R/fitNormal.r

In extremevalues: Univariate Outlier Detection

# file  : Lognormal.r
# author: Mark van der Loo (mark.vanderloo@gmail.com)
#
# Determine parameters mu = E(y) and sigma = Var(y)
# of a normal distributed variable Y, by fitting (part of) 
# the log(cdf) to an observed log(cdf). 
#
# INPUT
# y     : vector of observed values
# p     : vector of observed quantiles (y_i estimates the p_i'th quantile)
#
# OUTPUT (list)
# mu    : estimate of location parameter
# sigma : estimate of spread parameter
# R2    : R-squared value of fit.
#
# History
# 03.12.2009    version 1
#

fitNormal <- function(y, p)
{
   if ( !is.vector(y) ) 
      stop("First argument is not of type vector")
   if ( !is.vector(p)) 
      stop("First argument is not of type vector")
   if ( sum(p<=0) > 0 | sum(p>=1) >0 )
      stop("Second argument contains values out of range (0,1)")
   if (length(y) != length(p))
      stop("First and second argument have different length");

   N <- length(y);
   Y <- as.matrix(y,nrow=N)
   p <- as.matrix(p,nrow=N)


   A <- matrix(0,nrow=N,ncol=2)
   A[,1] <- 1+double(N);
   A[,2] <- sqrt(2)*invErf(2*p-1)
   param <- solve(t(A) %*% A) %*% t(A) %*% Y
   r2 <- 1 - var(A%*%param - y)/var(y);
   return(list(mu=param[1], sigma=param[2], R2=r2));
}