scholarly journals Estimation of different types of entropies for the Kumaraswamy distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0249027
Author(s):  
Abdulhakim A. Al-Babtain ◽  
Ibrahim Elbatal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood ◽  
Numerical Study ◽  
Beta Function ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Kumaraswamy Distribution ◽  
Random System ◽  
Entropy Measures

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

scholarly journals The Weibull Birnbaum-Saunders Distribution And Its Applications

2020 ◽  
Vol 9 (1) ◽  
pp. 61-81
Author(s):  
Lazhar BENKHELIFA
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Reliability Estimation ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Proposed Model ◽  
Modeling Data

A new lifetime model, with four positive parameters, called the Weibull Birnbaum-Saunders distribution is proposed. The proposed model extends the Birnbaum-Saunders distribution and provides great flexibility in modeling data in practice. Some mathematical properties of the new distribution are obtained including expansions for the cumulative and density functions, moments, generating function, mean deviations, order statistics and reliability. Estimation of the model parameters is carried out by the maximum likelihood estimation method. A simulation study is presented to show the performance of the maximum likelihood estimates of the model parameters. The flexibility of the new model is examined by applying it to two real data sets.

scholarly journals The Marshall-Olkin Extended Power Lomax Distribution with Applications

2020 ◽  
pp. 331-341
Author(s):  
JIJU GILLARIOSE ◽  
Lishamol Tomy
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Limiting Distributions ◽  
Lomax Distribution ◽  
New Distribution ◽  
Extended Power

In this article, we dened a new four-parameter model called Marshall-Olkin extended power Lomax distribution and studied its properties. Limiting distributions of sample maxima and sample minima are derived. The reliability of a system when both stress and strength follows the new distribution is discussed and associated characteristics are computed for simulated data. Finally, utilizing maximum likelihood estimation, the goodness of the distribution is tested for real data.

scholarly journals The Exponentiated Lindley Geometric Distribution with Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 510
Author(s):  
Bo Peng ◽  
Zhengqiu Xu ◽  
Min Wang
Keyword(s):  
Maximum Likelihood ◽  
Geometric Distribution ◽  
Residual Life ◽  
Information Matrix ◽  
Expectation Maximization Algorithm ◽  
Likelihood Estimation ◽  
Real Data ◽  
Quantile Function ◽  
Maximum Likelihood Estimates ◽  
Unknown Parameters

We introduce a new three-parameter lifetime distribution, the exponentiated Lindley geometric distribution, which exhibits increasing, decreasing, unimodal, and bathtub shaped hazard rates. We provide statistical properties of the new distribution, including shape of the probability density function, hazard rate function, quantile function, order statistics, moments, residual life function, mean deviations, Bonferroni and Lorenz curves, and entropies. We use maximum likelihood estimation of the unknown parameters, and an Expectation-Maximization algorithm is also developed to find the maximum likelihood estimates. The Fisher information matrix is provided to construct the asymptotic confidence intervals. Finally, two real-data examples are analyzed for illustrative purposes.

scholarly journals Maximum likelihood estimation of individual inbreeding coefficients and null allele frequencies

2012 ◽  
Vol 94 (3) ◽  
pp. 151-161 ◽  
Author(s):  
NATHAN HALL ◽  
LAINA MERCER ◽  
DAISY PHILLIPS ◽  
JONATHAN SHAW ◽  
AMY D. ANDERSON
Keyword(s):  
Maximum Likelihood ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Allele Frequencies ◽  
Maximum Likelihood Estimates ◽  
Null Alleles ◽  
Single Individual ◽  
Em Algorithms ◽  
Inbreeding Coefficients ◽  
Missing Genotypes

SummaryIn this paper, we developed and compared several expectation–maximization (EM) algorithms to find maximum likelihood estimates of individual inbreeding coefficients using molecular marker information. The first method estimates the inbreeding coefficient for a single individual and assumes that allele frequencies are known without error. The second method jointly estimates inbreeding coefficients and allele frequencies for a set of individuals that have been genotyped at several loci. The third method generalizes the second method to include the case in which null alleles may be present. In particular, it is able to jointly estimate individual inbreeding coefficients and allele frequencies, including the frequencies of null alleles, and accounts for missing data. We compared our methods with several other estimation procedures using simulated data and found that our methods perform well. The maximum likelihood estimators consistently gave among the lowest root-mean-square-error (RMSE) of all the estimators that were compared. Our estimator that accounts for null alleles performed particularly well and was able to tease apart the effects of null alleles, randomly missing genotypes and differing degrees of inbreeding among members of the datasets we analysed. To illustrate the performance of our estimators, we analysed previously published datasets on mice (Mus musculus) and white-tailed deer (Odocoileus virginianus).

