1977/09/01 by Lalitha Sanathanan · 1 citation
Computer Science · Mathematics · #Applied mathematics #Bayesian Methods and Mixture Models #Binomial (polynomial) #Binomial distribution #Census and Population Estimation #Combinatorics #Distribution (mathematics) #Econometrics #Mathematical analysis #Mathematics #Maximum likelihood #Negative binomial distribution #Observable #Physics #Poisson distribution #Sample size determination #Statistics #Survey Sampling and Estimation Techniques #Variable (mathematics)
paper · doi:10.2307/2286238
openalex publication_date 1977/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Consider N (unknown) values of a variable X (discrete or continuous) independently sampled from a distribution with density f(x, θ), where θ is an unknown vector parameter. Suppose that the values of X belonging to a certain region R are not observable. This article deals with the problem of estimating N and θ in such situations which arise, for instance, in life testing and capture-recapture census. Asymptotic theory for maximum likelihood estimation of N and θ is presented here and is shown to yield as corollaries both some existing results and a new result pertaining to the truncated negative binomial distribution.