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We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
This paper proposes a statistical mechanics approach to the analysis of income distribution and inequality. A new distribution function, having its roots in the framework of k-generalized statistics, is derived that is particularly suitable…
Competing styles of Statistical Mechanics have been introduced as practical succedaneous to the conventional well established Boltzmann-Gibbs statistical mechanics, when in the use of the latter the researcher is impaired in his/her…
A broad set of sufficient conditions that guarantees the existence of the maximum entropy (maxent) distribution consistent with specified bounds on certain generalized moments is derived. Most results in the literature are either focused on…
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…
The advent of data science has spurred interest in estimating properties of distributions over large alphabets. Fundamental symmetric properties such as support size, support coverage, entropy, and proximity to uniformity, received most…
A goodness-of-fit test for one-parameter count distributions with finite second moment is proposed. The test statistic is derived from the $L^1$ distance of a function of the probability generating function of the model under the null…
Entropy has emerged as a dynamic, interdisciplinary, and widely accepted quantitative measure of uncertainty across different disciplines. A unified understanding of entropy measures, supported by a detailed review of their theoretical…
The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…
We study distributional similarity measures for the purpose of improving probability estimation for unseen cooccurrences. Our contributions are three-fold: an empirical comparison of a broad range of measures; a classification of similarity…
In this paper we study the Exponentiated Hypoexponential Distribution with different parameters. The distribution added a parameter to the n parameters of the Hypoexponenial distribution. We first derive a closed expression of the…
Shannon's entropy is one of the building blocks of information theory and an essential aspect of Machine Learning methods (e.g., Random Forests). Yet, it is only finitely defined for distributions with fast decaying tails on a countable…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
A new family of distribution is proposed by using Kumaraswamy-G (Cordeiro and de Castro, 2011) distribution as the base line distribution in the Generalized Marshal-Olkin (Jayakumar and Mathew, 2008) Construction. A number of special cases…
In this paper a new long-term survival distribution is proposed. The so called long term Fr\'echet distribution allows us to fit data where a part of the population is not susceptible to the event of interest. This model may be used, for…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
In the article the $mm$-entropy (an entropy of a metric measure space) introduced by C. Shannon is evaluated for an $\alpha$-stable L\'evy process. For $\alpha<1$ the double-sided estimates of the same order are obtained for process…
A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of the marginal distributions and the…
We introduce a novel entropy-related function, \textit{non-repeatability}, designed to capture dynamical behaviors in complex systems. Its normalized form, \textit{mutability}, has been previously applied in statistical physics as a…
This paper proposes a new extension of the linear failure rate (LFR) model to better capture real-world lifetime data. The model incorporates an additional shape parameter to increase flexibility. It helps model the minimum survival time…