scholarly journals Extended Generalized Sinh-Normal Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2793
Author(s):  
Guillermo Martínez-Flórez ◽  
David Elal-Olivero ◽  
Carlos Barrera-Causil
Keyword(s):  
Reaction Time ◽  
Normal Distribution ◽  
Spatial Data ◽  
Goodness Of Fit ◽  
Natural Extension ◽  
Asymmetric Distribution ◽  
Data Sets ◽  
Agricultural Engineering ◽  
Proposed Model ◽  
Distribution Family

Positively skewed data sets are common in different areas, and data sets such as material fatigue, reaction time, neuronal reaction time, agricultural engineering, and spatial data, among others, need to be fitted according to their features and maintain a good quality of fit. Skewness and bimodality are two of the features that data sets like this could present simultaneously. So, flexible statistical models should be proposed in this sense. In this paper, a general extended class of the sinh-normal distribution is presented. Additionally, the asymmetric distribution family is extended, and as a natural extension of this model, the extended Birnbaum–Saunders distribution is studied as well. The proposed model presents a better goodness of fit compared to the other studied models.

scholarly journals An Improved Approach for Reduction of Defect Density Using Optimal Module Sizes

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Dinesh Verma ◽  
Shishir Kumar
Keyword(s):  
Goodness Of Fit ◽  
Defect Density ◽  
Optimal Size ◽  
Data Sets ◽  
Density Parameter ◽  
Proposed Model ◽  
Module Size ◽  
Curve Fitting Method ◽  
Improved Model ◽  
Effective Distribution

Nowadays, software developers are facing challenges in minimizing the number of defects during the software development. Using defect density parameter, developers can identify the possibilities of improvements in the product. Since the total number of defects depends on module size, so there is need to calculate the optimal size of the module to minimize the defect density. In this paper, an improved model has been formulated that indicates the relationship between defect density and variable size of modules. This relationship could be used for optimization of overall defect density using an effective distribution of modules sizes. Three available data sets related to concern aspect have been examined with the proposed model by taking the distinct values of variables and parameter by putting some constraint on parameters. Curve fitting method has been used to obtain the size of module with minimum defect density. Goodness of fit measures has been performed to validate the proposed model for data sets. The defect density can be optimized by effective distribution of size of modules. The larger modules can be broken into smaller modules and smaller modules can be merged to minimize the overall defect density.

scholarly journals Refining Coarse-Grained Spatial Data Using Auxiliary Spatial Data Sets with Various Granularities

2019 ◽  
Vol 33 ◽  
pp. 5091-5099 ◽  
Author(s):  
Yusuke Tanaka ◽  
Tomoharu Iwata ◽  
Toshiyuki Tanaka ◽  
Takeshi Kurashima ◽  
Maya Okawa ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Spatial Data ◽  
Coarse Grained ◽  
Model Parameters ◽  
Data Sets ◽  
Auxiliary Data ◽  
Fine Grained ◽  
Proposed Model ◽  
Spatial Data Sets ◽  
Target Data

We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data sets with various granularities by hierarchically incorporating Gaussian processes. With the proposed model, a distribution for each auxiliary data set on the continuous space is modeled using a Gaussian process, where the representation of uncertainty considers the levels of granularity. The finegrained target data are modeled by another Gaussian process that considers both the spatial correlation and the auxiliary data sets with their uncertainty. We integrate the Gaussian process with a spatial aggregation process that transforms the fine-grained target data into the coarse-grained target data, by which we can infer the fine-grained target Gaussian process from the coarse-grained data. Our model is designed such that the inference of model parameters based on the exact marginal likelihood is possible, in which the variables of finegrained target and auxiliary data are analytically integrated out. Our experiments on real-world spatial data sets demonstrate the effectiveness of the proposed model.

scholarly journals The Transmuted Muth Generated Class of Distributions with Applications

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1677
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Farrukh Jamal
Keyword(s):  
Survival Data ◽  
Natural Extension ◽  
Real Life ◽  
Environmental Data ◽  
Logistic Distribution ◽  
Data Sets ◽  
New Class ◽  
Real Life Data ◽  
Proposed Model ◽  
Mean And Variance

