| Type: | Package |
| Title: | Exponentially Modified Gaussian (EMG) Distribution |
| Version: | 1.0.9 |
| Date: | 2020-06-19 |
| Author: | Shawn Garbett, Mark Kozdoba |
| Maintainer: | Shawn Garbett <Shawn@Garbett.org> |
| Depends: | R (≥ 1.8.0), stats, stats4, moments |
| Description: | Provides basic distribution functions for a mixture model of a Gaussian and exponential distribution. |
| License: | GPL-2 | file LICENSE |
| LazyLoad: | yes |
| NeedsCompilation: | no |
| Repository: | CRAN |
| Packaged: | 2020-06-19 16:10:23 UTC; garbetsp |
| Date/Publication: | 2020-06-20 09:20:17 UTC |
Exponentially Modified Gaussian (EMG) Distribution
Description
Provide basic functions for a mixture of gaussian and exponential distributions.
Details
| Package: | emg |
| Type: | Package |
| Date: | 2012-01-03 |
| License: | GPL 2.0 |
| LazyLoad: | yes |
Provides basic distribution functions for the EMG model, pemg, demg, qemg and remg. As well as an MLE estimation routine emg.mle.
Author(s)
Shawn Garbett, Mark Kozdoba, Maintainer: Shawn Garbett <Shawn@Garbett.org>
References
Gladney H.M., B.F. Dowden, J.D. Swalen. Computer-Assisted Gas-Liquid Chromatography. Anal. Chem., 1969, 41(7):883-8.
Golubev A. Exponentially modified Gaussian (EMG) relevance to distributions related to cell proliferation and differentiation. J Theor Biol. 2010 Jan 21;262(2):257-66.
Grushka E. Charaterization of Exponentially Modified Peaks in Chromatography. Anal. Chem., 1972, 44(11):1733-38.
See Also
EMG
emg.mle
Normal
Exponential
Examples
y <- remg(200)
hist(y, freq=FALSE, ylim=c(0, 0.35), breaks=20)
x <- 1:100/100 * 11 - 3
lines(x, demg(x))
m <- emg.mle(y)
sqrt(diag(m@vcov)) # Show stderr in estimate
ks.test(y, "pemg", 0, 1, 1)
The Exponential Modified Gaussian (EMG) Distribution
Description
Density, distribution function, quantile function and random generation for the EMG distribution with three parameters, mu, sigma, lambda. The distribution is a mixture of an exponential and gaussian (normal) distribution.
Usage
demg(x, mu = 0, sigma = 1, lambda = 1, log = FALSE)
pemg(q, mu = 0, sigma = 1, lambda = 1, lower.tail = TRUE, log.p = FALSE)
qemg(p, mu = 0, sigma = 1, lambda = 1, lower.tail = TRUE, log.p = FALSE)
remg(n, mu = 0, sigma = 1, lambda = 1)
Arguments
x, q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
mu |
mu value, the mean of the normal component. Note: this is not the mean of the distribution. The mean is mu+1/lambda |
sigma |
sigma value, the deviation of the normal component. Note: this is not the deviation of the distribution |
lambda |
lambda value (1/kappa), the rate of the exponential component. |
log, log.p |
logical; if TRUE, probabilities p are given as log(p). |
lower.tail |
logical; if TRUE(default), probabilities are P[X <= x] otherwise, P[X > x]. |
Details
If mean or sd are not specified they assume the default
values of 0 and 1, respectively.
The EMG distribution has density
f(x) =
\frac{1}{2} \lambda e^{\frac{\lambda}{2} (2 \mu + \lambda \sigma^2 - 2 x)}
erfc((\mu + \lambda \sigma \sigma - x) / (\sqrt{2} \sigma))
where \mu is the mean of the normal distribution,
\sigma the standard deviation of the normal and
\lambda rate of the exponential. Note \mu does not represent the mean of the distribution. The mean is \mu + 1/\lambda
Value
demg gives the density,
pemg gives the distribution function,
qemg gives the quantile function, and
remg generates random deviates.
References
Golubev. Exponentially modified Gaussian (EMG) relevance to distributions related to cell proliferation and differentiation. J Theor Biol. 2010 Jan 21;262(2):257-66. Epub 2009 Oct 13.
Examples
plot(demg, -2, 5)
Maximum Likelihood estimate of parameters
Description
Compute the maximum likelihood model for the parameters given a set of observations. Returns a model with estimates for mu, sigma, and lambda.
Usage
emg.mle(x, lower=NULL, upper=NULL, start=NULL, ...)
Arguments
x |
vector of observations to estimate parameters for. |
lower |
list of lower bounds for parameters. |
upper |
list of upper bounds for parameters. |
start |
list of starting parameters for search. |
... |
optional parameters to pass to 'mle'. |
Value
An object of class mle-class.
Author(s)
Shawn Garbett
See Also
Examples
emg.mle(remg(200))
## a example involving fitting
data(pc9_3um_erlotinib)
intermitotic.time <- subset(pc9_3um_erlotinib, end.of.movie=='N' & died=='N')$observed
hist(intermitotic.time, freq=FALSE, main="PC9 in 3um erlotinib", xlab='intermitotic time (hours)')
fit <- emg.mle(intermitotic.time)
pdf <- function(x) demg(x, coef(fit)['mu'], coef(fit)['sigma'], coef(fit)['lambda'])
curve(pdf, from=0, to=170, add=TRUE, col='red')
Negative Log Likelihood for EMG
Description
Negative log likelihood function for EMG
Usage
emg.nllik(x, mu, sigma, lambda)
Arguments
x |
vector of observations |
mu |
mu of normal |
sigma |
sigma of normal |
lambda |
lambda of exponential |
Value
A single real value of the negative log likelihood that the given parameters explain the observations.
Author(s)
Shawn Garbett
See Also
Examples
y <- remg(200)
emg.nllik(y, 0, 1, 1)
PC9 cancer cell observations with 3 micro-molar erlotinib at time 0.
Description
PC9 cancer cell observations with 3um erlotinib applied at time 0. Experiment was performed on 2011/9/9 (F07) in the Vito Quaranta laboratory at Vanderbilt University Cancer Biology Center by Darren Tyson. Cells were tracked by nuclear labeling with histone H2B and imaged on a BD Pathway 855 for several days. All numerical values are in hours. Funding was provided by the National Cancer Institute (NCI).
This data set was specifically chosen to give the emg.mle function something difficult to work on.
Usage
data(pc9_3um_erlotinib)
Value
A data frame of lifespan PC9 observations.
Author(s)
Darren Tyson, Shawn Garbett
Examples
data(pc9_3um_erlotinib)