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This article presents a new class of generalized transmuted lifetime distributions which includes a large number of lifetime distributions as sub-family. Several important mathematical quantities such as density function, distribution…
In some inferential statistical methods, such as tests and confidence intervals, it is important to describe the stochastic behavior of statistical functionals, aside from their large sample properties. We study such behavior in terms of…
Importance weighting is a fundamental procedure in statistics and machine learning that weights the objective function or probability distribution based on the importance of the instance in some sense. The simplicity and usefulness of the…
Behavioural economics provides labels for patterns in human economic behaviour. Probability weighting is one such label. It expresses a mismatch between probabilities used in a formal model of a decision (i.e. model parameters) and…
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
Uncertainty quantification (UQ) is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this…
We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov…
Importance sampling is a well developed method in statistics. Given a random variable $X$, the problem of estimating its expected value $\mu$ is addressed. The standard approach is to use the sample mean as an estimator $\bar x$. In…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
The purpose of this paper is to introduce, study and analyze a new stochastic order which lies in the framework of the mean residual life and the combination convexity orders. Several preservation properties of the new order under…
In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the…
We consider some random iterated function systems on the interval and show that the invariant measure has density in $\mathcal{C}^\infty$. To prove this we use some techniques for contractions in cone metrics, applied to the transfer…
For Markov processes over discrete configurations, an asymptotic bound on the uncertainty of stochastic fluxes is derived in terms of the harmonic mean of decay rates with respect to the stationary distribution. This bound is necessarily…
This paper considers a general class of nonparametric time series regression models where the regression function can be time-dependent. We establish an asymptotic theory for estimates of the time-varying regression functions. For this…
We introduce the notion of relative volatility/intermittency and demonstrate how relative volatility statistics can be used to estimate consistently the temporal variation of volatility/intermittency when the data of interest are generated…
We establish convergence to an invariant measure as time tends to infinity, for a large class of (possibly non-Markovian) stochastic volatility models. Our arguments are based on a novel coupling idea for Markov chains which also extends to…
Multivariate Exponentially Weighted Moving Average, MEWMA, charts are popular, handy and effective procedures to detect distributional changes in a stream of multivariate data. For doing appropriate performance analysis, dealing with the…
This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time…
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse,…