The log-normal distribution is not an appropriate parametric model for shot length distributions of Hollywood films

摘要

We examine the assertion that the two-parameter log-normal distribution is an appropriate parametric model for the shot length distributions of Hollywood films. A review of the claims made in favour of assuming log-normality for shot length distributions finds them to be lacking in methodological detail and statistical rigour. We find there is no supporting evidence to justify the assumption of log-normality in general for shot length distributions. In order to test this assumption, we examined a total of 134 Hollywood films from 1935 to 2005, inclusive, to determine goodness-of-fit of a normal distribution to log-transformed shot lengths of these films using four separate measures: the ratio of the geometric mean to the median; the ratio of the shape factor sigma to the estimator sigma(star) = root(2 x ln ((x) over bar /M)); the Shapiro-Francia test; and the Jarque-Bera test. Normal probability plots were also used for visual inspection of the data. The results show that, while a small number of films are well modelled by a log-normal distribution, this is not the case for the overwhelming majority of films tested (125 out of 134). Therefore, we conclude there is no justification for claiming the log-normal distribution is an adequate parametric model of shot length data for Hollywood films and recommend the use of robust statistics that do not require underlying parametric models for the analysis of film style.