scholarly journals Nonparametric estimation of directional highest density regions

2021 ◽  
Author(s):  
Paula Saavedra-Nieves ◽  
Rosa M. Crujeiras
Keyword(s):  
Simulation Study ◽  
Hausdorff Distance ◽  
Level Sets ◽  
Kernel Smoothing ◽  
Real Data ◽  
Confidence Regions ◽  
Data Sets ◽  
Extensive Simulation ◽  
Bandwidth Selector ◽  
Animal Orientation

AbstractHighest density regions (HDRs) are defined as level sets containing sample points of relatively high density. Although Euclidean HDR estimation from a random sample, generated from the underlying density, has been widely considered in the statistical literature, this problem has not been contemplated for directional data yet. In this work, directional HDRs are formally defined and plug-in estimators based on kernel smoothing and associated confidence regions are proposed. We also provide a new suitable bootstrap bandwidth selector for plug-in HDRs estimation based on the minimization of an error criteria that involves the Hausdorff distance between the boundaries of the theoretical and estimated HDRs. An extensive simulation study shows the performance of the resulting estimator for the circle and for the sphere. The methodology is applied to analyze two real data sets in animal orientation and seismology.

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.

A two-step integrated approach to detect differentially expressed genes in RNA-Seq data

2016 ◽  
Vol 14 (06) ◽  
pp. 1650034 ◽  
Author(s):  
Naim Al Mahi ◽  
Munni Begum
Keyword(s):  
Simulation Study ◽  
Negative Binomial ◽  
Real Data ◽  
Integrated Approach ◽  
Differentially Expressed ◽  
Data Sets ◽  
Rna Seq ◽  
Software Packages ◽  
Treatment Conditions ◽  
Integrated Approaches

One of the primary objectives of ribonucleic acid (RNA) sequencing or RNA-Seq experiment is to identify differentially expressed (DE) genes in two or more treatment conditions. It is a common practice to assume that all read counts from RNA-Seq data follow overdispersed (OD) Poisson or negative binomial (NB) distribution, which is sometimes misleading because within each condition, some genes may have unvarying transcription levels with no overdispersion. In such a case, it is more appropriate and logical to consider two sets of genes: OD and non-overdispersed (NOD). We propose a new two-step integrated approach to distinguish DE genes in RNA-Seq data using standard Poisson and NB models for NOD and OD genes, respectively. This is an integrated approach because this method can be merged with any other NB-based methods for detecting DE genes. We design a simulation study and analyze two real RNA-Seq data to evaluate the proposed strategy. We compare the performance of this new method combined with the three [Formula: see text]-software packages namely edgeR, DESeq2, and DSS with their default settings. For both the simulated and real data sets, integrated approaches perform better or at least equally well compared to the regular methods embedded in these [Formula: see text]-packages.

scholarly journals Skew Arcsine Distribution

2021 ◽  
pp. 26-34
Author(s):  
Nuri Celik
Keyword(s):  
Brownian Motion ◽  
Simulation Study ◽  
Real Data ◽  
Statistical Modelling ◽  
Data Sets ◽  
Underlying Distribution ◽  
Arcsine Distribution ◽  
Motion Studies ◽  
New Distribution

The arcsine distribution is very important tool in statistics literature especially in Brownian motion studies. However, modelling real data sets, even when the potential underlying distribution is pre-defined, is very complicated and difficult in statistical modelling. For this reason, we desire some flexibility on the underlying distribution. In this study, we propose a new distribution obtained by arcsine distribution with Azzalini’s skewness procedure. The main characteristics of the proposed distribution are determined both with theoretically and simulation study.

scholarly journals The Effect of Microaggregation Procedures on the Estimation of Linear Models: A Simulation Study

2005 ◽  
Vol 225 (5) ◽  
Author(s):  
Matthias Schmid ◽  
Hans Schneeweiss
Keyword(s):  
Linear Regression ◽  
Simulation Study ◽  
Linear Models ◽  
Simulation Experiment ◽  
Ordinary Least Squares ◽  
Asymptotic Bias ◽  
Data Sets ◽  
Slope Parameter ◽  
Parameter Estimator ◽  
Extensive Simulation

SummaryMicroaggregation is a set of procedures that distort empirical data in order to guarantee their factual anonymity. At the same time the information content of data sets should not be reduced too much and should still be useful for scientific research. This paper investigates the effect of microaggregation on the estimation of a linear regression by ordinary least squares. It studies, by way of an extensive simulation experiment, the bias of the slope parameter estimator induced by various microaggregation techniques. Some microaggregation procedures lead to consistent estimates while others imply an asymptotic bias for the estimator.

