Package 'scModels'

Kummer's (confluent hypergeometric) function in log-scale

Description

Kummer's function (also: confluent hypergeometric function of the first kind) for numeric (non-complex) values and input parameters in log-scale.

Usage

chf_1F1(x, a, b)

Arguments

x	numeric value or vector
a, b	numeric parameters of the Kummer function

Details

Note that the output is in log-scale. So the evaluated function is:

$\log \left[\sum_{n=0}^\infty \frac{a^{(n)} x^n}{ b^(n) n!}\right]$

where $a^{(n)}$ and $b^{(n)}$ describe the rising factorial.

Examples

x <- chf_1F1(-100:100, 5, 7)
plot(-100:100, x, type='l')

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Functions to estimate parameters of probability distributions by fitting the distributions using optim()

Description

Functions to estimate parameters of probability distributions by fitting the distributions using optim()

Usage

fit_params(x, type, optim_control = list(maxit = 1000))

Arguments

x	Vector containing the discrete observations
type	Keyword for the probability distribution the data is to be fitted against. Possible values are ("pois", "nb", "del", pig", "pb", "pois2", "nb2", "del2", "pig2" "pb2", "zipois", "zinb", "zidel", "zipg", zipb", "zipois2", "zinb2", "zidel2", "zipig2", zipb2")
optim_control	List of options to override presets in the optim function; Set to list(maxit = 1000) by default. For more details, please refer to the 'control' parameter in the standard 'optim' function in package 'stats'.

Examples

x1 <- rnbinom(100, size = 13, mu = 9)
p1 <- fit_params(x1, "nb")
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x2 <- s*x1 + (1-s) * rnbinom(100, size = 15, mu = 53)
p2 <- fit_params(x2, "nb2")

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Gillespie algorithm for mRNA generating processes

Description

Gillespie algorithms allow synthetic data simulation via three different underlying mRNA generating processes: the basic process consists of a simple death-birth model of mRNA transcription and degradation; the switching process considers additionally gene activation and deactivation, with mRNA transcription only happening in active gene states; the bursting process, transcribes mRNA in bursts with geometrically distributed burst sizes. The basic_burst model combines both the basic and the burst model. The IGbasic burst model describes the basic model with non-constant transcription rates, but transcription rates follow an inverse Gaussian distribution governed by one parameter, the mean parameter of the inverse Gaussian distribution. Additionally a burst transcription occures (with NB distributed burst sizes), the whole burst (rate and burst sizes) are determined by the rate parameter.

Usage

gmRNA_basic(n, r.on, r.degr)

gmRNA_switch(n, r.act, r.deact, r.on, r.degr)

gmRNA_burst(n, r.burst, s.burst, r.degr)

gmRNA_basic_burst(n, r.on, r.burst, s.burst, r.degr)

gmRNA_IGbasic_burst(n, r.mu, r.burst, r.degr)

Arguments

n	Number of observations
r.on	Transcription rate during gene activation (Switching model)
r.degr	mRNA degradation rate (all models)
r.act	DNA activation rate (Switching Model)
r.deact	DNA deactivation rate (Switching Model)
r.burst	Bursty transcription rate (Bursting model, Basic Burst model and IG Basic Burst model)
s.burst	Mean burst size (Bursting Model and Basic Burst model)
r.mu	Mean parameter for the inverse Gaussian distribution (IG Basic Burst model)

Examples

x <- gmRNA_basic(100, 0.75, 0.001)
plot(density(x))
x <- gmRNA_switch(100, 0.23, 0.15, 0.75, 0.001)
plot(density(x))
x <- gmRNA_burst(10, 0.15, 0.75, 0.001)
plot(density(x))
x <- gmRNA_basic_burst(10, 0.75, 0.15, 0.5, 0.001)
plot(density(x))
x <- gmRNA_IGbasic_burst(10, 2, 0.5, 0.1)
plot(density(x))

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Inverse Gaussian Distribution

Description

random generation function for the inverse Gaussian distribution: Mu and lambda are the parameters of this distribution.

Usage

rInvGaus(n, mu, lambda)

Arguments

n	Number of observations
mu, lambda	Non-negative parameters of the inverse Gaussian distribution (mean and shape)

Examples

RV <- rInvGaus(n = 100, mu = 10, lambda = 2)

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Negative log Likelihood functions for Poisson, negative binomial, Delaporte, Poisson-inverse Gaussian and Poisson-beta distributions

Description

The negative log Likelihood functions for Poisson, negative binomial, Delaporte, Poisson-inverse Gaussian and Poisson-beta distributions. Mixing two distributions of the same kind and/or adding zero-inflation allows to take characteristics of real data into account. Additionally, one population and two population mixtures - with and without zero-inflation - allow distribution fitting of the Poisson, negative binomial, Delaporte, Poisson-inverse Gaussian and the Poisson-beta distribution.

