Showing papers on "Population proportion published in 1979"

Parameter estimation using transform estimation in time-evolving models

Abstract: Parameter estimation can be complex when populations change in time and p(t), the probability of an individual having a desired characteristic at time t, can only be estimated by the population proportion at time t having that characteristic. We consider sampling at the random time T where T has an exponential distribution; the population proportion then estimates the Laplace transform of p(t). This reduces the complications of parameter estimation in many common situations—for example, when p(t) is a convolution of functions, each involving different parameters. We show that a stratified random sampling technique gives a more efficient parameter estimation method, and that this lends itself to a relatively straightforward parameter estimation technique based on ordinary fixed sampling times. The efficiency of this method is explored in two ways: analytically in a simple case where p(t) is the probability of transition by time t of an organism in a two-stage model with Erlangian transition times; and by simulation in a model where p(t) is the probability of a biological organism being in a given stage of development and the parameters are the death rate and the maturing rates in each stage. Finally, data on the hatching of parasitic nematodes O.circumcincta are fitted by least squares and by transform methods. Particularly in the complex simulation context the transform method has several desirable properties; explicit parameter estimators can be found, and they compare well with other estimation methods.