Maximum Likelihood Estimation of the Mode of a Continuous Distribution (Without Grouping)

• Activity Number: 629 - Advanced Topics in Statistics Education
• Type: Contributed
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Education
• Author(s): John Paul DeLong*
• Keywords: Maximum Likelihood ; Numerical Estimation ; Continuous Distribution

Abstract

We show an example of a continuous distribution, expressed piecewise, with an unknown parameter which happens to be the mode of the distribution. It turns out that the likelihood function is not trivial to find and not trivial to maximize. We show how we calculate it numerically, resulting in an interesting estimator.