Mathematics and Statistics/ Analytics and Modeling
We examine the accuracy and precision of parameter estimates for both the normal and exponential distribution when using only a collection of sample extremes. That is, we consider a collection of m random variables, where each of the m random variables is either the maximum or minimum of a sample of nj independent, identically distributed random variables drawn from a normal or exponential distribution with unknown parameters. Previous work by Capaldi and Kolba (2019) derived estimators for the population parameters assuming the nj sample sizes are constant. Since sample sizes are often not constant in applications, we utilize Matlab to perform simulations to assess how the estimators from Capaldi and Kolba perform when the sample sizes are themselves random variables. Additionally, we explore how varying the mean, standard deviation, and probability distribution of the sample sizes affects the estimation error. Furthermore, we derive new unbiased estimators in the case where the sample sizes are drawn from a uniform distribution. Our estimation framework is applied to a biological example involving plant pollination.
Bruno, Alexander, "Estimation of Population Parameters Using Sample Extremes from Nonconstant Sample Sizes" (2020). Summer Interdisciplinary Research Symposium. 73.