Modelling Shot Lengths of Hollywood Motion Pictures with the Dagum Distribution




Dagum distribution, Skewness, Kurtosis, Shot length distribution, Motion pictures


This paper demonstrates the three-parameter Dagum distribution provides a good fit for shot lengths in Hollywood films due to its ability to model a wide range of skewness and kurtosis values and a variety of tail behaviours by virtue of its two shape parameters. The fit of this distribution is better across films in the sample than the two-parameter lognormal distribution, though animated films are an important exception to this. These results can be applied to more closely replicate the editing practice of film editors when generating film sequences using automated editing software.


F.ÁLVAREZ, F. SÁNCHEZ, G.HERNÁNDEZ-PEÑALOZA, D. JIMÉNEZ, J. M.MENÉNDEZ, G. CISNEROS (2019). On the influence of low-level visual features in film classification. PloS ONE, 14, no. 2, p. e0211406.

M. AUSLOOS, R. CERQUETI (2018). Intriguing yet simple skewness: Kurtosis relation in economic and demographic data distributions, pointing to preferential attachment processes. Journal of Applied Statistics, 45, no. 12, pp. 2202–2218.

M. BAXTER (2014). Notes on Cinemetric Data Analysis. Online; accessed 26 August 2019.

D. BORDWELL (2006). The Way Hollywood Tells It: Story and Style in Modern Movies. University of California Press, Berkeley, CA.

J. E. CUTTING, A. CANDAN (2015). Shot durations, shot classes, and the increased pace of popular movies. Projections, 9, no. 2, pp. 40–62.

J. E. CUTTING, J. D. LONG, C. E. NOTHELFER (2010). Attention and the evolution of Hollywood film. Psychological Science, 21, no. 3, pp. 432–439.

C. DAGUM (2008). A new model of personal income distribution: Specification and estimation. In D. CHOTIKAPANICH (ed.), Modeling Income Distributions and Lorenz Curves, Springer, New York, pp. 3–25.

M. L. DELIGNETTE-MULLER, C. DUTANG (2015). fitdistrplus: An R package for fitting distributions. Journal of Statistical Software, 64, no. 4, pp. 1–34.

C.DUTANG,V.GOULET, M. PIGEON (2008). actuar: AnRpackage for actuarial science. Journal of Statistical Software, 25, no. 7, pp. 1–37.

Q. GALVANE, R. RONFARD, M. CHRISTIE (2015a). Comparing film-editing. In Eurographics Workshop on Intelligent Cinematography and Editing, WICED '15, May 2015, Zurich, Switzerland. The Eurographics Association, pp. 5–12.

Q. GALVANE, R. RONFARD, C. LINO, M. CHRISTIE (2015b). Continuity editing for 3d animation. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence. pp. 753–761.

C. KLEIBER (1996). Dagum vs. Singh-Maddala income distributions. Economics Letters, 53, no. 3, pp. 265–268.

C. KLEIBER (2008). A guide to the Dagum distributions. In D. CHOTIKAPANICH (ed.), Modeling Income Distributions and Lorenz Curves, Springer, New York, pp. 97–117.

C. KLEIBER, S. KOTZ (2003). Statistical Size Distributions in Economics and Actuarial Sciences. JohnWiley & Sons, Hoboken, NJ.

I. KOHARA, R. NIIMI (2013). The shot length styles of Miyazaki, Oshii, and Hosoda: A quantitative analysis. Animation, 8, no. 2, pp. 163–184.

M. LEAKE, A. DAVIS, A. TRUONG, M. AGRAWALA (2017). Computational video editing for dialogue-driven scenes. ACM Transactions on Graphics, 36, no. 4, pp. 130–1.

J. MCDONALD, J. SORENSEN, P. A. TURLEY (2013). Skewness and kurtosis properties of income distribution models. Review of Income andWealth, 59, no. 2, pp. 360–374.

R CORE TEAM (2018). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL

A. E. RAFTERY (1995). Bayesian model selection in social research. Sociological Methodology, 25, pp. 111–164.

R. RONFARD (2017). Five challenges for intelligent cinematography and editing. In Eurographics Workshop on Intelligent Cinematography and Editing, Eurographics Association, April 2017, Lyon, France.

F. SATTIN, M. AGOSTINI, R. CAVAZZANA, G. SERIANNI, P. SCARIN, N. VIANELLO (2009). About the parabolic relation existing between the skewness and the kurtosis in time series of experimental data. Physica Scripta, 79, no. 4, p. 045006.

J. R. SMITH, D. JOSHI, B.HUET,W.HSU, J.COTA (2017). Harnessing A. I. for augmenting creativity: Application to movie trailer creation. In Proceedings of the 2017 ACM on Multimedia Conference - MM ’17. ACM Press, Mountain View, California, USA, p. 1799–1808. URL

C. TASKIRAN, E. DELP (2002). A study on the distribution of shot lengths for video analysis. In SPIE Conference on Storage and Retrieval for Media Databases. vol. 4315.

N. VASCONCELOS, A. LIPPMAN (2000). Statistical models of video structure for content analysis and characterization. IEEE Transactions on Image Processing, 9, no. 1, pp. 3–19.

P. H.WESTFALL (2014). Kurtosis as peakedness, 1905–2014. R.I.P. The American Statistician,68, no. 3, pp. 191–195.




How to Cite

Redfern, N. (2020). Modelling Shot Lengths of Hollywood Motion Pictures with the Dagum Distribution. Statistica, 80(1), 81–99.