Related papers: Products of Beta distributed random variables

Data on rates, percentages or proportions arise frequently in many different applied disciplines like medical biology, health care, psychology and several others. In this paper, we develop a robust inference procedure for the beta…

We study with some details a lifetime model of the class of beta generalized models, called the beta inverse Rayleigh distribution, which is a special case of the Beta Fr\'echet distribution. We provide a better foundation for some…

We present estimators for entropy and other functions of a discrete probability distribution when the data is a finite sample drawn from that probability distribution. In particular, for the case when the probability distribution is a joint…

We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…

We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders. We provide a probabilistic interpretation of our result by exploiting a…

We give the exact distribution of the average of n independent beta random variables weighted by the selected cuts of (0, 1) by the order statistics of a random sample of size n-1 from the uniform distribution U(0,1), for each n. A new…

A new characterization for power function distributions is obtained which is based on products of order statistics. This result may be considered as a generalization of some recent results for contractions. We note that in this new result…

We provide conditions on dependent and on non-stationary random variables $X_n$ ensuring that the mantissa of the sequence of products $\left(\prod_{1}^{n}X_k\right)$ is almost surely distributed following the Benford's law or converges in…

We determine the asymptotic behaviour of certain incomplete Betafunctions.

The theory of Barnes beta probability distributions is advanced and related to the Riemann xi function. The scaling invariance, multiplication formula, and Shintani factorization of Barnes multiple gamma functions are reviewed using the…

An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…

Lin's condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin's condition for functions of random variables have emerged. In this…

We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function $\beta$ defined by $\beta(p^a)=p^a-p^{a-1}+p^{a-2}-...+(-1)^a$ for every prime power $p^a$ ($a\ge 1$), and extended by multiplicativity. Certain open…

The explicit expression for the the probability distribution function of the endpoint fluctuations of one-dimensional directed polymers in random potential is derived in terms of the Bethe ansatz replica technique by mapping the replicated…

In this paper, we introduce a new four-parameter generalized version of the Gompertz model which is called Beta-Gompertz (BG) distribution. It includes some well-known lifetime distributions such as beta-exponential and generalized Gompertz…

In this work in progress, we study the asymptotic behaviour of the $p$-quantile of the Beta distribution, i.e. the quantity $q$ defined implicitly by $\int_0^q t^{a - 1} (1 - t)^{b - 1} \text{d} t = p B (a, b)$, as a function of the first…

Beta regression is often used to model the relationship between a dependent variable that assumes values on the open interval (0,1) and a set of predictor variables. An important challenge in beta regression is to find residuals whose…

In this note, we give an explicit expression for the quantile of a mixture of two random variables. We carefully examine all possible cases of discrete and continuous variables with possibly unbounded support. The result is useful for…

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…