The triangular distribution, although simpler than the beta distribution both for mathematical treatment and for natural interpretation, has not been widely used in the literature as a modelling tool. Applications of this distribution as an alternative to the beta distribution appear to be limited in financial contexts and specifically in the assessment of risk and uncertainty and in modelling ...

BACKGROUND For some phenomena the mean of population distributions predicts the proportion of people exceeding a threshold value. AIMS To investigate whether in depression, too, the population mean predicts the number of individuals at the extreme end of the distribution. METHOD We used data from the European Outcome in Depression International Network (ODIN) study from populations in Finla...

Radon risk maps have been produced in many countries using non-geologically based techniques utilising the lognormal and gamma distributions to display point estimates of the probability, P(RL), that indoor radon levels will exceed a reference level. Recent work on updating radon maps in Ireland prompted an examination of various statistical issues associated with non-geologically based radon m...

We consider the AR(1) time series model Xt − βXt−1 = ξt, β−p ∈ N {1}, when Xt has Beta distribution B(p, q), p ∈ (0, 1], q > 1. Special attention is given to the case p = 1 when the marginal distribution is approximated by the power law distribution closely connected with the Kumaraswamy distribution Kum(p, q), p ∈ (0, 1], q > 1. Using the Laplace transform technique, we prove that for p = 1 th...

The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The expert’s opinion and trust on each pairwise correlation is described by a beta distribution. Then, by comb...

A two-parameter family of distributions on (0, 1) is explored which has many similarities to the beta distribution and a number of advantages in terms of tractability (it also, of course, has some disadvantages). The minimax distribution, so-called because of its genesis in terms of uniform order statistics, particularly has straightforward distribution and quantile functions which do not depen...

Finite mixture models have come to play a very prominent role in modelling data. The finite mixture model is predicated on the assumption that distinct latent groups exist in the population. The finite mixture model therefore is based on a categorical latent variable that distinguishes the different groups. Often in practice distinct sub-populations do not actually exist. For example, disease s...

This work is motivated by a meta-analysis case study on antipsychotic medications. The Michaelis-Menten curve is employed to model the nonlinear relationship between the dose and D2 receptor occupancy across multiple studies. An intraclass correlation coefficient (ICC) is used to quantify the heterogeneity across studies. To interpret the size of heterogeneity, an accurate estimate of ICC and i...

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the b...