The length-biased version of the lognormal distribution and related estimation problems are considered and sized-biased data arising in the exploration of oil fields is analyzed. The properties of the estimators are studied using simulations and the use of sample mode as an estimate of the lognormal parameter is discussed.
Ratnaparkhi, Makarand V. and Naik-Nimbalkar, Uttara V.
"The Length-Biased Lognormal Distribution and Its Application in the Analysis of Data from Oil Field Exploration Studies,"
Journal of Modern Applied Statistical Methods:
1, Article 22.
Available at: http://digitalcommons.wayne.edu/jmasm/vol11/iss1/22