scholarly journals An Over and Underdispersed Biparametric Extension of the Waring Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 170
Author(s):  
Valentina Cueva-López ◽  
María José Olmo-Jiménez ◽  
José Rodríguez-Avi
Keyword(s):  
Simulation Study ◽  
Variance Components ◽  
Discrete Distribution ◽  
Identification Problem ◽  
Parameter Estimates ◽  
Data Sets ◽  
Proposed Model ◽  
Leibler Divergence ◽  
Specific Configuration ◽  
Waring Distribution

A new discrete distribution for count data called extended biparametric Waring (EBW) distribution is developed. Its name is related to the fact that, in a specific configuration of its parameters, it can be seen as a biparametric version of the univariate generalized Waring (UGW) distribution, a well-known model for the variance decomposition into three components: randomness, liability and proneness. Unlike the UGW distribution, the EBW can model both overdispersed and underdispersed data sets. In fact, the EBW distribution is a particular case of a UWG distribution when its first parameter is positive; otherwise, it is a particular case of a Complex Triparametric Pearson (CTP) distribution. Hence, this new model inherits most of their properties and, moreover, it helps to solve the identification problem in the variance components of the UGW model. We compare the EBW with the UGW by a simulation study, but also with other over and underdispersed distributions through the Kullback-Leibler divergence. Additionally, we have carried out a simulation study in order to analyse the properties of the maximum likelihood parameter estimates. Finally, some application examples are included which show that the proposed model provides similar or even better results than other models, but with fewer parameters.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

scholarly journals A discrete Ramos-Louzada distribution for asymmetric and over-dispersed data with leptokurtic-shaped: Properties and various estimation techniques with inference

2022 ◽  
Vol 7 (2) ◽  
pp. 1726-1741
Author(s):  
Ahmed Sedky Eldeeb ◽  
◽  
Muhammad Ahsan-ul-Haq ◽  
Mohamed. S. Eliwa ◽  
◽  
...  
Keyword(s):  
Count Data ◽  
Discrete Distribution ◽  
Real Data ◽  
Mass Function ◽  
Probability Mass Function ◽  
Data Sets ◽  
Estimation Techniques ◽  
Proposed Model ◽  
Probability Mass ◽  
Von Mises

<abstract> <p>In this paper, a flexible probability mass function is proposed for modeling count data, especially, asymmetric, and over-dispersed observations. Some of its distributional properties are investigated. It is found that all its statistical and reliability properties can be expressed in explicit forms which makes the proposed model useful in time series and regression analysis. Different estimation approaches including maximum likelihood, moments, least squares, Andersonӳ-Darling, Cramer von-Mises, and maximum product of spacing estimator, are derived to get the best estimator for the real data. The estimation performance of these estimation techniques is assessed via a comprehensive simulation study. The flexibility of the new discrete distribution is assessed using four distinctive real data sets ԣoronavirus-flood peaks-forest fire-Leukemia? Finally, the new probabilistic model can serve as an alternative distribution to other competitive distributions available in the literature for modeling count data.</p> </abstract>

scholarly journals The The Topp Leone-G Power Series Class of Distributions with Applications

2021 ◽  
pp. 827-846
Author(s):  
Fastel Chipepa ◽  
Boikanyo Makubate ◽  
Broderick Oluyede ◽  
Kethamile Rannona
Keyword(s):  
Maximum Likelihood ◽  
Power Series ◽  
Poisson Distribution ◽  
Simulation Study ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Sets ◽  
New Class ◽  
Proposed Model ◽  
Special Case

We present a new class of distributions called the Topp-Leone-G Power Series (TL-GPS) class of distributions. This model is obtained by compounding the Topp-Leone-G distribution with the power series distribution. Statistical prop- erties of the TL-GPS class of distributions are obtained. Maximum likelihood estimates for the proposed model were obtained. A simulation study is carried out for the special case of Topp-Leone Log-Logistic Poisson distribution to assess the performance of the maximum likelihood estimates. Finally, we apply Topp-Leone-log-logistic Poisson distribution to real data sets to illustrate the usefulness and applicability of the proposed class of distributions.

