Related papers: Guessing probability distributions from small samp…
We show how to store good approximations of probability distributions in small space.
We propose a method to derive the stationary size distributions of a system, and the degree distributions of networks, using maximisation of the Gibbs-Shannon entropy. We apply this to a preferential attachment-type algorithm for systems of…
We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…
Methods have been developed to identify the probability distribution of a random vector $Z$ from information consisting of its bounded range and the probability density function or moments of a quantity of interest, $Q(Z)$. The mapping from…
Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…
The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic…
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and…
Probability estimation is an elementary building block of every statistical data compression algorithm. In practice probability estimation is often based on relative letter frequencies which get scaled down, when their sum is too large.…
In this paper we will look at the distribution with which passwords are chosen. Zipf's Law is commonly observed in lists of chosen words. Using password lists from four different on-line sources, we will investigate if Zipf's law is a good…
Statistical inference for extreme values of random events is difficult in practice due to low sample sizes and inaccurate models for the studied rare events. If prior knowledge for extreme values is available, Bayesian statistics can be…
Probabilistic embeddings have several advantages over deterministic embeddings as they map each data point to a distribution, which better describes the uncertainty and complexity of data. Many works focus on adjusting the distribution…
Prompted by the realisation that the statistical entropy of an ideal gas in the micro-canonical ensemble should not fluctuate or change over time, the meaning of the H-theorem is re-interpreted from the perspective of information theory in…
We revisit the well-studied problem of estimating the Shannon entropy of a probability distribution, now given access to a probability-revealing conditional sampling oracle. In this model, the oracle takes as input the representation of a…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
In this article, a discrete analogue of continuous Teissier distribution is presented. Its several important distributional characteristics have been derived. The estimation of the unknown parameter has been done using the method of maximum…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…
We examine the extent to which random samplings from the values of a random set, determine the distribution of the random set itself. We also comment on how, given the statistics of the sampling, to detect the distribution. Several methods…
We analyse correspondence of a text to a simple probabilistic model. The model assumes that the words are selected independently from an infinite dictionary. The probability distribution correspond to the Zipf---Mandelbrot law. We count…
The decision whether a measured distribution complies with an equidistribution is a central element of many biostatistical methods. High throughput differential expression measurements, for instance, necessitate to judge possible…
We determine the distributions of lengths of runs in random sequences of elements from a totally ordered set (total order) or partially ordered set (partial order). In particular, we produce novel formulae for the expected value, variance,…