It will be shown that a solution exists for the parameters of a beta distribution given any combination of a lower quantile and upper quantile constraint. A numerical procedure is developed to solve for the parameters of the beta distribution given these quantile constraints. Example solutions are provided.

New continuous wavelets of compact support are introduced, which are related to the beta distribution. They can be built from probability distributions using ”blur”derivatives. These new wavelets have just one cycle, so they are termed unicycle wavelets. They can be viewed as a soft variety of Haar wavelets whose shape is fine-tuned by two parameters a and b. Close expressions for beta wavelets...

The Beta Distribution is almost exclusively used for situations, after range normalization, wherein a continuous random variable is defined on the closed range [0, 1]. Since the beta distribution is intrinsically a two parameter distribution, this creates problems in some applications where specification of more than one parameter is difficult. In this note, two new classes of single parameter ...

This paper gives a model of a structured population with respect to an autosomal locus with two alleles. The population reproduces in discrete and non-overlapping generations. The population is assumed to be in equilibrium in that exactly the same distribution of genotypic proportions is reproduced in each generation. The population is subdivided into `localities’ which are characterized by the...

– Recently an extension of beta function is defined by introducing an extra parameter is proved to be useful earlier (Aslam Chaudhry 1997 [8] and A. R. Miller 1998 [1]). In this research note, we generalize the incomplete beta function and obtained the various integral representations and properties. Furthermore, we obtained the beta distribution for generalized beta function. Keywords––Incompl...

BACKGROUND Health-related quality of life (HRQL) has become an increasingly important outcome parameter in clinical trials and epidemiological research. HRQL scores are typically bounded at both ends of the scale and often highly skewed. Several regression techniques have been proposed to model such data in cross-sectional studies, however, methods applicable in longitudinal research are less w...

OBJECTIVE To perform a Bayesian analysis of data from a previous meta-analysis of Papanicolaou (Pap) smear accuracy (Fahey et al. Am J Epidemiol 1995; 141:680-689) and compare the results. METHODS We considered two Bayesian models for the same data set used in the Fahey et al. study. Model I was a beta-binomial model which considered the number of true positives and false negatives as indepen...

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric Lévy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for Lévy flights is derived and solved analytically in the steady state. It is shown that Lévy flights are ...