Related papers: Interval extropy and weighted interval extropy

We introduce novel information-entropic variables -- a Point Divergence Gain (${\Omega}^{(l \rightarrow m)}_\alpha$), a Point Divergence Gain Entropy ($I_\alpha$), and a Point Divergence Gain Entropy Density ($P_\alpha$) -- which are…

For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…

For a random variable we can define a variational relationship with practical physical meaning as dI=dbar(x)-bar(dx), where I is called as uncertainty measurement. With the help of a generalized definition of expectation,…

We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…

In this article, the weighted empirical likelihood is applied to a general setting of two-sample semiparametric models, which includes biased sampling models and case-control logistic regression models as special cases. For various types of…

We define a measure of redundant information based on projections in the space of probability distributions. Redundant information between random variables is information that is shared between those variables. But in contrast to mutual…

In clinical and epidemiological research doubly truncated data often appear. This is the case, for instance, when the data registry is formed by interval sampling. Double truncation generally induces a sampling bias on the target variable,…

The routine definitions of both entropy, and differential entropy show inconsistencies that make them not reciprocally coherent. We propose a few possible modifications of these quantities so that 1) they no longer show incongruities, 2)…

In pharmaceutical and toxicological research, historical control data are increasingly used to validate concurrent control groups, typically via the construction of historical control limits. While methods have been described for continuous…

Uncertainty relations are central to quantum physics. While they were originally formulated in terms of variances, they have later been successfully expressed with entropies following the advent of Shannon information theory. Here, we…

Let $\{S_n=(X_n,W_n)\}_{n\ge0}$ be a random walk with $X_n\in \mathbb{R}$ and $W_n\in \mathbb{R}^m$. Let $\tau=\tau_a=\inf\{n:X_n>a\}$. The main results presented are two term asymptotic expansions for the joint distribution of $S_{\tau}$…

In this paper, we introduce a new three-parameter distribution based on the combination of re-parametrization of the so-called EGNB2 and transmuted exponential distributions. This combination aims to modify the transmuted exponential…

In this paper, we first investigate the estimation of the empirical joint Laplace transform of volatilities of two semi-martingales within a fixed time interval [0, T] by using overlapped increments of high-frequency data. The proposed…

Asymptotic expansion of a variation with anticipative weights is derived by the theory of asymptotic expansion for Skorohod integrals having a mixed normal limit. The expansion formula is expressed with the quasi-torsion, quasi-tangent and…

Entropy estimation plays a crucial role in various fields, such as information theory, statistical data science, and machine learning. However, traditional entropy estimation methods often struggle with complex data distributions.…

The present paper considers modified extension of the exponential distribution with three parameters. We study the main properties of this new distribution, with special emphasis on its median, mode and moments function and some…

For complex latent variable models, the likelihood function is not available in closed form. In this context, a popular method to perform parameter estimation is Importance Weighted Variational Inference. It essentially maximizes the…

I consider the effect of a finite sample size on the entropy of a sample of independent events. I propose formula for entropy which satisfies Shannon's axioms, and which reduces to Shannon's entropy when sample size is infinite. I discuss…

In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…

Shannon entropy is widely used to quantify the uncertainty of discrete random variables. But when normalized to the unit interval, as is often done in practice, it no longer conveys the alphabet sizes of the random variables being studied.…