mlelod {mlelod}

Estimates the parameters of the normal distribution.

Description

The function returns the two estimates for the parameters of the normal distribution.

Usage

mlelod(n, censoreddata, lod)

Arguments

n

n is the size of the sample

censoreddata

censoreddata is the vector containing the values of the sample which are greater than lod

lod

lod is the value of level of detection.

Value

muEst

Description of 'comp1'

sigmaEst

Description of 'comp2'

Author(s)

Gregor Sega

References

The article with the derived method is submited to Journal of Statistical Software

Examples

## The function is currently defined as
mlelod <- function (n, censoreddata, lod) 
{
    k <- length(censoreddata)
    s <- sum(censoreddata)
    s2 <- sum(censoreddata^2)
    g <- function(x, n, k, s, s2, lod) {
        a <- (k * (lod^2 - x^2) + s2 - 2 * lod * s)/(x * (k * 
            lod - s))
        b <- s - k * (k * x^2 + lod * s - s2)/(k * lod - s) - 
            x * (n - k) * dnorm(a, 0, 1)/pnorm(a, 0, 1)
        return(b)
    }
    h <- function(x) {
        return(g(x, n, k, s, s2, lod))
    }
    lsi <- sqrt(s2/k - (s/k)^2)
    sigmaEst <- uniroot(h, lower = lsi/4, upper = 4 * lsi, tol = 1e-06)$root
    muEst <- (k * sigmaEst^2 + lod * s - s2)/(k * lod - s)
    return(list(muEst = muEst, sigmaEst = sigmaEst))
  }
##define the parameters of the normal distribution
mu <- 5
sigma <- 4
##define the size of the sample and the value of lod
n <- 100
lod <- 2
##generate normally distributed data and extract the observable values (the ones exceeding lod)
data <- rnorm(n, mu, sigma)
data2 <-  Filter(function(x) x>lod,data)
##run the function to obtain the estimates
mlelod(n, data2, lod)