fitGammaDist {MethylIT}  R Documentation 
This function performs the nonlinear fit of GGamma CDF of a variable x
fitGammaDist(x, probability.x, parameter.values, location.par = FALSE, sample.size = 20, npoints = NULL, maxiter = 1024, ftol = 1e12, ptol = 1e12, maxfev = 1e+05, nlms = FALSE, verbose = TRUE)
x 
numerical vector 
probability.x 
probability vector of x. If not provided, the values are estimated using the empirical cumulative distribution function ('ecdf') from 'stats' R package. 
parameter.values 
initial parameter values for the nonlinear fit. If the locator paramter is included (mu != 0), this must be given as parameter.values = list(shape = 'value', scale = 'value', mu = 'value') or if mu = 0, as: parameter.values = list(shape = 'value', scale = 'value'). If not provided, then an initial guess is provided. 
location.par 
whether to consider the fitting to generalized gamma distribution (Gamma) including the location parameter, i.e., a Gamma with four parameters (GGamam3P). 
sample.size 
size of the sample. 
npoints 
number of points used in the fit. 
maxiter 
positive integer. Termination occurs when the number of iterations reaches maxiter. Default value: 1024. 
ftol 
nonnegative numeric. Termination occurs when both the actual and predicted relative reductions in the sum of squares are at most ftol. Therefore, ftol measures the relative error desired in the sum of squares. Default value: 1e12 
ptol 
nonnegative numeric. Termination occurs when the relative error between two consecutive iterates is at most ptol. Therefore, ptol measures the relative error desired in the approximate solution. Default value: 1e12. 
maxfev 
integer; termination occurs when the number of calls to fn has reached maxfev. Note that nls.lm sets the value of maxfev to 100*(length(par) + 1) if maxfev = integer(), where par is the list or vector of parameters to be optimized. 
nlms 
Logical. Whether to return the nonlinear model object

verbose 
if TRUE, prints the function log to stdout 
The algorithm tries to fit the twoparameter Gamma CDF ("Gamma2P") or the threeparameter Gamma ("Gamma3P") using a modification of LevenbergMarquardt algorithm implemented in function 'nls.lm' from 'minpack.lm' package that is used to perform the nonlinear fit. Crossvalidations for the nonlinear regressions (R.Cross.val) were performed in each methylome as described in reference [1]. In addition, Stein's formula for adjusted R squared (rho) was used as an estimator of the average crossvalidation predictive power [1].
If the number of values to fit is >10^6, the fitting to a GGamma CDF would be a time consuming task. To reduce the computational time, the data can be 'summarized' into 'npoints' (bins) and used as the new predictors.
Model table with coefficients and goodnessoffit results: Adj.R.Square, deviance, AIC, R.Cross.val, and rho, as well as, the coefficient covariance matrix.
Robersy Sanchez  06/03/2016
1. Stevens JP. Applied Multivariate Statistics for the Social Sciences. Fifth Edit. Routledge Academic; 2009.
set.seed(126) x < rgamma(1000, shape = 1.03, scale = 2.1) fitGammaDist(x)