On some properties of the “apparent length” distribution and a compound distribution

This paper extends and supplements some of the properties of the apparent length distribution introduced by Baker (J. Appl. Statist. 27(1) (2000) 2–21). Recurrence relations for moments and formulae for moments derived via difference and differential operators will be given. We also establish maximum likelihood estimator and Bayesian estimators of a parameter of this distribution. Compound distributions based on the apparent length distribution are also discussed.