scholarly journals Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

2021 ◽  
pp. 9-37
Author(s):  
Samuel U. Enogwe ◽  
Chisimkwuo John ◽  
Happiness O. Obiora-Ilouno ◽  
Chrisogonus K. Onyekwere
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Bathtub Shape ◽  
Asymptotic Confidence Intervals

In this paper, we propose a new lifetime distribution called the generalized weighted Rama (GWR) distribution, which extends the two-parameter Rama distribution and has the Rama distribution as a special case. The GWR distribution has the ability to model data sets that have positive skewness and upside-down bathtub shape hazard rate. Expressions for mathematical and reliability properties of the GWR distribution have been derived. Estimation of parameters was achieved using the method of maximum likelihood estimation and a simulation was performed to verify the stability of the maximum likelihood estimates of the model parameters. The asymptotic confidence intervals of the parameters of the proposed distribution are obtained. The applicability of the GWR distribution was illustrated with a real data set and the results obtained show that the GWR distribution is a better candidate for the data than the other competing distributions being investigated.

scholarly journals Evaluating the robustness of phylogenetic methods to among-site variability in substitution processes

2008 ◽  
Vol 363 (1512) ◽  
pp. 4013-4021 ◽  
Author(s):  
Mark T Holder ◽  
Derrick J Zwickl ◽  
Christophe Dessimoz
Keyword(s):  
Amino Acid ◽  
Maximum Likelihood ◽  
Simulated Data ◽  
Software Tool ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Codon Model ◽  
Phylogenetic Methods ◽  
Tree Inference ◽  
Inference Methods

Computer simulations provide a flexible method for assessing the power and robustness of phylogenetic inference methods. Unfortunately, simulated data are often obviously atypical of data encountered in studies of molecular evolution. Unrealistic simulations can lead to conclusions that are irrelevant to real-data analyses or can provide a biased view of which methods perform well. Here, we present a software tool designed to generate data under a complex codon model that allows each residue in the protein sequence to have a different set of equilibrium amino acid frequencies. The software can obtain maximum-likelihood estimates of the parameters of the Halpern and Bruno model from empirical data and a fixed tree; given an arbitrary tree and a fixed set of parameters, the software can then simulate artificial datasets. We present the results of a simulation experiment using randomly generated tree shapes and substitution parameters estimated from 1610 mammalian cytochrome b sequences. We tested tree inference at the amino acid, nucleotide and codon levels and under parsimony, maximum-likelihood, Bayesian and distance criteria (for a total of more than 650 analyses on each dataset). Based on these simulations, nucleotide-level analyses seem to be more accurate than amino acid and codon analyses. The performance of distance-based phylogenetic methods appears to be quite sensitive to the choice of model and the form of rate heterogeneity used. Further studies are needed to assess the generality of these conclusions. For example, fitting parameters of the Halpern Bruno model to sequences from other genes will reveal the extent to which our conclusions were influenced by the choice of cytochrome b . Incorporating codon bias and more sources heterogeneity into the simulator will be crucial to determining whether the current results are caused by a bias in the current simulation study in favour of nucleotide analyses.

scholarly journals Bayesian Estimation of The Ex-Gaussian Distribution

2021 ◽  
Vol 9 (4) ◽  
pp. 809-819
Author(s):  
Abir El Haj ◽  
Yousri Slaoui ◽  
Clara Solier ◽  
Cyril Perret
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Gaussian Distribution ◽  
Estimation Method ◽  
Reaction Times ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimated Parameters ◽  
Parameter Values

Fitting of the exponential modified Gaussian distribution to model reaction times and drawing conclusions from its estimated parameter values is one of the most popular method used in psychology. This paper aims to develop a Bayesian approach to estimate the parameters of the ex-Gaussian distribution. Since the chosen priors yield to posterior densities that are not of known form and that they are not always log-concave, we suggest to use the adaptive rejection Metropolis sampling method. Applications on simulated data and on real data are provided to compare this method to the standard maximum likelihood estimation method as well as the quantile maximum likelihood estimation. Results shows the effectiveness of the proposed Bayesian method by computing the root mean square error of the estimated parameters using the three methods.

