scholarly journals Generalized Cardioid Distributions for Circular Data Analysis

Stats ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 634-649
Author(s):  
Fernanda V. Paula ◽  
Abraão D. C. Nascimento ◽  
Getúlio J. A. Amaral ◽  
Gauss M. Cordeiro
Keyword(s):  
Data Analysis ◽  
Structural Properties ◽  
Real Data ◽  
Linear Representation ◽  
Circular Data ◽  
Mathematical Properties ◽  
Circular Distributions ◽  
New Models ◽  
C Distribution

The Cardioid (C) distribution is one of the most important models for modeling circular data. Although some of its structural properties have been derived, this distribution is not appropriate for asymmetry and multimodal phenomena in the circle, and then extensions are required. There are various general methods that can be used to produce circular distributions. This paper proposes four extensions of the C distribution based on the beta, Kumaraswamy, gamma, and Marshall–Olkin generators. We obtain a unique linear representation of their densities and some mathematical properties. Inference procedures for the parameters are also investigated. We perform two applications on real data, where the new models are compared to the C distribution and one of its extensions.

scholarly journals On generalized classes of exponential distribution using T-X family framework

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1259-1272 ◽  
Author(s):  
Muhammad Zubair ◽  
Ayman Alzaatreh ◽  
Gauss Cordeiro ◽  
M.H. Tahir ◽  
Muhammad Mansoor
Keyword(s):  
Exponential Distribution ◽  
Shannon Entropy ◽  
Hazard Rate ◽  
Real Data ◽  
Quantile Function ◽  
Exponential Families ◽  
Data Sets ◽  
Mathematical Properties ◽  
New Models ◽  
Generalized Classes

We introduce new generalized classes of exponential distribution, called T-exponential {Y} class using the quantile functions of well-known distributions. We derive some general mathematical properties of this class including explicit expressions for the quantile function, Shannon entropy, moments and mean deviations. Some generalized exponential families are investigated. The shapes of the models in these families can be symmetric, left-skewed, right-skewed and reversed-J, and the hazard rate can be increasing, decreasing, bathtub, upside-down bathtub, J and reverse-J shaped. Two real data sets are used to illustrate the applicability of the new models.

scholarly journals An IMM Filter Defined in the Linear-Circular Domain, Application to Maneuver Detection with Heading Only

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Karim El mokhtari ◽  
Serge Reboul ◽  
Georges Stienne ◽  
Jean Bernard Choquel ◽  
Benaissa Amami ◽  
...  
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Real Data ◽  
Circular Domain ◽  
Circular Data ◽  
Von Mises Distribution ◽  
A Posteriori ◽  
Circular Distributions ◽  
Vehicle Maneuver ◽  
Von Mises

In this article, we propose a multimodel filter for circular data. The so-called Circular Interacting Multimodel filter is derived in a Bayesian framework with the circular normal von Mises distribution. The aim of the proposed filter is to obtain the same performance in the circular domain as the classical IMM filter in the linear domain. In our approach, the mixing and fusion stages of the Circular Interacting Multimodel filter are, respectively, defined from the a priori and from the a posteriori circular distributions of the state angle knowing the measurements and according to a set of models. We propose in this article a set of circular models that will be used in order to detect the vehicle maneuvers from heading measurements. The Circular Interacting Multimodel filter performances are assessed on synthetic data and we show on real data a vehicle maneuver detection application.

scholarly journals Four generalized Weibull distributions: similar properties and applications

2020 ◽  
Vol 42 ◽  
pp. e10
Author(s):  
Edwin Moises Marcos Ortega ◽  
Fábio Prataviera ◽  
Gauss Moutinho Cordeiro
Keyword(s):  
Weibull Distribution ◽  
Real Data ◽  
Linear Representation ◽  
Data Sets ◽  
Weibull Distributions ◽  
Mathematical Properties ◽  
Generalized Distributions ◽  
Two Parameter

We derive a common linear representation for the densities of four generalizations of the two-parameter Weibull distribution in terms of Weibull densities. The four generalized Weibull distributions briefly studied are: the Marshall-Olkin-Weibull, beta-Weibull, gamma-Weibull and Kumaraswamy-Weibull distributions. We demonstrate that several mathematical properties of these generalizations can be obtained simultaneously from those of the Weibull properties. We present two applications to real data sets by comparing these generalized distributions. It is hoped that this paper encourage developments of further generalizations of the Weibull based on the same linear representation.

scholarly journals The McDonald Lindley-Poisson Distribution

2021 ◽  
pp. 1095-1112
Author(s):  
Ana Percontini ◽  
Ronaldo V. da Silva ◽  
Laba Handique ◽  
Pedro Rafael Diniz Marinho
Keyword(s):  
Data Analysis ◽  
Poisson Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Data Sets ◽  
Lifetime Data ◽  
Mathematical Properties ◽  
Lifetime Data Analysis ◽  
New Distribution ◽  
Flexible Model

We propose the McDonald Lindley-Poisson distribution and derive some of its mathematical properties including explicit expressions for moments, generating and quantile functions, mean deviations, order statistics and their moments. Its model parameters are estimated by maximum likelihood. A simulation study investigates the performance of the estimates. The new distribution represents a more flexible model for lifetime data analysis than other existing models as proved empirically by means of two real data sets.

