In this paper, we detail closed form estimators for beta distribution that are simpler than those proposed by Tamae, Irie and Kubokawa. The shown to have smaller asymptotic variances covariances compared Tamae maximum likelihood estimators. also perform better in real data applications.

The shape of a probability distribution is often summarized by the distribution’s skewness and kurtosis. Starting from a symmetric ”parent” density f on the real line, we can modify its shape (i.e. introduce skewness and in-/decrease kurtosis) if f is appropriately weighted. In particular, every density w on the interval (0, 1) is a specific weighting function. Within this work, we follow up a ...

Abstract: Let X,Y,B be three independent random variables such that X has the same distribution function as Y B. Assume that B is a Beta random variable with positive parameters α, β and Y has distribution function H with H(0) = 0. Pakes and Navarro (2007) show under some mild conditions that the distribution function Hα,β of X determines H . Based on that result we derive in this paper a recur...

We introduce the new continuous distribution, the so-called beta-Lindley distribution that extends the Lindley distribution. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the rth moment thus, generalizing some results in the literature. Expressions for the density, moment generating function, and rthmoment of the order stati...