Pólya-Eggenberger F-S models of order (k1, k2)

2006 ◽  
Vol 43 (1) ◽  
pp. 1-31 ◽  
Author(s):  
Kanwar Sen ◽  
Manju Agarwal ◽  
Sonali Bhattacharya
Keyword(s):  
Binomial Distribution ◽  
Discrete Distributions ◽  
Probability Functions ◽  
Distributions Of Order K

Pólya-Eggenberger F-S Models of order (k1, k2) are proposed and their probability functions obtained. The results are extended to obtain probability functions of Inverse Pólya-Eggenberger F-S models of order (k1, k2). The Binomial Distribution of order (k1, k2) (see[4]) and some new discrete distributions of order (k1, k2) are obtained as particular cases of these models.

scholarly journals Classification of RNA-Seq Data via Gaussian Copulas

2017 ◽  
Author(s):  
Qingyang Zhang
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Natural Extension ◽  
Real Data ◽  
Discrete Distributions ◽  
Gaussian Copula ◽  
Rna Seq ◽  
Independence Assumption ◽  
Discriminant Score

AbstractRNA-sequencing (RNA-Seq) has become a preferred option to quantify gene expression, because it is more accurate and reliable than microarrays. In RNA-Seq experiments, the expression level of a gene is measured by the count of short reads that are mapped to the gene region. Although some normal-based statistical methods may also be applied to log-transformed read counts, they are not ideal for directly modeling RNA-Seq data. Two discrete distributions, Poisson distribution and negative binomial distribution, have been commonly used in the literature to model RNA-Seq data, where the latter is a natural extension of the former with allowance of overdispersion. Due to the technical difficulty in modeling correlated counts, most existing classifiers based on discrete distributions assume that genes are independent of each other. However, as we show in this paper, the independence assumption may cause non-ignorable bias in estimating the discriminant score, making the classification inaccurate. To this end, we drop the independence assumption and explicitly model the dependence between genes using Gaussian copula. We apply a Bayesian approach to estimate covariance matrix and the overdispersion parameter in negative binomial distribution. Both synthetic data and real data are used to demonstrate the advantages of our model.

Niche Sharing in Intertidal Mollusks and Decapods in Rocky Shore of Easter Island

2019 ◽  
Vol 53 (5) ◽  
pp. 417-422
Author(s):  
P. De los Ríos ◽  
E. Ibáñez Arancibia
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Rocky Shore ◽  
Negative Binomial ◽  
Null Model ◽  
Easter Island ◽  
Published Data ◽  
Distribution Analysis ◽  
Field Works

Abstract The coastal marine ecosystems in Easter Island have been poorly studied, and the main studies were isolated species records based on scientific expeditions. The aim of the present study is to apply a spatial distribution analysis and niche sharing null model in published data on intertidal marine gastropods and decapods in rocky shore in Easter Island based in field works in 2010, and published information from CIMAR cruiser in 2004. The field data revealed the presence of decapods Planes minutus (Linnaeus, 1758) and Leptograpsus variegatus (Fabricius, 1793), whereas it was observed the gastropods Nodilittorina pyramidalis pascua Rosewater, 1970 and Nerita morio (G. B. Sowerby I., 1833). The available information revealed the presence of more species in data collected in 2004 in comparison to data collected in 2010, with one species markedly dominant in comparison to the other species. The spatial distribution of species reported in field works revealed that P. minutus and N. morio have aggregated pattern and negative binomial distribution, L. variegatus had uniform pattern with binomial distribution, and finally N. pyramidalis pascua, in spite of aggregated distribution pattern, had not negative binomial distribution. Finally, the results of null model revealed that the species reported did not share ecological niche due to competition absence. The results would agree with other similar information about littoral and sub-littoral fauna for Easter Island.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

2011 ◽  
Vol 10 (2) ◽  
pp. 1
Author(s):  
Y. ARBI ◽  
R. BUDIARTI ◽  
I G. P. PURNABA
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Financial Institution ◽  
Expected Value ◽  
Insurance Companies ◽  
Limited Data ◽  
Loss Distribution Approach ◽  
Potential Loss ◽  
The Impact

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

A note on the Berkowitz test with discrete distributions

2009 ◽  
Vol 3 (2) ◽  
pp. 3-10 ◽  
Author(s):  
Alfred Hamerle ◽  
Kilian Plank
Keyword(s):  
Discrete Distributions

An Introduction to Uncertain Futures

2018 ◽  
Author(s):  
Jens Beckert ◽  
Richard Bronk
Keyword(s):  
Optimal Strategies ◽  
Theoretical Framework ◽  
Objective Probability ◽  
Political Debate ◽  
Probability Functions ◽  
Market Economies ◽  
Socially Constructed ◽  
The Future ◽  
Radical Uncertainty ◽  
Calculative Practices

This chapter provides a theoretical framework for considering how imaginaries and narratives interact with calculative devices to structure expectations and beliefs in the economy. It analyses the nature of uncertainty in innovative market economies and examines how economic actors use imaginaries, narratives, models, and calculative practices to coordinate and legitimize action, determine value, and establish sufficient conviction to act despite the uncertainty they face. Placing the themes of the volume in the context of broader trends in economics and sociology, the chapter argues that, in conditions of widespread radical uncertainty, there is no uniquely rational set of expectations, and there are no optimal strategies or objective probability functions; instead, expectations are often structured by contingent narratives or socially constructed imaginaries. Moreover, since expectations are not anchored in a pre-existing future reality but have an important role in creating the future, they become legitimate objects of political debate and crucial instruments of power in markets and societies.

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