2016/01/24 by H. M. de Oliveira, de Oliveira, H. M., Renato J. Cintra +1
Computer Science · Mathematics · Physics and Astronomy · #60E05 #62B10 #62E15 #94A15 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1601.06412
openalex publication_date 2016/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are computed from a number of standard distributions, including uniform, normal, exponential, Pareto, logistic, Kumaraswamy, Rayleigh, Cauchy, Weibull, and Maxwell-Boltzmann. The case of joint information-weighted probability distribution is assessed. An additive property is derived in the case of independent variables. One-sided and two-sided information-weighting are considered. The asymptotic behavior of the tail of the new distributions is examined. It is proved that all probability densities proposed here define heavy-tailed distributions. It is shown that the weighting of distributions regularly varying with extreme-value index α> 0 still results in a regular variation distribution with the same index. This approach can be particularly valuable in applications where the tails of the distribution play a major role.