scholarly journals Weighted stochastic block model

2021 ◽  
Author(s):  
Tin Lok James Ng ◽  
Thomas Brendan Murphy
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulated Data ◽  
Important Case ◽  
Block Model ◽  
Data Set ◽  
Stochastic Block Model ◽  
Proposed Model ◽  
Variational Approaches ◽  
Number Of Classes

AbstractWe propose a weighted stochastic block model (WSBM) which extends the stochastic block model to the important case in which edges are weighted. We address the parameter estimation of the WSBM by use of maximum likelihood and variational approaches, and establish the consistency of these estimators. The problem of choosing the number of classes in a WSBM is addressed. The proposed model is applied to simulated data and an illustrative data set.

Messages of Oscillatory Correlograms: A Spike Train Model

2008 ◽  
Vol 20 (5) ◽  
pp. 1211-1238 ◽  
Author(s):  
Gaby Schneider
Keyword(s):  
Spike Train ◽  
Null Model ◽  
Simulated Data ◽  
Joint Analysis ◽  
Data Set ◽  
Proposed Model ◽  
Peak Asymmetry ◽  
Millisecond Range ◽  
Temporal Interactions ◽  
Underlying Processes

Oscillatory correlograms are widely used to study neuronal activity that shows a joint periodic rhythm. In most cases, the statistical analysis of cross-correlation histograms (CCH) features is based on the null model of independent processes, and the resulting conclusions about the underlying processes remain qualitative. Therefore, we propose a spike train model for synchronous oscillatory firing activity that directly links characteristics of the CCH to parameters of the underlying processes. The model focuses particularly on asymmetric central peaks, which differ in slope and width on the two sides. Asymmetric peaks can be associated with phase offsets in the (sub-) millisecond range. These spatiotemporal firing patterns can be highly consistent across units yet invisible in the underlying processes. The proposed model includes a single temporal parameter that accounts for this peak asymmetry. The model provides approaches for the analysis of oscillatory correlograms, taking into account dependencies and nonstationarities in the underlying processes. In particular, the auto- and the cross-correlogram can be investigated in a joint analysis because they depend on the same spike train parameters. Particular temporal interactions such as the degree to which different units synchronize in a common oscillatory rhythm can also be investigated. The analysis is demonstrated by application to a simulated data set.

Utilizarea teoriei valorilor extreme în climatologie

2019 ◽  
Author(s):  
Valentin Raileanu ◽  
Keyword(s):  
Maximum Likelihood ◽  
Extreme Values ◽  
Probability Distributions ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
R Software ◽  
Data Set ◽  
Data Format ◽  
Generalized Pareto ◽  
Distribution Parameters

The article briefly describes the history and fields of application of the theory of extreme values, including climatology. The data format, the Generalized Extreme Value (GEV) probability distributions with Bock Maxima, the Generalized Pareto (GP) distributions with Point of Threshold (POT) and the analysis methods are presented. Estimating the distribution parameters is done using the Maximum Likelihood Estimation (MLE) method. Free R software installation, the minimum set of required commands and the GUI in2extRemes graphical package are described. As an example, the results of the GEV analysis of a simulated data set in in2extRemes are presented.

scholarly journals A Family of Loss Distributions with an Application to the Vehicle Insurance Loss Data

2019 ◽  
pp. 731-744 ◽  
Author(s):  
Zubair Ahmad Ahmad ◽  
Eisa Mahmoudi Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Maximum Likelihood ◽  
Financial Risk ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Set ◽  
Loss Model ◽  
New Class ◽  
Proposed Model ◽  
Loss Distributions ◽  
Loss Data

Actuaries are often in search of nding an adequate loss model in the scenario of actuarial and financial risk management problems. In this work, we propose a new approach to obtain a new class of loss distributions. A special sub-model of the proposed family, called the Weibull-loss model isconsidered in detail. Some mathematical properties are derived and maximum likelihood estimates of the model parameters are obtained. Certain characterizations of the proposed family are also provided. A simulation study is done to evaluate the performance of the maximum likelihood estimators. Finally, an application of the proposed model to the vehicle insurance loss data set is presented.

scholarly journals General Results for the Transmuted Family of Distributions and New Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Marcelo Bourguignon ◽  
Indranil Ghosh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
New Models ◽  
Family Of Distributions

The transmuted family of distributions has been receiving increased attention over the last few years. For a baselineGdistribution, we derive a simple representation for the transmuted-Gfamily density function as a linear mixture of theGand exponentiated-Gdensities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.

