the diagonal to the data point in a PP plot, the Cramér-von Mises statistic (Anderson & Darling 1952;Stephens 1978;D'Agostino & Stephens 1986;Gan & Koehler 1990),…”

Section: Edf Statistics Based On Distance Measuresmentioning

confidence: 99%

“…A modified form of the Cramér-von Mises statistic is the Anderson-Darling statistic, (Anderson & Darling 1952;Stephens 1978;D'Agostino & Stephens 1986;Gan & Koehler 1990)…”

Section: Edf Statistics Based On Distance Measuresmentioning

confidence: 99%

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Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions

Maschberger

Kroupa²

2009

Monthly Notices of the Royal Astronomical Society

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Many objects studied in astronomy follow a power‐law distribution function (DF), for example the masses of stars or star clusters. A still used method by which such data is analysed is to generate a histogram and fit a straight line to it. The parameters obtained in this way can be severely biased, and the properties of the underlying DF, such as its shape or a possible upper limit, are difficult to extract. In this work, we review techniques available in the literature and present newly developed (effectively) bias‐free estimators for the exponent and the upper limit. Furthermore, we discuss various graphical representations of the data and powerful goodness‐of‐fit tests to assess the validity of a power law for describing the distribution of data. As an example, we apply the presented methods to the data set of massive stars in R136 and the young star clusters in the Large Magellanic Cloud. For R136 we confirm the result of Koen of a truncated power law with a bias‐free estimate for the exponent of 2.20 ± 0.78/2.87 ± 0.98 (where the Salpeter–Massey value is 2.35) and for the upper limit of 143 ± 9/163 ± 9 M⊙, depending on the stellar models used. The star clusters in the Large Magellanic Cloud (with ages up to 107.5 yr) follow a truncated power‐law distribution with exponent 1.62 ± 0.06 and upper limit 68 ± 12 × 103 M⊙. Using the graphical data representation, a significant change in the form of the mass function below 102.5 M⊙ can be detected, which is likely caused by incompleteness in the data.

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Section: Description Of the Goodness-of-fit Test Statisticsmentioning

confidence: 99%

“…The most prominent goodness-of-fit test is the Kolmogorov-Smirnov (KS) statistic (Stephens 1978;D'Agostino & Stephens 1986;Gan & Koehler 1990),…”

Section: Edf Statistics Based On Distance Measuresmentioning

confidence: 99%

Section: Edf Statistics Based On Distance Measuresmentioning

confidence: 99%

“…A modified form of the Cramér-von Mises statistic is the Anderson-Darling statistic, (Anderson & Darling 1952;Stephens 1978;D'Agostino & Stephens 1986;Gan & Koehler 1990)…”

Section: Edf Statistics Based On Distance Measuresmentioning

confidence: 99%

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Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions

Maschberger

Kroupa²

2009

Monthly Notices of the Royal Astronomical Society

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“…Different plotting techniques may also be used to visually investigate the behavior of the residuals (e.g. QQ plot [15] and standardized PP plot [16]). However, visual inspections are subjective; any visual discrepancies found by the practitioner should only raise suspicion for the presence of potential discrepancies.…”

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confidence: 99%

Testing the Fit of Regression Models Estimated with Extremely Small Samples: Application in Pharmaceutical Stability Studies

Mihalovits

Kemény

2022

Period. Polytech. Chem. Eng.

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Pharmaceutical stability studies are conducted to estimate the shelf life, i.e. the period during which the drug product maintains its identity and stability. In the evaluation of process, regression curve is fitted on the data obtained during the study and the shelf life is determined using the fitted curve. The evaluation process suggested by ICH considers only the case of the true relationship between the measured attribute and time being linear. However, no method is suggested for the practitioner to decide if the linear model is appropriate for their dataset. This is a major problem, as a falsely selected model may distort the estimated shelf life to a great extent, resulting in unreliable quality control. The difficulty of model misspecification detection in stability studies is that very few observations are available. The conventional methods applied for model verification might not be appropriate or efficient due to the small sample size. In this paper, this problem is addressed and some developed methods are proposed to detect model misspecification. The methods can be applied for any process where the regression estimation is performed on independent small samples. Besides stability studies, frequently performed construction of single calibration curves for an analytical measurement is another case where the methods may be applied. It is shown that our methods are statistically appropriate and some of them have high efficiency in the detection of model misspecification when applied in simulated situations which resemble pre-approval and post-approval stability studies.

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Probability Plots and Distribution Curves for Assessing the Fit of Probability Models

Gan

Koehler

Thompson

1991

The American Statistician

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Goodness-of-Fit Tests Based onP-PProbability Plots

Cited by 21 publications

References 19 publications

Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions

Estimators for the exponent and upper limit, and goodness-of-fit tests for (truncated) power-law distributions

Testing the Fit of Regression Models Estimated with Extremely Small Samples: Application in Pharmaceutical Stability Studies

Probability Plots and Distribution Curves for Assessing the Fit of Probability Models

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