On log-bimodal alpha-power distributions with application to nickel contents and erosion data

2021 ◽  
Vol 71 (6) ◽  
pp. 1565-1580
Author(s):  
Hugo S. Salinas ◽  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Heleno Bolfarine
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Power Distribution ◽  
Information Matrix ◽  
Likelihood Method ◽  
Model Parameters ◽  
Alpha Power ◽  
Log Normal ◽  
Log Normal Distribution

Abstract In this paper, we present a new parametric class of distributions based on the log-alpha-power distribution, which contains the well-known log-normal distribution as a special case. This new family is useful to deal with unimodal as well as bimodal data with asymmetry and kurtosis coefficients ranging far from that expected based on the log-normal distribution. The usual approach is considered to perform inferences, and the traditional maximum likelihood method is employed to estimate the unknown parameters. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. We also derive the observed and expected Fisher information matrices. As a byproduct of such study, it is shown that the Fisher information matrix is nonsingular throughout the sample space. Empirical applications of the proposed family of distributions to real data are provided for illustrative purposes.

scholarly journals The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1114
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
María Martínez-Guerra
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Score Functions ◽  
New Family ◽  
Two Parameters ◽  
Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

scholarly journals Generalized Truncation Positive Normal Distribution

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1361
Author(s):  
Héctor J. Gómez ◽  
Diego I. Gallardo ◽  
Osvaldo Venegas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Maximum Likelihood Estimators ◽  
Real Data ◽  
Data Sets ◽  
New Model ◽  
Positive Support

In this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model’s basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model’s good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption.

scholarly journals Multivariate Skew-Power-Normal Distributions: Properties and Associated Inference

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1509
Author(s):  
Guillermo Martínez-Flórez ◽  
Artur J. Lemonte ◽  
Hugo S. Salinas
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Multivariate Distributions ◽  
Likelihood Approach ◽  
Information Matrices ◽  
Univariate Distribution

The univariate power-normal distribution is quite useful for modeling many types of real data. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature, mainly skewed multivariate extensions that can be bimodal, for example. In this paper, based on the univariate power-normal distribution, we extend the univariate power-normal distribution to the multivariate setup. Structural properties of the new multivariate distributions are established. We consider the maximum likelihood method to estimate the unknown parameters, and the observed and expected Fisher information matrices are also derived. Monte Carlo simulation results indicate that the maximum likelihood approach is quite effective to estimate the model parameters. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.

scholarly journals The Skewed-Elliptical Log-Linear Birnbaum–Saunders Alpha-Power Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1297
Author(s):  
Guillermo Martínez-Flórez ◽  
Heleno Bolfarine ◽  
Yolanda M. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Power Distribution ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Data Sets ◽  
Alpha Power ◽  
Data Set ◽  
Special Cases ◽  
Standard Error Estimation ◽  
Log Linear

In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to the skew-elliptical log-linear Birnbaum–Saunders alpha-power distribution, previously studied in the literature. Special cases include the ordinary log-linear Birnbaum–Saunders and skewed log-linear Birnbaum–Saunders distributions. As shown, it is able to surpass the ordinary sinh-normal models when fitting data sets with high (above the expected with the sinh-normal) degrees of asymmetry. Maximum likelihood estimation is developed with the inverse of the observed information matrix used for standard error estimation. Large sample properties of the maximum likelihood estimators such as consistency and asymptotic normality are established. An application is reported for the data set previously analyzed in the literature, where performance of the new distribution is shown when compared with other proposed alternative models.

scholarly journals Generalized Exponential Power Distribution with Application to Complete and Censored Data

2021 ◽  
pp. 34-55
Author(s):  
M. M. E. Abd El-Monsef ◽  
M. M. El-Awady
Keyword(s):  
Maximum Likelihood ◽  
Censored Data ◽  
Power Distribution ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Type I ◽  
Sample Type ◽  
Exponential Power Distribution ◽  
Exponential Power