scholarly journals The Half-Logistic Lomax Distribution for Lifetime Modeling

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Masood Anwar ◽  
Jawaria Zahoor
Keyword(s):  
Maximum Likelihood ◽  
Residual Life ◽  
Information Matrix ◽  
Simulated Data ◽  
Quantile Function ◽  
Rate Function ◽  
Mean Residual Life ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Proposed Model

We introduce a new two-parameter lifetime distribution called the half-logistic Lomax (HLL) distribution. The proposed distribution is obtained by compounding half-logistic and Lomax distributions. We derive some mathematical properties of the proposed distribution such as the survival and hazard rate function, quantile function, mode, median, moments and moment generating functions, mean deviations from mean and median, mean residual life function, order statistics, and entropies. The estimation of parameters is performed by maximum likelihood and the formulas for the elements of the Fisher information matrix are provided. A simulation study is run to assess the performance of maximum-likelihood estimators (MLEs). The flexibility and potentiality of the proposed model are illustrated by means of real and simulated data sets.

scholarly journals Consistency of maximum-likelihood and variational estimators in the stochastic block model

2012 ◽  
Vol 6 (0) ◽  
pp. 1847-1899 ◽  
Author(s):  
Alain Celisse ◽  
Jean-Jacques Daudin ◽  
Laurent Pierre
Keyword(s):  
Maximum Likelihood ◽  
Block Model ◽  
Stochastic Block Model

scholarly journals Exact Recovery of Stochastic Block Model by Ising Model

Entropy ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 65
Author(s):  
Feng Zhao ◽  
Min Ye ◽  
Shao-Lun Huang
Keyword(s):  
Phase Transition ◽  
Maximum Likelihood ◽  
Ising Model ◽  
Optimization Problem ◽  
Model Parameters ◽  
Stochastic Algorithm ◽  
Block Model ◽  
Stochastic Block Model ◽  
Special Case ◽  
Transition Property

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.

scholarly journals Transmuted Alpha Power Inverse Rayleigh Distribution: Properties and Application

2019 ◽  
Vol 11 (2) ◽  
pp. 185-194
Author(s):  
A. S. Malik ◽  
S. P. Ahmad
Keyword(s):  
Parameter Estimation ◽  
Potential Application ◽  
Real Life ◽  
Rayleigh Distribution ◽  
Parameter Distribution ◽  
Alpha Power ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Proposed Model

This paper proposes a new three parameter-distribution through the technique known as Transmutation. The proposed distribution is named Transmuted Alpha power inverse Rayleigh Distribution. Several important properties of the distribution are derived. The parameter estimation is also carried out. Two real life data set are used at the end to describe the potential application of proposed model.

scholarly journals On Zero-Modified Poisson-Sujatha Distribution to Model Overdispersed Count Data

2018 ◽  
Vol 47 (3) ◽  
pp. 1-19
Author(s):  
Wesley Bertoli Da Silva ◽  
Angélica Maria Tortola Ribeiro ◽  
Katiane Silva Conceição ◽  
Marinho Gomes Andrade ◽  
Francisco Louzada Neto
Keyword(s):  
Biological Sciences ◽  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Count Data ◽  
Probability Function ◽  
Hurdle Model ◽  
Asymptotic Inference ◽  
Proposed Model

In this paper we propose the zero-modified Poisson-Sujatha distribution as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. It will be shown that the zero modification can be incorporated by using the zero-truncated Poisson-Sujatha distribution. A simple reparametrization of the probability function will allow us to represent the zero-modified Poisson-Sujatha distribution as a hurdle model. This trick leads to the fact that proposed model can be fitted without any previously information about the zero modification present in a given dataset. The maximum likelihood theory will be used for parameter estimation and asymptotic inference concerns. A simulation study will be conducted in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed model will be illustrated using real datasets of the biological sciences field and comparing it with other models available in the literature.

scholarly journals The Exponentiated Exponential Burr XII distribution: Theory and application to lifetime and simulated data

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248873
Author(s):  
Majdah Badr ◽  
Muhammad Ijaz
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Probability Distribution ◽  
Simulation Study ◽  
Probability Distributions ◽  
Simulated Data ◽  
Maximum Likelihood Estimators ◽  
Data Sets ◽  
Lifetime Data ◽  
Confidence Bounds

The paper addresses a new four-parameter probability distribution called the Exponentiated Exponential Burr XII or abbreviated as EE-BXII. We derive various statistical properties in addition to the parameter estimation, moments, and asymptotic confidence bounds. We estimate the precision of the maximum likelihood estimators via a simulation study. Furthermore, the utility of the proposed distribution is evaluated by using two lifetime data sets and the results are compared with other existing probability distributions. The results clarify that the proposed distribution provides a better fit to these data sets as compared to the existing probability distributions.

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