d.sum.of.mixtures.LNLN: Sums of mixtures of lognormal random variables
In stochprofML: Stochastic Profiling using Maximum Likelihood Estimation

Description Usage Arguments Details Value Author(s) References Examples

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.

1 2	d.sum.of.mixtures.LNLN(y, n, p.vector, mu.vector, sigma.vector, logdens = T) r.sum.of.mixtures.LNLN(k, n, p.vector, mu.vector, sigma.vector, N.matrix)

`y`	the argument at which the density is evaluated
`k`	number of i.i.d. random variables returned by this function (in the considered application: number of tissue samples)
`n`	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
`logdens`	if TRUE, the log of the density is returned
`N.matrix`	optional. Matrix, that shows the decomposition of samples to be generated. Each row stands for a future sample and the columns show the decomposition of types for the specific sample such that the row sum should be n (either a value, i.e. all the same or a vector).

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

'd.sum.of.mixtures.LNLN' gives the density, and 'r.sum.of.mixtures.LNLN' generates random variables.

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>

# generate random variables
p <- c(0.25,0.75)
mu <- c(2,-1)
sigma <- c(0.3,0.1)

set.model.functions("LN-LN")

r <- r.sum.of.mixtures.LNLN(10^4,10,p,mu,sigma)
hist(r,xlab="Sum of mixtures of lognormals",freq=FALSE,breaks=100,ylim=c(0,0.2))

# plot according theoretical density function
x <- seq(round(min(r)),round(max(r)),(round(max(r))-round(min(r)))/500)
y <- d.sum.of.mixtures.LNLN(x,10,p,mu,sigma,logdens=FALSE)
lines(x,y,col="blue",lwd=3)