Description Usage Arguments Details Value Author(s) References
View source: R/mix.d.sum.of.mixtures.EXPLN.R
Density of a sum of i.i.d. random variables, where each random variable is from the following mixture distribution: With probability p_i, it is of type i. For all but the largest i, it is lognormally distributed with log-mean mu_i and log-standard deviation sigma_i. Otherwise it is exponentially distributed with rate lambda. The density is somehow a "mixed" one, as for all values in n
the density of the random variable is calculated and the weighted average is taken to be the density of this specific value.
1 | mix.d.sum.of.mixtures.EXPLN(y, n.vector, p.vector, mu.vector, sigma.vector, lambda)
|
y |
the argument at which the density is evaluated |
n.vector |
the number of random variables entering each sum (in the considered application: number of cells per tissue sample). This can also be a vector stating how many cells are in each sample separatly |
p.vector |
vector (p1,p2,..,pT) containing the probabilities for each type of cell. Its elements have to sum up to one |
mu.vector |
vector (mu1,mu2,...,mu(T-1)) containing the log-means for each lognormal type (types 1 to T-1) |
sigma.vector |
vector (sigma1,...,sigma(T-1)) containing the log-standard deviations sigma for each lognormal type (types 1 to T-1) |
lambda |
the rate for the exponential type (type T) |
The lengths of mu.vector and sigma.vector have to be identical. p.vector has to have one component more. Its length automatically determines the number of different types. lambda has to be a scalar.
'mix.d.sum.of.mixtures.EXPLN' gives the density of a random variable originating from one of the tissue samples in the mixed n-vector.
Lisa Amrhein, Christiane Fuchs
Maintainer: Lisa Amrhein <amrheinlisa@gmail.com>
"Parameterizing cell-to-cell regulatory heterogeneities via stochastic transcriptional profiles" by Sameer S Bajikar*, Christiane Fuchs*, Andreas Roller, Fabian J Theis^ and Kevin A Janes^: PNAS 2014, 111(5), E626-635 (* joint first authors, ^ joint last authors) <doi:10.1073/pnas.1311647111>
"Pheno-seq - linking visual features and gene expression in 3D cell culture systems" by Stephan M. Tirier, Jeongbin Park, Friedrich Preusser, Lisa Amrhein, Zuguang Gu, Simon Steiger, Jan-Philipp Mallm, Teresa Krieger, Marcel Waschow, Bjoern Eismann, Marta Gut, Ivo G. Gut, Karsten Rippe, Matthias Schlesner, Fabian Theis, Christiane Fuchs, Claudia R. Ball, Hanno Glimm, Roland Eils & Christian Conrad: Sci Rep 9, 12367 (2019) <doi:10.1038/s41598-019-48771-4>
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