Recently, the Muth generated class of distributions has been shown to be useful for diverse statistical purposes. Here, we make some contributions to this class by first discussing new theoretical facts and then introducing a natural extension of it via the transmuted scheme. The extended class is described in detail, emphasizing the characteristics of its probability and reliability functions, as well as its moments. Among other things, we show that it can extend the possible values of the mean and variance of the parental distribution, while maintaining symmetry or creating various types of asymmetry. The mathematical inference of the parameters is also discussed. Special attention is paid to the distribution of the new class using the log-logistic distribution as a parent. In an applied work, we evaluate the behavior of the corresponding model by using simulated and practical data. In particular, we employ it to fit two real-life data sets, one with environmental data and the other with survival data. Standard statistical criteria validate the importance of the proposed model.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

Human Activity Recognition using Fourier Transform Inspired Deep Learning Combination Model

2019 ◽  
Vol 9 (1) ◽  
pp. 16-31
Author(s):  
Kyungkoo Jun
Keyword(s):  
Fourier Transform ◽  
Deep Learning ◽  
Short Term Memory ◽  
Window Size ◽  
Sensor Data ◽  
Data Sets ◽  
Data Set ◽  
Proposed Model ◽  
Testing Data ◽  
Labeling Scheme

Background & Objective: This paper proposes a Fourier transform inspired method to classify human activities from time series sensor data. Methods: Our method begins by decomposing 1D input signal into 2D patterns, which is motivated by the Fourier conversion. The decomposition is helped by Long Short-Term Memory (LSTM) which captures the temporal dependency from the signal and then produces encoded sequences. The sequences, once arranged into the 2D array, can represent the fingerprints of the signals. The benefit of such transformation is that we can exploit the recent advances of the deep learning models for the image classification such as Convolutional Neural Network (CNN). Results: The proposed model, as a result, is the combination of LSTM and CNN. We evaluate the model over two data sets. For the first data set, which is more standardized than the other, our model outperforms previous works or at least equal. In the case of the second data set, we devise the schemes to generate training and testing data by changing the parameters of the window size, the sliding size, and the labeling scheme. Conclusion: The evaluation results show that the accuracy is over 95% for some cases. We also analyze the effect of the parameters on the performance.

scholarly journals Goodness-of-Fit Tests for Bivariate Time Series of Counts

Econometrics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 10
Author(s):  
Šárka Hudecová ◽  
Marie Hušková ◽  
Simos G. Meintanis
Keyword(s):  
Goodness Of Fit ◽  
Probability Generating Function ◽  
Parametric Bootstrap ◽  
Real Data ◽  
Data Sets ◽  
Test Statistics ◽  
Finite Sample ◽  
Generalized Poisson ◽  
Goodness Of Fit Tests ◽  
Monte Carlo Experiments

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

scholarly journals An ABC-optimized fuzzy ELECTRE approach for assessing petroleum potential at the petroleum system level

2020 ◽  
Vol 12 (1) ◽  
pp. 580-597
Author(s):  
Mohamad Hamzeh ◽  
Farid Karimipour
Keyword(s):  
Spatial Data ◽  
Spatial Models ◽  
Model Performance ◽  
Essential Elements ◽  
Petroleum System ◽  
Petroleum Exploration ◽  
System Level ◽  
Data Sets ◽  
Petroleum Potential ◽  
Spatial Data Sets

AbstractAn inevitable aspect of modern petroleum exploration is the simultaneous consideration of large, complex, and disparate spatial data sets. In this context, the present article proposes the optimized fuzzy ELECTRE (OFE) approach based on combining the artificial bee colony (ABC) optimization algorithm, fuzzy logic, and an outranking method to assess petroleum potential at the petroleum system level in a spatial framework using experts’ knowledge and the information available in the discovered petroleum accumulations simultaneously. It uses the characteristics of the essential elements of a petroleum system as key criteria. To demonstrate the approach, a case study was conducted on the Red River petroleum system of the Williston Basin. Having completed the assorted preprocessing steps, eight spatial data sets associated with the criteria were integrated using the OFE to produce a map that makes it possible to delineate the areas with the highest petroleum potential and the lowest risk for further exploratory investigations. The success and prediction rate curves were used to measure the performance of the model. Both success and prediction accuracies lie in the range of 80–90%, indicating an excellent model performance. Considering the five-class petroleum potential, the proposed approach outperforms the spatial models used in the previous studies. In addition, comparing the results of the FE and OFE indicated that the optimization of the weights by the ABC algorithm has improved accuracy by approximately 15%, namely, a relatively higher success rate and lower risk in petroleum exploration.

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