Usage

nlogL_pois(data, par.pois)

nlogL_nb(data, par.nb)

nlogL_del(data, par.del)

nlogL_pig(data, par.pig)

nlogL_pb(data, par.pb)

nlogL_pois2(data, par.pois2)

nlogL_nb2(data, par.nb2)

nlogL_del2(data, par.del2)

nlogL_pig2(data, par.pig2)

nlogL_pb2(data, par.pb2)

nlogL_zipois(data, par.zipois)

nlogL_zinb(data, par.zinb)

nlogL_zidel(data, par.zidel)

nlogL_zipig(data, par.zipig)

nlogL_zipb(data, par.zipb)

nlogL_zipois2(data, par.zipois2)

nlogL_zinb2(data, par.zinb2)

nlogL_zidel2(data, par.zidel2)

nlogL_zipig2(data, par.zipig2)

nlogL_zipb2(data, par.zipb2)

Arguments

data	Vector containing the discrete observations
par.pois	Scalar containing the lambda parameter of the Poisson distribution
par.nb	Vector of length 2, containing the size and the mu parameter of the negative binomial distribution
par.del	Vector of length 3, containing the mu, sigma and the nu parameter of the Delaporte distribution
par.pig	Vector of length 2, containing the mu and the sigma parameter of the Poisson-inverse Gaussian distribution
par.pb	Vector of length 3, containing the alpha, beta and c parameter of the Poisson-beta distribution
par.pois2, par.nb2, par.del2, par.pig2, par.pb2	Vector containing the parameters of the two mixing distributions. First entry represents the fraction of the first distribution, followed by all parameters of the first, then all of the second distribution.
par.zipois, par.zinb, par.zidel, par.zipig, par.zipb	Vector containing the respective zero-inflated distribution parameters. The additional first entry is the inflation parameter for all cases.
par.zipois2, par.zinb2, par.zidel2, par.zipig2, par.zipb2	Parameters for the zero-inflated two population model.

Details

Functions nlogL_pois, nlogL_nb, nlogL_del, nlogL_pig, nlogL_pb compute the negative log-likelihood of Poisson, negative binomial, Poisson-inverse Gaussian and the Poisson-beta distributions given the data. Functions nlogL_pois2, nlogL_nb2, nlogL_del2, nlogL_pig2 and nlogL_pb2 compute the negative log-likelihood values for a two population mixture of distributions whereas nlogL_zipois, nlogL_zinb, nlogL_zidel, nlogL_zipig, nlogL_zipb compute the same for the zero-inflated distributions. Furthermore, nlogL_zipois2, nlogL_zinb2, nlogL_zidel2, nlogL_zipig2 and nlogL_zipb2 are for two population mixtures with zero-inflation.

