Related papers: The Probabilities of Large Deviations Associated w…
Contemporary statistical publications rely on simulation to evaluate performance of new methods and compare them with established methods. In the context of meta-analysis of log-odds-ratios, we investigate how the ways in which simulations…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
In this paper we introduce a new probability distribution on (0,1), associated with the I-function, namely, the I-function distribution. This distribution generalizes several known distributions with positive support. It is also shown that…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
The origin of the erraticity behaviour observed recently in the experiment is studied in some detail. The negative-binomial distribution is used to fit the experimental multiplicity distribution. It is shown that, with the multiplicity…
The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise $q$-Stirling's formula. The $\alpha $-divergence (or $q$-divergence) is uniquely derived from the generalized binomial…
A new large deviation results for the Pearson chi-square and Log-likelihood ratio statistics are obtained. Here attention is focused on the case when the number of groups increases to infinity and the probabilities of groups decreases to…
Power-law distributions occur in wide variety of physical, biological, and social phenomena. In this paper, we propose a statistical hypothesis test based on the log-likelihood ratio to assess whether two samples of discrete data are drawn…
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world…
Multiple root estimation problems in statistical inference arise in many contexts in the literature. In the context of maximum likelihood estimation, the existence of multiple roots causes uncertainty in the computation of maximum…
We generalize standard credal set models for imprecise probabilities to include higher order credal sets -- confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing…
The notions of disintegration and Bayesian inversion are fundamental in conditional probability theory. They produce channels, as conditional probabilities, from a joint state, or from an already given channel (in opposite direction). These…
Exponential distributions appear in a wide range of applications including chemistry, nuclear physics, time series analyses, and stock market trends. There are conceivable circumstances in which one would be interested in the cumulative…
This article brings in two new discrete distributions: multidimensional Binomial distribution and multidimensional Poisson distribution. Those distributions were created in eventology as more correct generalizations of Binomial and Poisson…
Modifications of quantum mechanics are considered, in which the state vector of any system, large or small, undergoes a stochastic evolution. The general class of theories is described, in which the probability distribution of the state…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed…
We will discuss the link between scientific explanations and probabilities, specially in relationship with statistical mechanics and the derivation of macroscopic laws from microscopic ones.
Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher ($>$ two) order correlations, they offer a better measure…