A Chaotic Continuous Map Generates All Probability Distributions

Probability Distributions: Discrete vs. Continuous

Formalization of Continuous Probability Distributions

Continuous probability distributions are widely used to mathematically describe random phenomena in engineering and physical sciences. In this paper, we present a methodology that can be used to formalize any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Our methodology is primarily based on the Standard ...

Summarizing CSP Hardness with Continuous Probability Distributions

We present empirical evidence that the distribution of eeort required to solve CSPs randomly generated at the 50% satissable point, when using a backtracking algorithm, can be approximated by two standard families of continuous probability distribution functions. Solvable problems can be modelled by the Weibull distribution , and unsolvable problems by the lognormal distribution. These distribu...

Continuous probability distributions from finite data.

Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This paper presents a more general form for the prior distribution that has a geometrical interpretation and can improve the specificity of likely solutions. It is also demonstrated that a numerical samp...

A Continuous-time Delay Chaotic System Obtained from a Chaotic Logistic Map

This paper presents a procedure to transform a chaotic logistic map into a continuous-time delay chaotic system by using sampled-data representation of continuous-time models. Because of this, the chaotic behavior of the resultant scheme is easy to proofread. A numerical illustration is also realized by utilizing Matlab/Simulink, where the new resultant chaotic attractor is shown.