| Title: | MLE for Normally Distributed Data Censored by Limit of Detection |
|---|---|
| Description: | Values below the limit of detection (LOD) are a problem in several fields of science, and there are numerous approaches for replacing the missing data. We present a new mathematical solution for maximum likelihood estimation that allows us to estimate the true values of the mean and standard deviation for normal distributions and is significantly faster than previous implementations. The article with the details was submitted to JSS and can be currently seen on <https://www2.arnes.si/~tverbo/LOD/Verbovsek_Sega_2_Manuscript.pdf>. |
| Authors: | Gregor Sega [aut, cre] |
| Maintainer: | Gregor Sega <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.0.1 |
| Built: | 2025-02-11 04:11:10 UTC |
| Source: | https://github.com/cran/mlelod |
Values below the limit of detection (LOD) are a problem in several fields of science, and there are numerous approaches for replacing the missing data. We present a new mathematical solution for maximum likelihood estimation that allows us to estimate the true values of the mean and standard deviation for normal distributions and is significantly faster than previous implementations. The article with the details was submitted to JSS and can be currently seen on <https://www2.arnes.si/~tverbo/LOD/Verbovsek_Sega_2_Manuscript.pdf>.
The DESCRIPTION file:
| Package: | mlelod |
| Type: | Package |
| Title: | MLE for Normally Distributed Data Censored by Limit of Detection |
| Version: | 1.0.0.1 |
| Date: | 2024-05-14 |
| Description: | Values below the limit of detection (LOD) are a problem in several fields of science, and there are numerous approaches for replacing the missing data. We present a new mathematical solution for maximum likelihood estimation that allows us to estimate the true values of the mean and standard deviation for normal distributions and is significantly faster than previous implementations. The article with the details was submitted to JSS and can be currently seen on <https://www2.arnes.si/~tverbo/LOD/Verbovsek_Sega_2_Manuscript.pdf>. |
| Authors@R: | person("Gregor", "Sega", , "[email protected]", role = c("aut", "cre")) |
| Author: | Gregor Sega [aut, cre] |
| Maintainer: | Gregor Sega <[email protected]> |
| License: | GPL-2 |
| NeedsCompilation: | no |
| Packaged: | 2024-05-14 16:12:17 UTC; grego |
| Date/Publication: | 2024-05-15 15:10:02 UTC |
| Repository: | https://gregorsega.r-universe.dev |
| RemoteUrl: | https://github.com/cran/mlelod |
| RemoteRef: | HEAD |
| RemoteSha: | 25b97f1cb811fddb5eec956275da3679409d344f |
Index of help topics:
mlelod Estimates the parameters of the normal
distribution.
mlelod-package MLE for Normally Distributed Data Censored by
Limit of Detection
Values below the limit of detection (LOD) are a problem in several fields of science, and there are numerous approaches for replacing the missing data. Thic package uses a new mathematical solution for maximum likelihood estimation that allows us to estimate the true values of the mean and standard deviation for normal distributions and is significantly faster than previous implementations. The core function is the function mlelod with three parameters: the size of the sample, the values of the sample and the value of limit of detection. The function returns two estimates: for mu (expected value) and sigma (standard deviation).
Gregor Sega [aut, cre]
Maintainer: Gregor Sega <[email protected]>
The article with the derived method is submited to Journal of Statistical Software
The function returns the two estimates for the parameters of the normal distribution.
mlelod(n, censoreddata, lod)mlelod(n, censoreddata, lod)
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. |
muEst |
Description of 'comp1' |
sigmaEst |
Description of 'comp2' |
Gregor Sega
The article with the derived method is submited to Journal of Statistical Software
## 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)$root muEst <- (k * sigmaEst^2 + lod * s - s2)/(k * lod - s) return(list(muEst = muEst, sigmaEst = sigmaEst)) } ##define the parameters of the normal distribution mu <- 5 sigma <- 4 ##define the size of the sample and the value of lod n <- 100 lod <- 2 ##generate normally distributed data and extract the observable values (the ones exceeding lod) data <- rnorm(n, mu, sigma) data2 <- Filter(function(x) x>lod,data) ##run the function to obtain the estimates mlelod(n, data2, lod)## The function is currently defined as mlelod <- function (n, censoreddata, lod) { k <- length(censoreddata) s <- sum(censoreddata) s2 <- sum(censoreddata^2) g <- function(x, n, k, s, s2, lod) { a <- (k * (lod^2 - x^2) + s2 - 2 * lod * s)/(x * (k * lod - s)) b <- s - k * (k * x^2 + lod * s - s2)/(k * lod - s) - x * (n - k) * dnorm(a, 0, 1)/pnorm(a, 0, 1) return(b) } h <- function(x) { return(g(x, n, k, s, s2, lod)) } lsi <- sqrt(s2/k - (s/k)^2) sigmaEst <- uniroot(h, lower = lsi/4, upper = 4 * lsi, tol = 1e-06)$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)