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. 2024 Dec 30;14(1):31936.
doi: 10.1038/s41598-024-83436-x.

The wrapped Rama distribution

William Bell  1 , Saralees Nadarajah  2
Affiliations

The wrapped Rama distribution

William Bell et al. Sci Rep. .

Abstract

A new one-parameter distribution is proposed for circular data based on wrapping. Most distributions constructed via wrapping do not yield elementary expressions for their mathematical properties. Yet the new distribution yields elementary expressions for all of its mathematical properties. Better fits of the new distribution over the three-parameter distribution due to Jones and Pewsey10 and six other wrapped distributions including four that have two parameters each are shown for at least two data sets. Better fits were assessed in terms of probability plots, density plots, values of Akaike information criterion and values of Bayesian information criterion.

Keywords: Circular data; Maximum likelihood; Trigonometric moments.

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Conflict of interest statement

Declarations. Competing interests: Both authors declare no conflicts of interest. Ethical approval: Not applicable. Consent to participate: Not applicable. Consent to publish: Both authors gave explicit consent to publish this manuscript.

Figures

Fig. 1
Fig. 1
Possible shapes of the probability density function (8).
Fig. 2
Fig. 2
Biases versus formula image.
Fig. 3
Fig. 3
Mean squared errors versus formula image.
Fig. 4
Fig. 4
Coverage lengths versus formula image.
Fig. 5
Fig. 5
Coverage probabilities versus formula image.
Fig. 6
Fig. 6
Probability plot (top) and density plot (bottom) of the fitted distributions for the feldspar laths data set.
Fig. 7
Fig. 7
Probability plot (top) and density plot (bottom) of the fitted distributions for the pebbles data set.
See this image and copyright information in PMC

References

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