Goodness of fit tests for discrete distributions

1986 ◽  
Vol 15 (3) ◽  
pp. 815-829 ◽  
Author(s):  
S Kocherlakota ◽  
K Kocherlakota
Keyword(s):  
Goodness Of Fit ◽  
Discrete Distributions ◽  
Goodness Of Fit Tests

Review of Probability Distributions

2018 ◽  
pp. 25-73
Keyword(s):  
Confidence Intervals ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Discrete Distributions ◽  
Continuous Distributions ◽  
R Language ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Analysis And Study ◽  
Waiting Lines

In Chapter 2, probability distributions are presented; the distributions exposed are those with more relation to the analysis and study of waiting lines; discrete distributions: binomial, geometric, Poisson; continuous distributions: uniform, exponential, erlang, and normal. Confidence intervals are calculated for some of the parameters of the distributions. A brief example of the generation of pseudorandom exponential times using a spreadsheet is presented. The chapter closes with the goodness-of-fit tests of probability distributions, especially the Anderson-Darling test. The statistical language of programming R is used in the exercises performed. Several codes are proposed in R Language to perform calculations automatically.

scholarly journals Visual Assessment vs. Statistical Goodness of Fit Tests for Identifying Parent Population

1988 ◽  
Vol 32 (7) ◽  
pp. 460-464
Author(s):  
Mari Berry ◽  
Brian Peacock ◽  
Bobbie Foote ◽  
Lawrence Leemis
Keyword(s):  
Goodness Of Fit ◽  
Statistical Tests ◽  
Visual Assessment ◽  
Discrete Distributions ◽  
Human Observer ◽  
Chi Square ◽  
Data Set ◽  
Goodness Of Fit Tests ◽  
Parent Distribution ◽  
Chi Square Test

Statistical tests are used to identify the parent distribution corresponding to a data set. A human observer looking at a histogram can also identify a probability distribution that models the parent distribution. The accuracy of a human observer was compared to the chi-square test for discrete data and the Kolmogorov-Smirnov and chi-square tests for continuous data. The human observer proved more accurate in identifying continuous distributions and the chi-square test proved to be superior in identifying discrete distributions. The effect of sample size and number of intervals in the histogram was included in the experimental design.

scholarly journals Testing for goodness rather than lack of fit of continuous probability distributions

PLoS ONE ◽  
2021 ◽  
Vol 16 (9) ◽  
pp. e0256499
Author(s):  
Stefan Wellek
Keyword(s):  
Goodness Of Fit ◽  
Alternative Hypothesis ◽  
Probability Distributions ◽  
Testing Procedure ◽  
Discrete Distributions ◽  
Testing Procedures ◽  
Continuous Type ◽  
Goodness Of Fit Tests ◽  
True Distribution

The vast majority of testing procedures presented in the literature as goodness-of-fit tests fail to accomplish what the term is promising. Actually, a significant result of such a test indicates that the true distribution underlying the data differs substantially from the assumed model, whereas the true objective is usually to establish that the model fits the data sufficiently well. Meeting that objective requires to carry out a testing procedure for a problem in which the statement that the deviations between model and true distribution are small, plays the role of the alternative hypothesis. Testing procedures of this kind, for which the term tests for equivalence has been coined in statistical usage, are available for establishing goodness-of-fit of discrete distributions. We show how this methodology can be extended to settings where interest is in establishing goodness-of-fit of distributions of the continuous type.

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