scholarly journals Multiple Tests Based on a Gaussian Approximation of the Unitary Events Method with Delayed Coincidence Count

2014 ◽  
Vol 26 (7) ◽  
pp. 1408-1454 ◽  
Author(s):  
Christine Tuleau-Malot ◽  
Amel Rouis ◽  
Franck Grammont ◽  
Patricia Reynaud-Bouret
Keyword(s):  
Point Processes ◽  
Gaussian Approximation ◽  
Real Data ◽  
Spike Trains ◽  
Previous Method ◽  
Unknown Parameters ◽  
Multiple Tests ◽  
The Past ◽  
False Discovery ◽  
Unitary Events

The unitary events (UE) method is one of the most popular and efficient methods used over the past decade to detect patterns of coincident joint spike activity among simultaneously recorded neurons. The detection of coincidences is usually based on binned coincidence count (Grün, 1996 ), which is known to be subject to loss in synchrony detection (Grün, Diesmann, Grammont, Riehle, & Aertsen, 1999 ). This defect has been corrected by the multiple shift coincidence count (Grün et al., 1999 ). The statistical properties of this count have not been further investigated until this work, the formula being more difficult to deal with than the original binned count. First, we propose a new notion of coincidence count, the delayed coincidence count, which is equal to the multiple shift coincidence count when discretized point processes are involved as models for the spike trains. Moreover, it generalizes this notion to nondiscretized point processes, allowing us to propose a new gaussian approximation of the count. Since unknown parameters are involved in the approximation, we perform a plug-in step, where unknown parameters are replaced by estimated ones, leading to a modification of the approximating distribution. Finally the method takes the multiplicity of the tests into account via a Benjamini and Hochberg approach (Benjamini & Hochberg, 1995 ), to guarantee a prescribed control of the false discovery rate. We compare our new method, MTGAUE (multiple tests based on a gaussian approximation of the unitary events) and the UE method proposed in Grün et al. ( 1999 ) over various simulations, showing that MTGAUE extends the validity of the previous method. In particular, MTGAUE is able to detect both profusion and lack of coincidences with respect to the independence case and is robust to changes in the underlying model. Furthermore MTGAUE is applied on real data.

scholarly journals On Local Linear Approximations to Diffusion Processes

2011 ◽  
Vol 2011 ◽  
pp. 1-26
Author(s):  
X. L. Duan ◽  
Z. M. Qian ◽  
W. A. Zheng
Keyword(s):  
Maximum Likelihood ◽  
Diffusion Processes ◽  
Gaussian Approximation ◽  
Diffusion Models ◽  
Likelihood Method ◽  
Unknown Parameters ◽  
Likelihood Functions ◽  
The Past ◽  
Local Linear ◽  
Exact Maximum Likelihood

Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth. Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.

scholarly journals New Method for Generating New Families of Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 726
Author(s):  
Lamya A. Baharith ◽  
Wedad H. Aljuhani
Keyword(s):  
Exponential Distribution ◽  
Real Data ◽  
Rate Function ◽  
New Method ◽  
Likelihood Method ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Failure Rate Function ◽  
New Approach ◽  
Numerical Studies

This article presents a new method for generating distributions. This method combines two techniques—the transformed—transformer and alpha power transformation approaches—allowing for tremendous flexibility in the resulting distributions. The new approach is applied to introduce the alpha power Weibull—exponential distribution. The density of this distribution can take asymmetric and near-symmetric shapes. Various asymmetric shapes, such as decreasing, increasing, L-shaped, near-symmetrical, and right-skewed shapes, are observed for the related failure rate function, making it more tractable for many modeling applications. Some significant mathematical features of the suggested distribution are determined. Estimates of the unknown parameters of the proposed distribution are obtained using the maximum likelihood method. Furthermore, some numerical studies were carried out, in order to evaluate the estimation performance. Three practical datasets are considered to analyze the usefulness and flexibility of the introduced distribution. The proposed alpha power Weibull–exponential distribution can outperform other well-known distributions, showing its great adaptability in the context of real data analysis.

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

Experience

2021 ◽  
Vol 13 (1) ◽  
pp. 1-16
Author(s):  
Michela Fazzolari ◽  
Francesco Buccafurri ◽  
Gianluca Lax ◽  
Marinella Petrocchi
Keyword(s):  
Relative Frequency ◽  
Service Providers ◽  
Real Data ◽  
Online Reviews ◽  
Purchase Decision ◽  
The Past ◽  
Supervised Classifiers ◽  
Relative Frequency Distribution ◽  
Opinion Spam ◽  
Fake Reviews

Over the past few years, online reviews have become very important, since they can influence the purchase decision of consumers and the reputation of businesses. Therefore, the practice of writing fake reviews can have severe consequences on customers and service providers. Various approaches have been proposed for detecting opinion spam in online reviews, especially based on supervised classifiers. In this contribution, we start from a set of effective features used for classifying opinion spam and we re-engineered them by considering the Cumulative Relative Frequency Distribution of each feature. By an experimental evaluation carried out on real data from Yelp.com, we show that the use of the distributional features is able to improve the performances of classifiers.

scholarly journals Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 934
Author(s):  
Yuxuan Zhang ◽  
Kaiwei Liu ◽  
Wenhao Gui
Keyword(s):  
Bayesian Method ◽  
Real Data ◽  
Loss Functions ◽  
Type I ◽  
Statistical Efficiency ◽  
Unknown Parameters ◽  
Data Set ◽  
Hybrid Censoring ◽  
Bayesian Estimations ◽  
Generalized Type

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.

scholarly journals On the Estimation of Reliability of Weighted Weibull Distribution: A Comparative Study

