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.

Shape averages and their Bias

1994 ◽  
Vol 26 (2) ◽  
pp. 334-340 ◽  
Author(s):  
K. V. Mardia ◽  
I. L. Dryden
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Normal Model ◽  
Likelihood Estimator ◽  
Distributional Properties ◽  
Exact Maximum Likelihood

The paper considers the bias of Bookstein's mean estimator for shape under the isotropic normal model. This work depends on certain distributional properties of shape variables. An alternative unbiased modified estimator is proposed and its performance is compared with various estimators, including Procrustes and the exact maximum likelihood estimator, in a simulation study.

scholarly journals Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Marwa Khalil
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Minimum Variance ◽  
Strength Model ◽  
Practical Application ◽  
Likelihood Estimator ◽  
Lindley Distribution ◽  
Minimum Variance Unbiased Estimator ◽  
Proposed Model

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.

scholarly journals Classical and Bayesian Approach in Estimation of Scale Parameter of Nakagami Distribution

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Kaisar Ahmad ◽  
S. P. Ahmad ◽  
A. Ahmed
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Bayesian Approach ◽  
Simulation Study ◽  
Bayesian Method ◽  
Scale Parameter ◽  
Loss Functions ◽  
Likelihood Estimator ◽  
R Software ◽  
Nakagami Distribution

Nakagami distribution is considered. The classical maximum likelihood estimator has been obtained. Bayesian method of estimation is employed in order to estimate the scale parameter of Nakagami distribution by using Jeffreys’, Extension of Jeffreys’, and Quasi priors under three different loss functions. Also the simulation study is conducted in R software.

scholarly journals Maximum likelihood estimation of the geometric niche preemption model

2021 ◽  
Author(s):  
Jan Graffelman
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Maximum Likelihood Estimator ◽  
Ecological Model ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Likelihood Estimator ◽  
Two Samples ◽  
Multinomial Sampling ◽  
Geometric Decay

AbstractThe geometric series or niche preemption model is an elementary ecological model in biodiversity studies. The preemption parameter of this model is usually estimated by regression or iteratively by using May’s equation. This article proposes a maximum likelihood estimator for the niche preemption model, assuming a known number of species and multinomial sampling. A simulation study shows that the maximum likelihood estimator outperforms the classical estimators in this context in terms of bias and precision. We obtain the distribution of the maximum likelihood estimator and use it to obtain confidence intervals for the preemption parameter and to develop a preemption t test that can address the hypothesis of equal geometric decay in two samples. We illustrate the use of the new estimator with some empirical data sets taken from the literature and provide software for its use.

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 A Maximum-Likelihood Estimator for Trial-to-Trial Variations in Noisy MEG/EEG Data Sets

2004 ◽  
Vol 51 (12) ◽  
pp. 2123-2128 ◽  
Author(s):  
J.C. de Munck ◽  
F. Bijma ◽  
P. Gaura ◽  
C.A. Sieluzycki ◽  
M.I. Branco ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Data Sets ◽  
Likelihood Estimator ◽  
Eeg Data

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.

A mutual information estimator with exponentially decaying bias

2015 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhiyi Zhang ◽  
Lukun Zheng
Keyword(s):  
Maximum Likelihood ◽  
Mutual Information ◽  
Asymptotic Normality ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Type I Error ◽  
Type I ◽  
Nonparametric Estimator ◽  
Likelihood Estimator

AbstractA nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

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