This function calculates the mean resultant length as defined in Mardia et al. (2000).
mrl(data)numeric vector of dimension q with the mean resultant lengths. The i element is the mean resultant lenght of the i population which is in the row i of the matrix data.
matrix with the data
Author(s): Sandra Barragán. Maintainer: <sandra.barragan@gmail.com>
It is supposed that we have n replications for each population. $$\overline{R}=\frac{1}{n}\sqrt{S^{2}+C^{2}}$$ $$where\hspace{0.5cm} S=\sum_{k=1}^{n}\sin{\theta_k}\hspace{0.5cm} and \hspace{0.5cm} C=\sum_{k=1}^{n}\cos{\theta_k}$$
The argument data could be a matrix with n columns and q rows, q is the number of populations. data could also be a vector. For both cases the function rho.circular from the package circular is used in the calculations.
Missing values in the replications are allowed.
Mardia, K. and Jupp, P. (2000). Directional Statistics, Chichester: Wiley.
Rueda, C., Fernandez, M. A. and Peddada, S. D. (2009). Estimation of parameters subject to order restrictions on a circle with application to estimation of phase angles of cell-cycle genes. Journal of the American Statistical Association, 104, n485; pp 338--347. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2742472/
Fernandez, M. A., Rueda, C. and Peddada, S. D. (2012). Identification of a core set of signature cell cycle genes whose relative order of time to peak expression is conserved across species, Nucl. Acids Res. 40, n7: pp 2823--2832. doi:10.1093/nar/gkr1077. https://academic.oup.com/nar/article/40/7/2823/1183140
CIRE, sce, cond.test.
data(datareplic)
mrl(datareplic)
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