Using the sample maximum to estimate the parameters of the underlying distribution.

We propose novel estimators for the parameters of an exponential distribution and a normal distribution when the only known information is a sample of sample maxima; i.e., the known information consists of a sample of m values, each of which is the maximum of a sample of n independent random variables drawn from the underlying exponential or normal distribution.

Parameter estimation and uncertainty quantification for an epidemic model.

We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0)---an epidemiologically significant parameter grouping. We find that estimates of different parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0.