Examples

x <- rpois(100, 11)
nl1 <- nlogL_pois(x, 11)
nl2 <- nlogL_pois(x, 13)
x <- rnbinom(100, size = 13, mu = 9)
nl <- nlogL_nb(x, c(13, 9))
x <- gamlss.dist::rDEL(100, mu = 5, sigma = 0.2, nu= 0.5)
nl <- nlogL_del(x, c(5, 0.2, 0.5))
x <- gamlss.dist::rPIG(100, mu = 5, sigma = 0.2)
nl <- nlogL_pig(x, c(5, 0.2))
x <- rpb(n = 1000, alpha=5, beta= 3, c=20)
nl <- nlogL_pb(x, c(5, 3, 20))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s*rpois(100, 7) + (1-s)*rpois(100, 13)
nl <- nlogL_pois2(x, c(0.3, 13, 7))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s*rnbinom(100, size = 13, mu = 9) + (1-s)*rnbinom(100, size = 17, mu = 29)
nl <- nlogL_nb2(x, c(0.3, 17, 29, 13, 9))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s * gamlss.dist::rDEL(100, mu = 5, sigma = 0.2, nu = 0.5) +
     (1 - s) * gamlss.dist::rDEL(100, mu = 20, sigma = 2, nu = 0.1)
nl <- nlogL_del2(x, c(0.7,5, 0.2, 20, 2))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s * gamlss.dist::rPIG(100, mu = 5, sigma = 0.2) +
     (1 - s) * gamlss.dist::rPIG(100, mu = 20, sigma = 2)
nl <- nlogL_pig2(x, c(0.7, 5, 0.2, 20, 2))
s <- sample(x = c(0,1), size = 100, replace = TRUE, prob = c(0.3,0.7))
x <- s*rpb(100, 5, 3, 20) + (1-s)*rpb(100, 7, 13, 53)
nl <- nlogL_pb2(x, c(0.7, 7, 13, 53, 5, 3, 20))
x <- c(rep(0, 10), rpois(90, 7))
nl <- nlogL_zipois(x, c(0.1, 7))
x <- c(rep(0,10), rnbinom(90, size = 13, mu = 9))
nl <- nlogL_zinb(x, c(0.1, 13, 9))
x <- c(rep(0,10), gamlss.dist::rDEL(90, mu = 13, sigma = 2, nu = 0.5))
nl <- nlogL_zidel(x, c(0.1, 13, 2, 0.5))
x <- c(rep(0,10), gamlss.dist::rPIG(90, mu = 13, sigma = 2))
nl <- nlogL_zipig(x, c(0.1, 13, 2))
x <- c(rep(0, 10), rpb(n = 90, alpha=5, beta= 3, c=20))
nl <- nlogL_zipb(x, c(0.1, 5, 3, 20))
s <- sample(x = c(0, 1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * rpois(90, 7) + (1 - s) * rpois(90, 13))
nl1 <- nlogL_zipois2(x, c(0.1, 0.63, 7, 13))
s <- sample(x = c(0, 1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * rnbinom(90, size = 13, mu = 9) + (1 - s) * rnbinom(90, size = 17, mu = 29))
nl <- nlogL_zinb2(x, c(0.1, 0.63, 13, 9, 17, 29))
s <- sample(x = c(0, 1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * gamlss.dist::rDEL(90, mu = 13, sigma = 9, nu = 0.5) +
             (1 - s) * gamlss.dist::rDEL(90, mu = 17, sigma = 29, nu = 0.1))
nl <- nlogL_zidel2(x, c(0.1, 0.63, 13, 9, 0.5, 17, 29, 0.1))
s <- sample(x = c(0,1), size = 90, replace = TRUE, prob = c(0.3, 0.7))
x <- c(rep(0, 10), s * gamlss.dist::rPIG(90, mu = 13, sigma = 0.2) +
               (1-s) * gamlss.dist::rPIG(90, mu = 17, sigma = 2))
nl <- nlogL_zipig2(x, c(0.1, 0.63, 13, 0.2, 17, 2))
s <- sample(x = c(0,1), size = 90, replace = TRUE, prob = c(0.3,0.7))
x <- c(rep(0,10), s*rpb(90, 5, 3, 20) + (1-s)*rpb(90, 7, 13, 53))
nl <- nlogL_zipb2(x, c(0.1, 0.63, 7, 13, 53, 5, 3, 20))

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Poisson-beta Distribution

Description

Density, distribution function, quantile function and random generation for the Poisson-beta distribution: a Poisson distribution whose parameter itself follows a beta distribution. Alpha and beta are the parameters of this specific beta distribution which is scaled on (0, c) in contrast to the usual scaling of the standard beta distribution on (0,1).

Usage

dpb(x, alpha, beta, c = 1, log = FALSE)

ppb(q, alpha, beta, c = 1, lower.tail = TRUE, log.p = FALSE)

qpb(p, alpha, beta, c = 1, lower.tail = TRUE, log.p = FALSE)

rpb(n, alpha, beta, c = 1)

Arguments

x, q	Vector of (non-negative integer) quantiles
alpha, beta	Non-negative parameters of the beta distribution (shape1 and shape2)
c	Numeric scaling parameter of the beta distribution. The standard beta is scaled on (0,1) (default) and can be transformed to (0,c).
log, log.p	Logical; if TRUE, probabilities p are given as log(p)
lower.tail	Logical; if TRUE (default), probabilities are $P[X \le x]$ otherwise, $P[X > x]$.
p	Vector of probabilities
n	Number of observations

Examples

X <- dpb(x=0:200, alpha=5, beta=3, c=20)
 plot(0:200, X, type='l')
 Y <- dpb(0:10, seq(10.0,11.0,by=0.1), seq(30.0,31.0,by=0.1), seq(10.2,11.2,by=0.1))
 Y <- ppb(q= 0 :200, alpha=5, beta= 3, c=20)
 plot(0:200, Y, type="l")
 Z <- qpb(p= seq(0,1, by= 0.01), alpha=5, beta= 3, c=20)
 plot(seq(0,1, by= 0.01),Z, type="l")
 RV <- rpb(n = 1000, alpha=5, beta= 3, c=20)
 plot(0 : 200, X, type="l")
 lines(density(RV), col="red")
 R2 <- rpb(11, seq(10.0,11.0,by=0.1), seq(30.0,31.0,by=0.1), seq(10.2,11.2,by=0.1))

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