A Numerical Comparison of Some BAYESian Methods of Estimating a Binomial Parameter

This note considers the optimal and suboptimal sequential and fixed sample size estimation of the unknown binomial parameter, p, for a beta prior distribution for p and under quadratic loss and constant observation cost. A numerical comparison of the methods is presented.     

The Planning of Sample Sizes for Maximum Likelihood Estimation of the Parameters of the Weibull Distribution

Based on maximum likelihood estimators the problem of setting confidence limits for the scale and shape parameters of the Weibull distribution with two parameters is considered. Approximation formulae for the determination of sample sizes for the parameter estimation are given for complete and type II censored samples.     

Bayesian Reliability Estimation of a Two-parameter Cauchy Distribution

This paper gives an approximate Bayes procedure for the estimation of the reliability function of a two-parameter Cauchy distribution using Jeffreys' non-informative prior with a squared-error loss function, and with a log-odds ratio squared-error loss function. Based on a Monte Carlo simulation study, two such Bayes estimators of the reliability are compared with the maximum likelihood estimator.     

Point and Interval Estimation of the Population Size Using a Zero‐Truncated Negative Binomial Regression Model

This paper presents the zero‐truncated negative binomial regression model to estimate the population size in the presence of a single registration file. The model is an alternative to the zero‐truncated Poisson regression model and it may be useful if the data are overdispersed due to unobserved heterogeneity. Horvitz–Thompson point and interval estimates for the population size are derived, and the performance of these estimators is evaluated in a simulation study. To illustrate the model, the size of the population of opiate users in the city of Rotterdam is estimated. In comparison to the Poisson model, the zero‐truncated negative binomial regression model fits these data better and yields a substantially higher population size estimate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimation of the Distribution of a Genetically Determined Enzyme Polymorphism by a Stochastical Outside Criterion

The remaining cholinesterase activity after incubation with paraoxon (as an indicator of the activity of human serumparaoxonase) shows a distribution with three clusters which could be explained, after an investigation of families, by a simple two-allele-model. A Stochastical outside criterion is given by the constellations of the values within the families. By modification of an iteration method described by FANGMEYER (1964) it is possible to estimate the distributions and frequencies of the three groups. A simulation study shows that the combination of the used method with the pure cluster analysis is advantageous.     

Managing for naturalness alone is not an effective way to preserve all the valuable natural features of the Białowieża Forest – a reply to Jaroszewicz et al.

Currently, Brzeziecki et al. 2016 (Journal of Vegetation Science 27: 460–467.) are using data from permanent study plots established in 1936 in Bia?owie?a National Park (NE Poland) to develop theoretical equilibrium tree size distributions and to then compare modelled and actual distributions with a view to assessing the population dynamics of the species involved. As part of their discussion, the authors address the question of possible consequences for the overall diversity of forest ecosystems under strict protection if long‐term trends relating to tree population densities and size structures are maintained. In the overall context of the above, the goal of the present paper is to respond to Jaroszewicz et al. (Journal of Vegetation Science 28: 218–222.) who suggest that the paper of Brzeziecki et al. (2016) is not representative for the whole Bia?owie?a National Park, and that – in this connection – strict protection should not be seen as a cause for concern. In this paper, we show that the data analysed by Brzeziecki et al. (2016) adequately characterize conditions in the wider Park. We also point out that the thorough scientific understanding of the long‐term dynamics of woodland communities under strict protection should indeed be taken into account as efforts are made to arrive at an effective conservation strategy capable of ensuring that the uniquely valuable features of the Bia?owie?a Forest are retained.