Two models of binary fragmentation are introduced in which a time dependent transition size produces two regions of fragment sizes above and below the transition size. In the models we consider a fixed rate of fragmentation for the largest fragment and two different rates of fragmentation for the two regions of sizes above and below the transition size. The models are solved exactly in the long...

The problem of assessing occupational exposure using the mean or an upper percentile of a lognormal distribution is addressed. Inferential methods for constructing an upper confidence limit for an upper percentile of a lognormal distribution and for finding confidence intervals for a lognormal mean based on samples with multiple detection limits are proposed. The proposed methods are based on t...

The generalized lognormal distribution plays an important role in various aspects of life testing experiments. We examine Bayesian analysis of this distribution using objective priors (in the general sense of priors constructed using some formal rules) for the model parameters in this paper. Specifically, the derivation of explicit expressions for multiple types of the Jeffreys priors, the refe...

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity an...

BACKGROUND The basophil activation test (BAT) using CD63 expression is a sensitive and specific tool for the diagnostic workup of autoimmune chronic spontaneous urticaria (CSU). The definition of a positive BAT is directly dependent on the reference range and the cutoff values established in control populations. As of now, the pediatric reference range and cutoff values of the CD63 BAT remain t...

Methods for interval estimation of the ratio of two independent coefficients of variation (CVs) of the delta-lognormal distribution are proposed based on the concept of the generalized variable approach (GPA) and the method of variance estimates recovery (MOVER). The performances of both methods are assessed through Monte Carlo simulation in terms of the coverage probabilities and average lengths.

Many natural and economical phenomena are described through power law or log-normal distributions. In these cases, probability decreases very slowly with step size compared to normal distribution. Thus it is essential to cut-off these distributions for larger step size. Recently we introduce the gradually truncated power law distribution to successfully describe variation of financial, educatio...