Justifying the data analytical choice in single case research in relation to the expected data pattern

2019 ◽  
Author(s):  
Rumen Manolov
Keyword(s):  
Data Analysis ◽  
Visual Analysis ◽  
Multilevel Models ◽  
Single Case ◽  
Analytical Techniques ◽  
Real Data ◽  
Small Scale ◽  
Data User ◽  
Single Case Research ◽  
User Friendly

The lack of consensus regarding the most appropriate analytical techniques for single-case experimental designs data requires justifying the choice of any specific analytical option. The current text mentions some of the arguments, provided by methodologists and statisticians, in favor of several analytical techniques. Additionally, a small-scale literature review is performed in order to explore if and how applied researchers justify the analytical choices that they make. The review suggests that certain practices are not sufficiently explained. In order to improve the reporting regarding the data analytical decisions, it is proposed to choose and justify the data analytical approach prior to gathering the data. As a possible justification for data analysis plan, we propose using as a basis the expected the data pattern (specifically, the expectation about an improving baseline trend and about the immediate or progressive nature of the intervention effect). Although there are multiple alternatives for single-case data analysis, the current text focuses on visual analysis and multilevel models and illustrates an application of these analytical options with real data. User-friendly software is also developed.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

Accuracy and sensitivity of different Bayesian methods for genomic prediction using simulation and real data

2020 ◽  
Vol 19 (3) ◽  
Author(s):  
Saheb Foroutaifar
Keyword(s):  
Data Analysis ◽  
Bayesian Methods ◽  
Milk Fat ◽  
Prediction Accuracy ◽  
Real Data ◽  
Fat Percentage ◽  
Real Data Analysis ◽  
Wide Range ◽  
High Heritability ◽  
Qtl Effects

AbstractThe main objectives of this study were to compare the prediction accuracy of different Bayesian methods for traits with a wide range of genetic architecture using simulation and real data and to assess the sensitivity of these methods to the violation of their assumptions. For the simulation study, different scenarios were implemented based on two traits with low or high heritability and different numbers of QTL and the distribution of their effects. For real data analysis, a German Holstein dataset for milk fat percentage, milk yield, and somatic cell score was used. The simulation results showed that, with the exception of the Bayes R, the other methods were sensitive to changes in the number of QTLs and distribution of QTL effects. Having a distribution of QTL effects, similar to what different Bayesian methods assume for estimating marker effects, did not improve their prediction accuracy. The Bayes B method gave higher or equal accuracy rather than the rest. The real data analysis showed that similar to scenarios with a large number of QTLs in the simulation, there was no difference between the accuracies of the different methods for any of the traits.

A New Method for Characterizing Replacement Rate Variation in Molecular Sequences: Application of the Fourier and Wavelet Models to Drosophila and Mammalian Proteins

Genetics ◽  
2000 ◽  
Vol 154 (1) ◽  
pp. 381-395
Author(s):  
Pavel Morozov ◽  
Tatyana Sitnikova ◽  
Gary Churchill ◽  
Francisco José Ayala ◽  
Andrey Rzhetsky
Keyword(s):  
Wavelet Transforms ◽  
Parametric Bootstrap ◽  
Real Data ◽  
New Method ◽  
Rate Variation ◽  
Discrete Wavelet ◽  
Data Sets ◽  
Ratio Test ◽  
Replacement Rate ◽  
New Models

Abstract We propose models for describing replacement rate variation in genes and proteins, in which the profile of relative replacement rates along the length of a given sequence is defined as a function of the site number. We consider here two types of functions, one derived from the cosine Fourier series, and the other from discrete wavelet transforms. The number of parameters used for characterizing the substitution rates along the sequences can be flexibly changed and in their most parameter-rich versions, both Fourier and wavelet models become equivalent to the unrestricted-rates model, in which each site of a sequence alignment evolves at a unique rate. When applied to a few real data sets, the new models appeared to fit data better than the discrete gamma model when compared with the Akaike information criterion and the likelihood-ratio test, although the parametric bootstrap version of the Cox test performed for one of the data sets indicated that the difference in likelihoods between the two models is not significant. The new models are applicable to testing biological hypotheses such as the statistical identity of rate variation profiles among homologous protein families. These models are also useful for determining regions in genes and proteins that evolve significantly faster or slower than the sequence average. We illustrate the application of the new method by analyzing human immunoglobulin and Drosophilid alcohol dehydrogenase sequences.

Empirical Likelihood Testing for Longitudinal Varying Coefficient Models

2014 ◽  
Vol 518 ◽  
pp. 356-360
Author(s):  
Chang Qing Liu
Keyword(s):  
Data Analysis ◽  
Empirical Likelihood ◽  
Real Data ◽  
Likelihood Method ◽  
Varying Coefficient Models ◽  
Empirical Likelihood Method ◽  
Real Data Analysis ◽  
Varying Coefficient ◽  
Testing Method

By using the empirical likelihood method, a testing method is proposed for longitudinal varying coefficient models. Some simulations and a real data analysis are undertaken to investigate the power of the empirical likelihood based testing method.

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