2016 ◽  
Vol 5 (4) ◽  
pp. 1
Author(s):  
Bander Al-Zahrani
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Real Data ◽  
Reliability Function ◽  
Nonparametric Methods ◽  
Empirical Method ◽  
Density Estimator ◽  
Bayes Estimators ◽  
Unknown Parameters ◽  
Data Set

The paper gives a description of estimation for the reliability function of weighted Weibull distribution. The maximum likelihood estimators for the unknown parameters are obtained. Nonparametric methods such as empirical method, kernel density estimator and a modified shrinkage estimator are provided. The Markov chain Monte Carlo method is used to compute the Bayes estimators assuming gamma and Jeffrey priors. The performance of the maximum likelihood, nonparametric methods and Bayesian estimators is assessed through a real data set.

scholarly journals Bivariate Nonlinear Diffusion Degradation Process Modeling via Copula and MCMC

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Huibing Hao ◽  
Chun Su
Keyword(s):  
Nonlinear Diffusion ◽  
Goodness Of Fit ◽  
Real Data ◽  
Degradation Process ◽  
Copula Function ◽  
Assessment Method ◽  
Unknown Parameters ◽  
Degradation Data ◽  
Proposed Model ◽  
Frank Copula

A novel reliability assessment method for degradation product with two dependent performance characteristics (PCs) is proposed, which is different from existing work that only utilized one dimensional degradation data. In this model, the dependence of two PCs is described by the Frank copula function, and each PC is governed by a random effected nonlinear diffusion process where random effects capture the unit to unit differences. Considering that the model is so complicated and analytically intractable, Markov Chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about LED lamp is given to demonstrate the usefulness and validity of the proposed model and method. Numerical results show that the random effected nonlinear diffusion model is very useful by checking the goodness of fit of the real data, and ignoring the dependence between PCs may result in different reliability conclusion.

Sub-array equalization technique for the parametric array loudspeaker to reduce nonlinear distortion

2021 ◽  
Vol 263 (5) ◽  
pp. 1497-1504
Author(s):  
Chi Zhang ◽  
Jing Ren ◽  
Chuang Shi
Keyword(s):  
Nonlinear Distortion ◽  
Ultrasonic Transducer ◽  
Previous Method ◽  
Ultrasonic Transducers ◽  
Acoustic Effect ◽  
The Past ◽  
Comparison Results ◽  
Equalization Technique ◽  
Nonlinear Acoustic ◽  
Parametric Array

The parametric array loudspeaker (PAL) is a directional loudspeaker which uses the nonlinear acoustic effect, namely the parametric array, to produce an audio beam from narrow ultrasonic beams. The PAL can efficiently deliver audible information, without generating noise to the surroundings. One significant drawback of the PAL is the nonlinear distortion. Therefore, many sophisticated methods have been proposed to preprocess the input signal of the PAL. However, those methods usually request a flat frequency response of the ultrasonic transducer array (UTA). In the past, equalization has been tried out for the whole UTA, but the performance was sometimes not satisfactory due to the inconsistent productions of ultrasonic transducers. This paper proposes to group the ultrasonic transducers by their impedances. Several sub-arrays are thereafter formed and equalized individually. The comparison results demonstrate that the propose sub-array equalization technique can suppress the nonlinear distortion of the PAL more effectively than the previous method.

scholarly journals Open Data Release and Privacy Concerns: Complexity in Mitigating Vulnerability with Controlled Perturbation

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Shah Imran Alam ◽  
Ihtiram Raza Khan ◽  
Syed Imtiyaz Hassan ◽  
Farheen Siddiqui ◽  
M. Afshar Alam ◽  
...  
Keyword(s):  
Data Quality ◽  
Open Data ◽  
Real Data ◽  
Privacy Concerns ◽  
The Past ◽  
Privacy Laws ◽  
Data Quality Assessment ◽  
Anonymized Data ◽  
Evaluation Parameters ◽  
Technology Domain

The benefits of open data were realised worldwide since the past decades, and the efforts to move more data under the license of open data intensified. There was a steep rise of open data in government repositories. In our study, we point out that privacy is one of the consistent and leading barriers among others. Strong privacy laws restrict data owners from opening the data freely. In this paper, we attempted to study the applied solutions and to the best of our knowledge, we found that anonymity-preserving algorithms did a substantial job to protect privacy in the release of the structured microdata. Such anonymity-preserving algorithms argue and compete in objectivethat not only could the released anonymized data preserve privacy but also the anonymized data preserve the required level of quality. K-anonymity algorithm was the foundation of many of its successor algorithms of all privacy-preserving algorithms. l-diversity claims to add another dimension of privacy protection. Both these algorithms used together are known to provide a good balance between privacy and quality control of the dataset as a whole entity. In this research, we have used the K-anonymity algorithm and compared the results with the addon of l-diversity. We discussed the gap and reported the benefits and loss with various combinations of K and l values, taken in combination with released data quality from an analyst’s perspective. We first used dummy fictitious data to explain the general expectations and then concluded the contrast in the findings with the real data from the food technology domain. The work contradicts the general assumptions with a specific set of evaluation parameters for data quality assessment. Additionally, it is intended to argue in favour of pushing for research contributions in the field of anonymity preservation and intensify the effort for major trends of research, considering its importance and potential to benefit people.

scholarly journals Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249028
Author(s):  
Ehsan Fayyazishishavan ◽  
Serpil Kılıç Depren
Keyword(s):  
Information Matrix ◽  
Gumbel Distribution ◽  
Sampling Technique ◽  
Real Data ◽  
Record Values ◽  
Unknown Parameters ◽  
Data Set ◽  
Credible Intervals ◽  
Lower Records ◽  
Two Parameter

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

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