scholarly journals Nonparametric estimate remarks

2006 ◽  
Vol 54 (3) ◽  
pp. 93-100 ◽  
Author(s):  
Jitka Poměnková
Keyword(s):  
Regression Model ◽  
Kernel Smoothing ◽  
Real Data ◽  
Linear Estimator ◽  
Data Sets ◽  
Nonparametric Estimate ◽  
Fixed Design ◽  
Local Linear Estimator ◽  
Kernel Smoothers ◽  
Fixed Design Regression

Kernel smoothers belong to the most popular nonparametric functional estimates. They provide a simple way of finding structure in data. The idea of the kernel smoothing can be applied to a simple fixed design regression model. This article is focused on kernel smoothing for fixed design regresion model with three types of estimators, the Gasser-Müller estimator, the Nadaraya-Watson estimator and the local linear estimator. At the end of this article figures for ilustration of desribed estimators on simulated and real data sets are shown.

scholarly journals Extended Reciprocal Rayleigh Distribution: Copula, Properties and Real Data Modeling

2020 ◽  
pp. 35-52
Author(s):  
Hoda Ragab Rezk
Keyword(s):  
Simulation Study ◽  
Estimation Method ◽  
Data Modeling ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Simple Type ◽  
Data Sets ◽  
New Model ◽  
Graphical Simulation ◽  
Better Than

Abstract: A new extension of the reciprocal Rayleigh distribution is introduced. Simple type copula-based construction is presented for deriving and many bivariate and multivariate type distributions of the reciprocal Rayleigh model. The new reciprocal Rayleigh model generalizes another three reciprocal Rayleigh distributions. The performance of the estimation method is assessed using a graphical simulation study. The new model is better than some other important competitive models in modeling different real data sets.

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 New Families of Generalized Lomax Distributions: Properties and Applications

2019 ◽  
Vol 8 (6) ◽  
pp. 51 ◽  
Author(s):  
Ahmad Alzaghal ◽  
Duha Hamed
Keyword(s):  
Maximum Likelihood ◽  
Structural Properties ◽  
Simulation Study ◽  
Real Data ◽  
Extreme Value ◽  
Data Sets ◽  
Extreme Value Distributions ◽  
Method Of Maximum Likelihood ◽  
The Right ◽  
Family Of Distributions

In this paper, we propose new families of generalized Lomax distributions named T-LomaxfYg. Using the methodology of the Transformed-Transformer, known as T-X framework, the T-Lomax families introduced are arising from the quantile functions of exponential, Weibull, log-logistic, logistic, Cauchy and extreme value distributions. Various structural properties of the new families are derived including moments, modes and Shannon entropies. Several new generalized Lomax distributions are studied. The shapes of these T-LomaxfYg distributions are very flexible and can be symmetric, skewed to the right, skewed to the left, or bimodal. The method of maximum likelihood is proposed for estimating the distributions parameters and a simulation study is carried out to assess its performance. Four applications of real data sets are used to demonstrate the flexibility of T-LomaxfYg family of distributions in fitting unimodal and bimodal data sets from di erent disciplines.

scholarly journals A New Inference Approach for Type-II Generalized Birnbaum-Saunders Distribution

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 148-163
Author(s):  
Naijun Sha
Keyword(s):  
Simulation Study ◽  
Real Data ◽  
Type Ii ◽  
Sample Sizes ◽  
Extensive Simulation ◽  
Convenient Procedure ◽  
Parameter Values

The Birnbaum-Saunders (BS) distribution, with its generalizations, has been successfully applied in a wide variety of fields. One generalization, type-II generalized BS (denoted as GBS-II), has been developed and attracted considerable attention in recent years. In this article, we propose a new simple and convenient procedure of inference approach for GBS-II distribution. An extensive simulation study is carried out to assess performance of the methods under various settings of parameter values with different sample sizes. Real data are analyzed for illustrative purposes to display the efficiency of the proposed method.

scholarly journals On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1805
Author(s):  
Abd M. Abd El-Raheem ◽  
Mona Hosny ◽  
Mahmoud H. Abu-Moussa
Keyword(s):  
Competing Risks ◽  
Simulation Study ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Competing Risks Data ◽  
Competing Risk Models

Competing risks are frequently overlooked, and the event of interest is analyzed with conventional statistical techniques. In this article, we consider the analysis of bi-causes of failure in the context of competing risk models using the extension of the exponential distribution under progressive Type-II censoring. Maximum likelihood estimates for the unknown parameters via the expectation-maximization algorithm are obtained. Moreover, the Bayes estimates of the unknown parameters are approximated using Tierney-Kadane and MCMC techniques. Interval estimates using Bayesian and classical techniques are also considered. Two real data sets are investigated to illustrate the different estimation methods, and to compare the suggested model with Weibull distribution. Furthermore, the estimation methods are compared through a comprehensive simulation study.

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