The exponential power distribution (EP) is a lifetime model that can exhibit increasing and bathtub hazard rate function. This paper proposed a generalization of EP distribution, named generalized exponential power (GEP) distribution. Some properties of GEP distribution will be investigated. Recurrence relations for single moments of generalized ordered statistics from GEP distribution are established and used for characterizing the GEP distribution. Estimation of the model parameters are derived using maximum likelihood method based on complete sample, type I, type II and random censored samples. A simulation study is performed in order to examine the accuracy of the maximum likelihood estimators of the model parameters. Three applications to real data, two with censored data, are provided in order to show the superiority of the proposed model to other models.

scholarly journals The Generalized DUS Transformed Log-Normal Distribution and Its Applications to Cancer and Heart Transplant Datasets

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3113
Author(s):  
Muhammed Rasheed Irshad ◽  
Christophe Chesneau ◽  
Soman Latha Nitin ◽  
Damodaran Santhamani Shibu ◽  
Radhakumari Maya
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Biological Data ◽  
Hazard Rate Function ◽  
Bayesian Techniques ◽  
Log Normal ◽  
Log Normal Distribution ◽  
New Distribution

Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primarily for use with biological data. The hazard rate function, quantile function, and several other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has increasing, decreasing, bathtub, and upside-down bathtub shapes. The maximum likelihood and Bayesian techniques are both used to estimate unknown parameters. Based on the proposed distribution, we also present a parametric regression model and a Bayesian regression approach. As an assessment of the longstanding performance, simulation studies based on maximum likelihood and Bayesian techniques of estimation procedures are also conducted. Two real datasets are used to demonstrate the applicability of the new distribution. The efficiency of the third parameter in the new model is tested by utilizing the likelihood ratio test. Furthermore, the parametric bootstrap approach is used to determine the effectiveness of the suggested model for the datasets.

scholarly journals Likelihood-Based Inference for the Asymmetric Beta-Skew Alpha-Power Distribution

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 613
Author(s):  
Guillermo Martínez-Flórez ◽  
Roger Tovar-Falón ◽  
Marvin Jimémez-Narváez
Keyword(s):  
Power Distribution ◽  
Information Matrix ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
New Family ◽  
Asymmetric Distributions ◽  
Two Parameters

This paper introduces a new family of asymmetric distributions that allows to fit unimodal as well as bimodal and trimodal data sets. The model extends the normal model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new distribution are studied in detail. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrix is derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. Finally, two data set are considered to illustrate the developed methodology.

Estimation of thermal time model parameters for seed germination in 15 species: the importance of distribution function

2021 ◽  
pp. 1-8
Author(s):  
Dali Chen ◽  
Xianglai Chen ◽  
Jingjing Wang ◽  
Zuxin Zhang ◽  
Yan Wang ◽  
...  
Keyword(s):  
Distribution Function ◽  
Seed Germination ◽  
Normal Distribution ◽  
Distribution Functions ◽  
Thermal Time ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Time Model ◽  
Log Normal ◽  
Log Normal Distribution

Abstract Thermal time models have been widely applied to predict temperature requirements for seed germination. Generally, a log-normal distribution for thermal time [θT(g)] is used in such models at suboptimal temperatures to examine the variation in time to germination arising from variation in θT(g) within a seed population. Recently, additional distribution functions have been used in thermal time models to predict seed germination dynamics. However, the most suitable kind of the distribution function to use in thermal time models, especially at suboptimal temperatures, has not been determined. Five distributions (log-normal, Gumbel, logistic, Weibull and log-logistic) were used in thermal time models over a range of temperatures to fit the germination data for 15 species. The results showed that a more flexible model with the log-logistic distribution, rather than the log-normal distribution, provided the best explanation of θT(g) variation in 13 species at suboptimal temperatures. Thus, at least at suboptimal temperatures, the log-logistic distribution is an appropriate candidate among the five distributions used in this study. Therefore, the distribution of parameters [θT(g)] should be considered when using thermal time models to prevent large deviations; furthermore, an appropriate equation should be selected before using such a model to make predictions.

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