scholarly journals Marshll–Olkin Extended Inverse Pareto Distribution and its Application

2017 ◽  
Vol 6 (6) ◽  
pp. 71
Author(s):  
M- Gharib ◽  
B-I- Mohammed ◽  
W-E-R- Aghel
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Simulation Study ◽  
Pareto Distribution ◽  
Real Data ◽  
Failure Criteria ◽  
Data Sets ◽  
New Model ◽  
Proposed Model ◽  
Family Of Distributions

This paper introduces a new extension of the Inverse Pareto distribution along with in the framework of Marshal-Olkin (1997) family of distributions. This model is capable of modeling various shapes of aging and failure criteria. The statistical properties of the new model are discussed and the maximum likelihood and maximum product spacing’s methods are used to estimate the parameters involved. Explicit expressions are derived for the moments and the order statistics are examined for the new proposed model. Finally, the usefulness of the new model for modeling reliability data is illustrated using two real data sets with simulation study.

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 Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

scholarly journals Kumaraswamy Generalized Power Lomax Distributionand Its Applications

Stats ◽  
2021 ◽  
Vol 4 (1) ◽  
pp. 28-45
Author(s):  
Vasili B.V. Nagarjuna ◽  
R. Vishnu Vardhan ◽  
Christophe Chesneau
Keyword(s):  
Hazard Rate ◽  
Real Data ◽  
Rate Function ◽  
Maximum Likelihood Estimates ◽  
Parameter Estimates ◽  
Parameter Distribution ◽  
Data Sets ◽  
Lomax Distribution ◽  
Entropy Measures ◽  
Modeling Behavior

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible; it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely; parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

scholarly journals Additive genetic variance and covariance between relatives in synthetic wheat crosses with variable parental ploidy levels

Genetics ◽  
2021 ◽  
Vol 217 (2) ◽  
Author(s):  
L E Puhl ◽  
J Crossa ◽  
S Munilla ◽  
P Pérez-Rodríguez ◽  
R J C Cantet
Keyword(s):  
Hexaploid Wheat ◽  
Variance Components ◽  
Bayesian Model ◽  
Synthetic Hexaploid Wheat ◽  
Data Sets ◽  
Hierarchical Bayesian Model ◽  
Additive Variance ◽  
Ploidy Levels ◽  
Breeding Values ◽  
Synthetic Hexaploid

Abstract Cultivated bread wheat (Triticum aestivum L.) is an allohexaploid species resulting from the natural hybridization and chromosome doubling of allotetraploid durum wheat (T. turgidum) and a diploid goatgrass Aegilops tauschii Coss (Ae. tauschii). Synthetic hexaploid wheat (SHW) was developed through the interspecific hybridization of Ae. tauschii and T. turgidum, and then crossed to T. aestivum to produce synthetic hexaploid wheat derivatives (SHWDs). Owing to this founding variability, one may infer that the genetic variances of native wild populations vs improved wheat may vary due to their differential origin and evolutionary history. In this study, we partitioned the additive variance of SHW and SHWD with respect to their breed origin by fitting a hierarchical Bayesian model with heterogeneous covariance structure for breeding values to estimate variance components for each breed category, and segregation variance. Two data sets were used to test the proposed hierarchical Bayesian model, one from a multi-year multi-location field trial of SHWD and the other comprising the two species of SHW. For the SHWD, the Bayesian estimates of additive variances of grain yield from each breed category were similar for T. turgidum and Ae. tauschii, but smaller for T. aestivum. Segregation variances between Ae. tauschii—T. aestivum and T. turgidum—T. aestivum populations explained a sizable proportion of the phenotypic variance. Bayesian additive variance components and the Best Linear Unbiased Predictors (BLUPs) estimated by two well-known software programs were similar for multi-breed origin and for the sum of the breeding values by origin for both data sets. Our results support the suitability of models with heterogeneous additive genetic variances to predict breeding values in wheat crosses with variable ploidy levels.

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.

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

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