This article is about the statistical techniques. The method of maximum likelihood is used with natural log of normal pdf ml estimate wide range of statistical analyses.

MLE while only knowing the heights of some sample of the overall population. MLE would accomplish that by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable given the normal model. Intuitively, this selects the parameter values that make the data most probable. For some problems, there may be multiple values that maximize the likelihood. MLEs converges in probability to the value being estimated. Second-order efficiency after correction for bias. Thus, true consistency does not occur in practical applications.

Nevertheless, consistency is often considered to be a desirable property for an estimator to have. To establish consistency, the following conditions are sufficient. The identification condition is absolutely necessary for the ML estimator to be consistent. The identification condition establishes that the log-likelihood has a unique global maximum. Compactness is only a sufficient condition and not a necessary condition.