Related papers: Construction of Benford Random Variables: Generato…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…
In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density…
We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an…
Signal processing techniques will lean on blind methods in the near future, where no redundant, resource allocating information will be transmitted through the channel. To achieve a proper decision, however, it is essential to know at least…
The following work is written in easy language for college level students. It shows how the first digit probabilities of a group of continuous real-valued functions can be calculated. Thus, examples explaining how the probabilities are…
A random variable (r.v.) X is said to follow Benford's law if log(X) is uniform mod 1. Many experimental data sets prove to follow an approximate version of it, and so do many mathematical series and continuous random variables. This…
The probability density function (PDF) of a random variable associated with the solution of a partial differential equation (PDE) with random parameters is approximated using a truncated series expansion. The random PDE is solved using two…
An elaboration of Dempster's method of constructing belief functions suggests a broadly applicable strategy for constructing lower probabilities under a variety of evidentiary constraints.
We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables…
We introduce a new functional representation of probability density functions (PDFs) of non-negative random variables via a product of a monomial factor and linear combinations of decaying exponentials with complex exponents. This…
A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
The empirical probability density function for the conditional distribution of the true value of Poisson distribution parameter on one measurement is constructed by computer experiment. The analysis of the obtained distributions confirms…
If two probability density functions (PDFs) have values for their first $n$ moments which are quite close to each other (upper bounds of their differences are known), can it be expected that the PDFs themselves are very similar? Shown below…
Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…
We define a growing model of random graphs. Given a sequence of nonnegative integers $\{d_n\}_{n=0}^\infty$ with the property that $d_i\leq i$, we construct a random graph on countably infinitely many vertices $v_0,v_1\ldots$ by the…
This paper investigates the usage of generating functions (GFs) encoding measures over the program variables for reasoning about discrete probabilistic programs. To that end, we define a denotational GF-transformer semantics for…
We show a general relation between the spatially disjoint product of probability density functions and the sum of their Fisher information metric tensors. We then utilise this result to give a method for constructing the probability density…
We study random trees which are invariant in law under the operation of contracting each edge independently with probability $p\in(0,1)$. We show that all such trees can be constructed through Poissonian sampling from a certain class of…
We survey several methods of generating large random lambda-terms, focusing on their closed and simply-typed variants. We discuss methods of exact- and approximate-size generation, as well as methods of achieving size-uniform and…