A maximum likelihood approach for identifying dive bouts improves accuracy, precision and objectivity

Behaviour ◽  
2007 ◽  
Vol 144 (11) ◽  
pp. 1315-1332 ◽  
Author(s):  
Sebastián Luque ◽  
Christophe Guinet
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Simulated Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Systematic Effect ◽  
Fur Seals ◽  
Accuracy And Precision

AbstractForaging behaviour frequently occurs in bouts, and considerable efforts to properly define those bouts have been made because they partly reflect different scales of environmental variation. Methods traditionally used to identify such bouts are diverse, include some level of subjectivity, and their accuracy and precision is rarely compared. Therefore, the applicability of a maximum likelihood estimation method (MLM) for identifying dive bouts was investigated and compared with a recently proposed sequential differences analysis (SDA). Using real data on interdive durations from Antarctic fur seals (Arctocephalus gazella Peters, 1875), the MLM-based model produced briefer bout ending criterion (BEC) and more precise parameter estimates than the SDA approach. The MLM-based model was also in better agreement with real data, as it predicted the cumulative frequency of differences in interdive duration more accurately. Using both methods on simulated data showed that the MLM-based approach produced less biased estimates of the given model parameters than the SDA approach. Different choices of histogram bin widths involved in SDA had a systematic effect on the estimated BEC, such that larger bin widths resulted in longer BECs. These results suggest that using the MLM-based procedure with the sequential differences in interdive durations, and possibly other dive characteristics, may be an accurate, precise, and objective tool for identifying dive bouts.

scholarly journals Maximum likelihood estimation based on type-i hybrid progressive censored competing risks data

2016 ◽  
Vol 4 (1) ◽  
pp. 20
Author(s):  
Samir Ashour ◽  
Wael Abu El Azm
Keyword(s):  
Maximum Likelihood ◽  
Competing Risks ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Type I ◽  
Data Set ◽  
Special Cases ◽  
Competing Risks Data

<p>This paper is concerned with the estimators problems of the generalized Weibull distribution based on Type-I hybrid progressive censoring scheme (Type-I PHCS) in the presence of competing risks when the cause of failure of each item is known. Maximum likelihood estimates and the corresponding Fisher information matrix are obtained. We generalized Kundu and Joarder [7] results in the case of the exponential distribution while, the corresponding results in the case of the generalized exponential and Weibull distributions may be obtained as a special cases. A real data set is used to illustrate the theoretical results.</p>

scholarly journals Directional Selection and the Site-Frequency Spectrum

Genetics ◽  
2001 ◽  
Vol 159 (4) ◽  
pp. 1779-1788 ◽  
Author(s):  
Carlos D Bustamante ◽  
John Wakeley ◽  
Stanley Sawyer ◽  
Daniel L Hartl
Keyword(s):  
Maximum Likelihood ◽  
High Power ◽  
Negative Selection ◽  
Likelihood Estimation ◽  
Directional Selection ◽  
Likelihood Ratio Tests ◽  
Maximum Likelihood Estimates ◽  
Likelihood Methods ◽  
Ancestral States ◽  
Asymptotic Variances

Abstract In this article we explore statistical properties of the maximum-likelihood estimates (MLEs) of the selection and mutation parameters in a Poisson random field population genetics model of directional selection at DNA sites. We derive the asymptotic variances and covariance of the MLEs and explore the power of the likelihood ratio tests (LRT) of neutrality for varying levels of mutation and selection as well as the robustness of the LRT to deviations from the assumption of free recombination among sites. We also discuss the coverage of confidence intervals on the basis of two standard-likelihood methods. We find that the LRT has high power to detect deviations from neutrality and that the maximum-likelihood estimation performs very well when the ancestral states of all mutations in the sample are known. When the ancestral states are not known, the test has high power to detect deviations from neutrality for negative selection but not for positive selection. We also find that the LRT is not robust to deviations from the assumption of independence among sites.

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