dnormgam: Normal-gamma density
In NormalGamma: Normal-gamma convolution model

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the convolution product of a normal and a gamma densities.

dnormgam(par, x = NULL, N0 = 65536, plot = TRUE, 
                  log = FALSE, tail.cor = TRUE, cor = 1e-15, 
                  mu = par[1], sigma = par[2], k = par[3], theta = par[4])

`par`	vector of parameters; `(par[1],par[2])` are the mean and standard deviation of the normal distribution and `(par[3],par[4])` are the shape and scale parameters of the gamma distribution.
`x`	vector of values where the density is computed; if `x == NULL`, the density is computed on a sequence of values from `0` to `par[1]+5*par[2]+q` where `q` is the quantile of probability `0.99999` of the gamma distribution.
`N0`	number of equally spaced values in the Fast Fourier Transform (see details).
`plot`	logical; if `TRUE` plot of the density.
`log`	logical; if `TRUE` density `d` is given as `log(d)`.
`tail.cor`	logical; if `TRUE` a linear approximation of right tail adjusts numerical instability.
`cor`	limit of right tail correction; if `tail.cor == TRUE`, linear approximation is applied to values with density estimate smaller than `cor`.
`mu, sigma`	alternative definition of mean and standard deviation of the normal distribution.
`k, theta`	alternative definition of shape and scale parameters of the gamma distribution.

The convoluted density is computed using the fft function (Fast Fourier Transform). See details in Plancade S., Rozenholc Y. and Lund E., BMC Bioinfo 2012.

Only one definition of the parameters is required, either par or (mu, sigma, k, theta). If both are specified and do not match, an error message is returned.

`xout`	vector of values where normal-gamma density is computed; equal to `x` when `x` is not `NULL`.
`dout`	vector of values of normal-gamma density.

Plancade S. and Rozenholc Y.

Plancade S., Rozenholc Y. and Lund E. "Generalization of the normal-exponential model : exploration of a more accurate parametrisation for the signal distribution on Illumina BeadArrays", BMC Bioinfo 2012, 13(329).

normgam.fit computes the Maximum Likelihood Estimator and normgam.signal implements the background correction using the normal-gamma model.

## Example 1

par = c(-10, 5, 2, 20)
F = dnormgam(par)

## Example 2 

n = 50000
par = c(60,5,0.15,400)
F = dnormgam(par, plot=FALSE)

X = rnorm(n, mean=par[1], sd=par[2]) + rgamma(n, shape=par[3], scale=par[4]) 
H = histogram(X, type='irregular', verbose=FALSE, plot=FALSE)
plot(H, xlim=c(0,500))
lines(F$xout, F$dout, col='red')