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>.