scholarly journals A Unimodal/Bimodal Skew/Symmetric Distribution Generated from Lambert’s Transformation

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 269
Author(s):  
Yuri A. Iriarte ◽  
Mário de Castro ◽  
Héctor W. Gómez
Keyword(s):  
Parameter Estimation ◽  
Maximum Likelihood ◽  
Structural Properties ◽  
Maximum Likelihood Method ◽  
Bimodal Distribution ◽  
Symmetric Distribution ◽  
Likelihood Method ◽  
Simulation Experiments ◽  
Special Cases ◽  
New Distribution

The generalized bimodal distribution is especially efficient in modeling univariate data exhibiting symmetry and bimodality. However, its performance is poor when the data show important levels of skewness. This article introduces a new unimodal/bimodal distribution capable of modeling different skewness levels. The proposal arises from the recently introduced Lambert transformation when considering a generalized bimodal baseline distribution. The bimodal-normal and generalized bimodal distributions can be derived as special cases of the new distribution. The main structural properties are derived and the parameter estimation is carried out under the maximum likelihood method. The behavior of the estimators is assessed through simulation experiments. Finally, two applications are presented in order to illustrate the utility of the proposed distribution in data modeling in different real settings.

scholarly journals The Weibull-Gamma Distribution: Properties and Applications

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 438 ◽  
Author(s):  
Hadeel S. Klakattawi
Keyword(s):  
Maximum Likelihood ◽  
Gamma Distribution ◽  
Maximum Likelihood Method ◽  
Data Distribution ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Great Flexibility ◽  
Special Cases ◽  
New Distribution ◽  
Family Of Distributions

A new member of the Weibull-generated (Weibull-G) family of distributions—namely the Weibull-gamma distribution—is proposed. This four-parameter distribution can provide great flexibility in modeling different data distribution shapes. Some special cases of the Weibull-gamma distribution are considered. Several properties of the new distribution are studied. The maximum likelihood method is applied to obtain an estimation of the parameters of the Weibull-gamma distribution. The usefulness of the proposed distribution is examined by means of five applications to real datasets.

scholarly journals Estimation of the Average Kappa Coefficient of a Binary Diagnostic Test in the Presence of Partial Verification

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1694
Author(s):  
José Antonio Roldán-Nofuentes ◽  
Saad Bouh Regad
Keyword(s):  
Maximum Likelihood ◽  
Multiple Imputation ◽  
Diagnostic Test ◽  
Gold Standard ◽  
Maximum Likelihood Method ◽  
Disease Prevalence ◽  
Kappa Coefficient ◽  
Likelihood Method ◽  
Simulation Experiments ◽  
Asymptotic Behaviors

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In this manuscript the estimation of the average kappa coefficient of a diagnostic test in the presence of verification bias is studied. Confidence intervals for the average kappa coefficient are studied applying the methods of maximum likelihood and multiple imputation by chained equations. Simulation experiments have been carried out to study the asymptotic behaviors of the proposed intervals, given some application rules. The results obtained in our simulation experiments have shown that the multiple imputation by chained equations method provides better results than the maximum likelihood method. A function has been written in R to estimate the average kappa coefficient by applying multiple imputation. The results have been applied to the diagnosis of liver disease.

POTENTIAL FEATURES OF THE MAXIMUM LIKELIHOOD METHOD

2021 ◽  
Vol 1 (6) ◽  
pp. 28-44
Author(s):  
Valery A. Pakhotin ◽  
◽  
Ksenia V. Vlasova ◽  
Roman V. Simonov ◽  
Sergey V. Petrov ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Communication Systems ◽  
Maximum Likelihood Method ◽  
Spectral Lines ◽  
Likelihood Method ◽  
Model Calculations ◽  
Radio Engineering ◽  
Signal Parameters ◽  
Special Cases ◽  
Statistical Problems

In this paper, the potential possibilities of the maximum likelihood method for solving statistical problems of radio engineering are analyzed. A condition is introduced for the correlation interval of a random vector of parameters of a set of signals, which expands the scope of the maximum likelihood method under conditions of a priori and parametric uncertainty. Proofs are given that the known methods of spectral, correlation analysis, and angular spectral analysis are special cases of the maximum likelihood method. The scope of their application for signal processing is limited. They determine the optimal estimates of the signal parameters only when the adopted implementation contains a single signal. The substantiation of the possibility of obtaining solutions to statistical problems of radio engineering in the field of nonorthogonality of signals, when spectral lines, correlation functions, radiation patterns partially coincide, is given. The issues of solving the problem of separate detection of a set of signals based on the proposed optimal receiver are discussed. The issues of separate estimation of signal parameters in the area of their nonorthogonality are discussed. The conditions of the maximum resolution of signals are analyzed. The possibility of creating maximum likelihood filters based on likelihood equations is discussed. It is shown that such filters allow separating signals in the area of their nonorthogonality. They are the basis for solving the problem of channel sealing in communication systems. They make it possible to develop communication systems with nonorthogonal carrier frequencies. A concrete example shows the possibility of exceeding the speed of information transmission in nonorthogonal communication systems in comparison with the maximum speed, which follows from the Shannon theorem. The paper presents the results of model calculations illustrating the provisions of the theory.

scholarly journals Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1459 ◽  
Author(s):  
Ramadan A. ZeinEldin ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Maximum Likelihood ◽  
Probability Density ◽  
Goodness Of Fit ◽  
Maximum Likelihood Method ◽  
Information Criteria ◽  
Likelihood Method ◽  
Type Ii ◽  
Asymptotic Results ◽  
Kumaraswamy Distribution ◽  
New Distribution

In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics.

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