scholarly journals The Extended Birnbaum–Saunders Distribution Based on the Scale Shape Mixture of Skew Normal Distributions

2021 ◽  
Vol 20 (4) ◽  
pp. 481-517
Author(s):  
Tahereh Poursadeghfard ◽  
Alireza Nematollahi ◽  
Ahad Jamalizadeh
Keyword(s):  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Parameter Estimates ◽  
Asymptotic Covariance Matrix ◽  
Finite Sample ◽  
Data Set ◽  
Normal Distributions ◽  
Skew Normal Distributions ◽  
Skew Normal

AbstractIn this article, a large class of univriate Birnbaum–Saunders distributions based on the scale shape mixture of skew normal distributions is introduced which generates suitable subclasses for modeling asymmetric data in a variety of settings. The moments and maximum likelihood estimation procedures are disscused via an ECM-algorithm. The observed information matrix to approximate the asymptotic covariance matrix of the parameter estimates is then derived in some subclasses. A simulation study is also performed to evaluate the finite sample properties of ML estimators and finally, a real data set is analyzed for illustrative purposes.

scholarly journals On Properties of the Bimodal Skew-Normal Distribution and an Application

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 703
Author(s):  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco ◽  
Osvaldo Venegas ◽  
Heleno Bolfarine ◽  
Héctor W. Gómez
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Skew Normal Distribution ◽  
Data Set ◽  
Normal Distributions ◽  
Stochastic Representations ◽  
Skew Normal

The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results.

scholarly journals Closed form expressions for moments of the beta Weibull distribution

2011 ◽  
Vol 83 (2) ◽  
pp. 357-373 ◽  
Author(s):  
Gauss M Cordeiro ◽  
Alexandre B Simas ◽  
Borko D Stošic
Keyword(s):  
Weibull Distribution ◽  
Closed Form ◽  
Cumulative Distribution Function ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Set ◽  
Expected Information ◽  
Beta Weibull Distribution

The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

Topp–Leone Linear Exponential Distribution

2018 ◽  
Vol 33 (1) ◽  
pp. 31-43
Author(s):  
Bol A. M. Atem ◽  
Suleman Nasiru ◽  
Kwara Nantomah
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Exponential Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Simulation Studies ◽  
Finite Sample ◽  
Data Set ◽  
Finite Sample Properties ◽  
Linear Exponential Distribution

Abstract This article studies the properties of the Topp–Leone linear exponential distribution. The parameters of the new model are estimated using maximum likelihood estimation, and simulation studies are performed to examine the finite sample properties of the parameters. An application of the model is demonstrated using a real data set. Finally, a bivariate extension of the model is proposed.

scholarly journals A Family of Skew-Normal Distributions for Modeling Proportions and Rates with Zeros/Ones Excess

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1439
Author(s):  
Guillermo Martínez-Flórez ◽  
Víctor Leiva ◽  
Emilio Gómez-Déniz ◽  
Carolina Marchant
Keyword(s):  
Normal Distribution ◽  
Real Data ◽  
Continuous Variable ◽  
Likelihood Method ◽  
Skew Normal Distribution ◽  
Normal Distributions ◽  
New Type ◽  
Skew Normal Distributions ◽  
Information Matrices ◽  
Skew Normal

In this paper, we consider skew-normal distributions for constructing new a distribution which allows us to model proportions and rates with zero/one inflation as an alternative to the inflated beta distributions. The new distribution is a mixture between a Bernoulli distribution for explaining the zero/one excess and a censored skew-normal distribution for the continuous variable. The maximum likelihood method is used for parameter estimation. Observed and expected Fisher information matrices are derived to conduct likelihood-based inference in this new type skew-normal distribution. Given the flexibility of the new distributions, we are able to show, in real data scenarios, the good performance of our proposal.

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 Analysis of antibody data using Finite Mixture Models based on Scale Mixtures of Skew-Normal distributions

2021 ◽  
Author(s):  
Tiago Dias Domingues ◽  
Helena Mouriño ◽  
Nuno Sepúlveda
Keyword(s):  
Data Analysis ◽  
Mixture Models ◽  
Finite Mixture Models ◽  
Finite Mixture ◽  
Data Set ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Skew Normal Distributions ◽  
Serological Data ◽  
Skew Normal

AbstractFinite mixture models have been widely used in antibody (or serological) data analysis in order to help classifying individuals into either antibody-positive or antibody-negative. The most popular models are the so-called Gaussian mixture models which assume a Normal distribution for each component of a mixture. In this work, we propose the use of finite mixture models based on a flexible class of scale mixtures of Skew-Normal distributions for serological data analysis. These distributions are sufficiently flexible to describe right and left asymmetry often observed in the distributions associated with hypothetical antibody-negative and antibody-positive individuals, respectively. We illustrate the advantage of these alternative mixture models with a data set of 406 individuals in which antibodies against six different human herpesviruses were measured in the context of Myalgic Encephalomyelitis/Chronic Fatigue Syndrome.

scholarly journals Multivariate extremes of generalized skew-normal distributions

2009 ◽  
Vol 79 (4) ◽  
pp. 525-533 ◽  
Author(s):  
Natalia Lysenko ◽  
Parthanil Roy ◽  
Rolf Waeber
Keyword(s):  
Multivariate Extremes ◽  
Normal Distributions ◽  
Skew Normal Distributions ◽  
Skew Normal

scholarly journals Mixture of Inverse Weibull and Lognormal Distributions: Properties, Estimation, and Illustration

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Sultan ◽  
A. S. Al-Moisheer
Keyword(s):  
Information Matrix ◽  
Real Data ◽  
Likelihood Method ◽  
Model Parameters ◽  
Component Mixture ◽  
Data Set ◽  
Hazard Functions ◽  
Lognormal Distributions ◽  
Proposed Model ◽  
Estimation Of Model Parameters

We discuss the two-component mixture of the inverse Weibull and lognormal distributions (MIWLND) as a lifetime model. First, we discuss the properties of the proposed model including the reliability and hazard functions. Next, we discuss the estimation of model parameters by using the maximum likelihood method (MLEs). We also derive expressions for the elements of the Fisher information matrix. Next, we demonstrate the usefulness of the proposed model by fitting it to a real data set. Finally, we draw some concluding remarks.

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