Related papers: Applications of the Quantile-Based Probabilistic M…

A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…

We discuss two distinct approaches, for distorting risk measures of sums of dependent random variables, which preserve the property of coherence. The first, based on distorted expectations, operates on the survival function of the sum. The…

We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…

Circular variables arise in a multitude of data-modelling contexts ranging from robotics to the social sciences, but they have been largely overlooked by the machine learning community. This paper partially redresses this imbalance by…

We introduce a new notion of conditional nonlinear expectation under probability distortion. Such a distorted nonlinear expectation is not sub-additive in general, so it is beyond the scope of Peng's framework of nonlinear expectations. A…

Hypothesis testing results often rely on simple, yet important assumptions about the behaviour of the distribution of p-values under the null and the alternative. We examine tests for one dimensional parameters of interest that converge to…

Population attributable fractions aim to quantify the proportion of the cases of an outcome (for example, a disease) that would have been avoided had no individuals in the population been exposed to a given exposure. This quantity thus…

A new distribution on (0, 1), generalized Log-Lindley distribution, is proposed by extending the Log-Lindley distribution. This new distribution is shown to be a weighted Log-Lindley distribution. Important probabilistic and statistical…

Uncertainty requires suitable techniques for risk assessment. Combining stochastic approximation and stochastic average approximation, we propose an efficient algorithm to compute the worst case average value at risk in the face of tail…

Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider…

We study optimal risk sharing among $n$ agents endowed with distortion risk measures. Our model includes market frictions that can either represent linear transaction costs or risk premia charged by a clearing house for the agents. Risk…

Distortion (Denneberg 1990) is a well known premium calculation principle for insurance contracts. In this paper, we study sensitivity properties of distortion functionals w.r.t. the assumptions for risk aversion as well as robustness…

It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional…

An approach to inference for relative sparsity was developed in prior work, and an adaptive lasso asymptotic normality theorem was given there, but this theorem was not fully used when estimating the variance of the policy coefficients.…

There are some real life issues that are exists in nature which has early failure. This type of problems can be modelled either by a complex distribution having more than one parameter or by finite mixture of some distribution. In this…

In computational social choice, the distortion of a voting rule quantifies the degree to which the rule overcomes limited preference information to select a socially desirable outcome. This concept has been investigated extensively, but…

We derive new approximations for the Value at Risk and the Expected Shortfall at high levels of loss distributions with positive skewness and excess kurtosis, and we describe their precisions for notable ones such as for exponential, Pareto…

We study Pareto optimality in a decentralized peer-to-peer risk-sharing market where agents' preferences are represented by robust distortion risk measures that are not necessarily convex. We obtain a characterization of Pareto-optimal…

Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if…

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…