相关论文: Characterization of beta distribution on symmetric…

The Lukacs property of the free Poisson distribution is studied here. We prove that if free $\X$ and $\Y$ are free Poisson distributed with suitable parameters, then $\X+\Y$ and…

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…

It is shown that the exponential is the only distribution which satisfies a certain regression equation. This characterization equation involves the conditional expectation (regression function) of a record value given a pair of record…

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent random variables, and $\eta$ be a counting random variable independent of this sequence. In addition, let $S_0:=0$ and $S_n:=\xi_1+\xi_2+\cdots+\xi_n$ for $n\geqslant1$. We consider…

Let $Y$ be a standard Gamma(k) distributed random variable, $k>0$, and let $X$ be an independent positive random variable. We prove that if $X$ has a hyperbolically monotone density of order $k$ ($HM_k$), then the distributions of $Y\cdot…

We show that, for two non-trivial random variables X and Y under a sublinear expectation space, if X is independent from Y and Y is independent from X, then X and Y must be maximally distributed.

Let $X_1, X_2,\ldots, X_n$ be $n$ independent and identically distributed random variables, here $n \geq 2.$ Let $X_{(1)}, X_{(2)}, \ldots, X_{(n)}$ be the order statistics of $X_1, X_2,..., X_n.$ In this note we proved that: (I) If $X_1,…

Dual Lukacs type characterizations of random variables in free probability are studied here. First, we develop a freeness property satisfied by Lukacs type transformations of free-Poisson and free-Binomial non-commutative variables which…

The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random…

This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.

Let $X$ and $Y$ be independent variance-gamma random variables with zero location parameter; then the exact probability density function of the product $XY$ is derived. Some basic distributional properties are also derived, including…

The beta family owes its privileged status within unit interval distributions to several relevant features such as, for example, easyness of interpretation and versatility in modeling different types of data. However, its flexibility at the…

We study the conditional distribution of low-dimensional projections from high-dimensional data, where the conditioning is on other low-dimensional projections. To fix ideas, consider a random d-vector Z that has a Lebesgue density and that…

Let $X_1,\ldots,X_n$ be an i.i.d. sample from symmetric stable distribution with stability parameter $\alpha$ and scale parameter $\gamma$. Let $\varphi_n$ be the empirical characteristic function. We prove an uniform large deviation…

Let $X$ and $Y$ be two independent identically distributed random variables with density $p(x)$ and $Z=\alpha X+\beta Y$ for some constants $\alpha>0$ and $\beta>0$. We consider the problem of estimating $p(x)$ by means of the samples from…

Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where…

We consider the problem of testing whether pairs of univariate random variables are associated. Few tests of independence exist that are consistent against all dependent alternatives and are distribution free. We propose novel tests that…

This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…

We revisit the computation of the beta function in the two-dimensional $\mathbb{CP}(1)$ sigma model. We show that in different schemes, different diagrams are responsible for the running, such as momentum-independent tadpoles or even…

In this paper, we propose a regression model where the response variable is beta prime distributed using a new parameterization of this distribution that is indexed by mean and precision parameters. The proposed regression model is useful…