23 papers · ranked by Valyu relevance
Raghu Kacker, Ingram Olkin
This article is a survey of the tables of probability distributions published about or after the publication in 1964 of the Handbook of Mathematical Functions, edited by Abramowitz and Stegun
Abdullah Alomair, Muhammad Ahsan-ul-Haq, Kumer Das
Several research investigations have stressed the importance of discrete data analysis and its relevance to actual events. The current work focuses on a new discrete distribution with a single parameter that can be derived using the Poisson mixing technique. The new distribution is named the Poisson Entropy-Based…
Kai-Tai Fang, Yu-Xuan Lin, Yu-Hui Deng, Nikolai Leonenko + 1 more
Statistical modeling is fundamentally based on probability distributions, which can be discrete or continuous and univariate or multivariate. This review focuses on the methods used to construct these distributions, covering both traditional and newly developed approaches. We first examine classic distributions such as…
E.A. Kushnirenko
In this paper the generalization of the Poisson distribution is derived for the case when each consecutive event changes event rate. A simple formula for the probability of observing of a given number of events for the selected period of time is derived for a given set of rates. Application of this distribution in…
Huiqing Gao, Zhanshou Chen, Fuxiao Li, Carlos Alberto De Bragança Pereira + 2 more
'Carlos Alberto De Bragança Pereira' 'Paulo Canas Rodrigues' 'Mark Andrew Gannon'] Parameter estimation is an important component of statistical inference, and how to improve the accuracy of parameter estimation is a key issue in research. This paper proposes a linear Bayesian estimation for estimating parameters in a…
Mohamed Y. Hassan
In this study, we propose an Equi-Under-dispersed Poisson distribution derived from a finite mixture of weighted Poisson distributions. This probability distribution is a simple, parsimonious, and flexible option suitable for modeling under-dispersed count data. It aims to overcome some of the weaknesses of existing…
Carl P. Dettmann
Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson…
Muhammad Ahsan-ul-Haq, Afrah Al-Bossly, Mahmoud El-Morshedy, Mohamed S. Eliwa
'Mohamed S. Eliwa'] In this study, a new one-parameter count distribution is proposed by combining Poisson and XLindley distributions. Some of its statistical and reliability properties including order statistics, hazard rate function, reversed hazard rate function, mode, factorial moments, probability generating…
Suryo Adi Rakhmawan, Tahir Mahmood, Nasir Abbas, Muhammad Riaz
Forecasting mortality rates is crucial for evaluating life insurance company solvency, especially amid disruptions caused by phenomena like COVID-19. The Lee-Carter model is commonly employed in mortality modelling; however, extensions that can encompass count data with diverse distributions, such as the Generalized…
David I. Inouye, Eunho Yang, Genevera I. Allen, Pradeep Ravikumar
The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime…
G. Böhm, G. Zech
The statistics of the sum of random weights where the number of weights is Poisson distributed has important applications in nuclear physics, particle physics and astrophysics. Events are frequently weighted according to their acceptance or relevance to a certain type of reaction. The sum is described by the compound…
Xinyu Wang, Youming Li, Chen Jia
Stochastic gene expression dynamics can be modeled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner’s Poisson representation. Here we systematically investigate the Poisson…
Anupama Nandi, Subrata Chakraborty, Aniket Biswas
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the geometric, transmuted geometric, and PoiG distributions. Various important statistical…
Anum Fatima, Gesine Reinert
The distribution of the maximum of a zero truncated Poisson number of i.i.d. exponentially distributed random variables is known as a Poisson-Exponential distribution. It arises for example as a model for monotone hazard rates, and also as a limiting distribution for example, of a Generalized Poisson-Exponential…
Danillo Xavier, Manoel Santos‐Neto, Marcelo Bourguignon, Vera Tomazella
'Vera Tomazella'] aUniversidade Federal de Campina Grande Departamento de EstatAstica, Bairro Universit ´ario, 58429-900, Campina Grande, PB, Brazil ˜ bUniversidade Federal de S˜ao Carlos Departamento de EstatAstica, Rodovia Washington Luis, km 235, 13565-905, S˜ao Carlos, SP, Brazil ˜ cUniversidade Federal do Rio…
Authors not listed
Relation between triple point temperature and the Rydberg constant based on the semi-phenomenological approach is found. To explain squared number 17 set in factor of proportionality, we use the Poisson distribution to be valid for some groups of thermal vibrations in pure water. We formulate a theorem explaining…
PETER CARDEW, Keith Gregory, Adam Lechmere
In order to meet the EU requirement of compliance with the 10 µg/l lead standard utility companies in England and Wales implemented a large-scale plumbosolvency treatment programme based around the addition of orthophosphate. This was largely delivered by the end of 2003. This solution has resulted in a major…
Sean Bellew, Ian Flint, Yan Wang
Poisson processes have become a prominent tool in species distribution modelling when analysing citizen science data based on presence records. This study examines four distinct statistical approaches, each of which utilises a different approximation to fit a Poisson point process. These include two Poisson regressions…
Authors not listed
Quantitative analysis of small extracellular vesicles (sEVs) at single-particle resolution remains challenging due to their nanoscale dimensions and compositional heterogeneity. Existing methods often rely on specialized and costly instrumentation, limiting accessibility for many researchers and necessitates extensive…
Lisa Amrhein, Kumar Harsha, Christiane Fuchs
Several tools analyze the outcome of single-cell RNA-seq experiments, and they often assume a probability distribution for the observed sequencing counts. It is an open question of which is the most appropriate discrete distribution, not only in terms of model estimation, but also regarding interpretability, complexity…
Authors not listed
The screening of chemical libraries is an essential starting point in the drug discovery process. While some researchers desire a more thorough screening of drug targets against a narrower scope of molecules, it is not uncommon for diverse screening sets to be favored during early stages of drug discovery. However, a…
Authors not listed
The polarizable continuum model (PCM) is a computationally efficient way to incorporate dielectric boundary conditions into electronic structure calculations, via a boundary-element reformulation of Poisson's equation. This transformation is only rigorously valid for an isotropic dielectric medium. To simulate…
Lucian Smith, Herbert M. Sauro
In this technical note we describe modifications to Antimony (Biochemical model specification language) that allows modelers to use the SBML distributions package. In addition the article describes best practice for using distributions, including when they should and should not be used.