A chi-square goodness-of-fit test for continuous distributions against a known alternative

@article{Rolke2021ACG,
  title={A chi-square goodness-of-fit test for continuous distributions against a known alternative},
  author={Wolfgang Rolke and Cristian Gutierrez Gongora},
  journal={Comput. Stat.},
  year={2021},
  volume={36},
  pages={1885-1900}
}
The chi square goodness-of-fit test is among the oldest known statistical tests, first proposed by Pearson in 1900 for the multinomial distribution. It has been in use in many fields ever since. However, various studies have shown that when applied to data from a continuous distribution it is generally inferior to other methods such as the Kolmogorov-Smirnov or Anderson-Darling tests. However, the performance, that is the power, of the chi square test depends crucially on the way the data is… 
Discrete Weibull distribution: different estimation methods under ranked set sampling and simple random sampling
The discrete Weibull (DW) is a discretized version of the well-known Weibull distribution, and, as such can be considered in reliability and survival analyses where the variable of interest involves
Reservoir operation under influence of the joint uncertainty of inflow and evaporation
Reservoirs play a major role as an essential source of surface water, especially in arid and semi-arid regions. To optimize the operation of a reservoir and determine its storage, which varies in
Beneficial Neglect
TLDR
The results showed that receiving messages and frequent checking occur during class and that problematic behaviors exist related to instant messaging in learning contexts and recommends further study to devise effective intervention mechanisms.
Supplemental Studies for Simultaneous Goodness-of-Fit Testing
Testing to see whether a given data set comes from some specified distribution is among the oldest types of problems in Statistics. Many such tests have been developed and their performance studied.

References

SHOWING 1-10 OF 34 REFERENCES
The Number of Classes in Chi-Squared Goodness-of-Fit Tests
Abstract The power of Pearson chi-squared and likelihood ratio goodness-of-fit tests based on different partitions is studied by considering families of densities “between” the null density and fixed
Chi-Squared Goodness-of-Fit Tests: Cell Selection and Power
To use the Pearson chi-squared statistic to test the fit of a continuous distribution, it is necessary to partition the support of the distribution into k cells. A common practice is to partition the
Data driven versions of pearson's chisquare test for uniformity
The test statistic of Pearson's Chi-square test for uniformity can be seen as the L 2-distance between the null density and the histogram density estimator. The power of this test depends heavily on
The Choice of the Number and Width of Classes for the Chi-Square Test of Goodness of Fit
Abstract This article describes in non-mathematical fashion the technique suggested by H. B. Mann and A. Wald for selecting the number and width of class intervals for the chi-square test of goodness
CHOOSING THE OPTIMUM NUMBER OF CLASSES IN THE CHI-SQUARE TEST FOR ARBITRARY POWER LEVELS
When values of a random variable X19 X2, .., XN are fitted to a hypothe sized statistical distribution, the x2 tes* is sometimes used to determine whether the fit is accep table. When the postulated
EFFICIENCIES OF CHI-SQUARE AND LIKELIHOOD RATIO GOODNESS-OF-FIT TESTS
The classical problem of choice of number of classes in testing goodness of fit is considered for a class of alternatives, for the chi-square and likelihood ratio statistics. Pitman and Bahadur
How Many Classes in the Pearson Chi-Square Test?
Abstract The asymptotic non-null distribution is obtained for the modified form of the Pearson chi-square statistic studied by Dahiya and Gurland [3]. By utilizing this result the power is obtained
THE CHOICE OF CELLS IN CHI–SQUARE TESTS
The choice of cells in chi–square goodness of fit tests is a classical problem. Some recent results in this area are discussed. It is shown that the likelihood ratio of alternatives w.r.t. null
The Kolmogorov-Smirnov Test for Goodness of Fit
Abstract The test is based on the maximum difference between an empirical and a hypothetical cumulative distribution. Percentage points are tabled, and a lower bound to the power function is charted.
Pearsons-X2 and the loglikelihood ratio statistic-G2: a comparative review
Summary The importance of developing useful and appropriate statistical methods for analyzing discrete multivariate data is apparent from the enormous amount of attention this subject has commanded
...
...