# mix.d.sum.of.mixtures.rLNLN: Density of the sum of mixtures of lognormal random variables... In stochprofML: Stochastic Profiling using Maximum Likelihood Estimation

## Description

Density and random generation 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. In that case, it is lognormally distributed with log-mean mu_i and log-standard deviation sigma_i. 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.

## Usage

 `1` ```mix.d.sum.of.mixtures.rLNLN(y, n.vector, p.vector, mu.vector, sigma.vector) ```

## Arguments

 `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,...,muT) containing the log-means for each type `sigma.vector` vector (sigma1,...,sigmaT) containing the log-standard deviations sigma for each type

## Details

The lengths of p.vector, mu.vector and sigma.vector have to be identical. Their lengths automatically determine the number of different types.

## Value

'mix.d.sum.of.mixtures.LNLN' gives the density of a random variable originating from one of the tissue samples in the mixed n-vector.

## Author(s)

Lisa Amrhein, Christiane Fuchs

Maintainer: Lisa Amrhein <amrheinlisa@gmail.com>

## References

"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>

stochprofML documentation built on July 1, 2020, 5:18 p.m.