Marginal likelihood estimation of negative binomial parameters with applications to RNA-seq data

Biostatistics ◽  
2017 ◽  
Vol 18 (4) ◽  
pp. 637-650 ◽  
Author(s):  
Luis León-Novelo ◽  
Claudio Fuentes ◽  
Sarah Emerson
Keyword(s):  
Negative Binomial ◽  
Marginal Likelihood ◽  
Hypothesis Test ◽  
Likelihood Estimation ◽  
Real Data ◽  
Rna Seq ◽  
Data Set ◽  
Bayesian Hierarchical ◽  
Proposed Model ◽  
Bayesian Hypothesis Test

SUMMARY RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in any proposed model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the dispersion parameter of the negative binomial distribution, and propose instead to use an estimator obtained via maximization of the marginal likelihood in a conjugate Bayesian framework. We show, via simulation studies, that the marginal MLE can better control this variation and produce a more stable and reliable estimator. We then formulate a conjugate Bayesian hierarchical model, and use this new estimator to propose a Bayesian hypothesis test to detect differentially expressed genes in RNA-Seq data. We use numerical studies to show that our much simpler approach is competitive with other negative binomial based procedures, and we use a real data set to illustrate the implementation and flexibility of the procedure.

Negative binomial improved second degree lindley distribution and its application

2020 ◽  
pp. 569-581
Author(s):  
R. Ashly ◽  
C. S. Rajitha
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Data Set ◽  
Factorial Moments ◽  
Lindley Distribution ◽  
Second Degree

The objective of this paper is to introduce a new two parameter mixed negative binomial distribution, namely negative binomial-improved second degree Lindley(NB-ISL) distribution. This distribution is obtained by mixing the negative binomial distribution with the improved second degree Lindley distribution. Many mixed distributions have been used in the literature for modeling the over dispersed count data, which provide a better fit compared to the Poisson and negative binomial distribution. In addition, we present the basic statistical properties of the new distribution such as factorial moments, mean and variance and the behavior of mean, variance and coefficient of variation are also discussed. Parameter estimation is implemented by using maximum likelihood estimation method. The performance of the NB-ISL distribution is shown in practice by applying it on real data set and compare it with some well-known count distributions. The result shows that the negative binomial-improved second degree Lindley distribution provides a better fit compared to Poisson, negative binomial and negative binomial-Lindley distributions.

scholarly journals Proportional Hazard Birnbaum-Saunders Distribution With Application to the Survival Data Analysis

2016 ◽  
Vol 39 (1) ◽  
pp. 129-147
Author(s):  
Germán Moreno Arenas ◽  
Guillermo Martínez Flórez ◽  
Carlos Barrera Causil
Keyword(s):  
Survival Data ◽  
Likelihood Estimation ◽  
Real Data ◽  
Model Parameters ◽  
Lifetime Data ◽  
Proportional Hazard ◽  
Data Set ◽  
Proposed Model ◽  
Log Linear ◽  
Skewness And Kurtosis

<p>Birnbaum Saunders (1969b) used a probability distribution to explain the lifetime data and stress produced in materials. Based on this distribution, we propose a generalization of the Birnbaum-Saunders distribution, referred to as the proportional hazard Birnbaum-Saunders distribution, which includes a new parameter that provides more flexibility in terms of skewness and kurtosis than existing models. We derive the main properties of the model. We discuss maximum likelihood estimation of the model parameters. As a natural step, we define the log-linear proportional hazard Birnbaum-Saunders regression model. An empirical application to a real data set is presented in order to illustrate the usefulness of the proposed model. The results showed that the proportional hazard Birnbaum-Saunders model can be used quite effectively in analyzing survival data, reliability problems and fatigue life studies.</p>

scholarly journals Generating New Flexible Lifetime Class of Distributions Based on Competing Risks and Frailty Models

2021 ◽  
pp. 1-19
Author(s):  
M. M. E. Abd El-Monsef ◽  
M. M. El-Awady
Keyword(s):  
Competing Risks ◽  
Hazard Function ◽  
Likelihood Estimation ◽  
Real Data ◽  
Lifetime Distribution ◽  
Frailty Models ◽  
Estimation Technique ◽  
Data Set ◽  
Egg Distribution ◽  
Proposed Model

New classes of continuous distributions have been generated, in the last decad, based on a compounding procedure arises on a latent competing risks problem. This procedure assumes the homogeneity between the population individuals. In this paper, a new lifetime distribution is generated, assuming the heterogeneity at both population and individual levels, called Extended Gamma Gompertz (EGG) distribution. This distribution shows very desirable exibility of its hazard function. Some properties of the proposed distribution are given. Maximum likelihood estimation technique is used to estimate the parameters. A simulation study is performed to examine the performance of the proposed model. Finally, application to a real data set is given to exemplify the utility of the EGG distribution.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

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.

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.

Multilevel Zero-inflated Censored Beta Regression Modeling for Proportions and Rate Data with Extra-zeros

2019 ◽  
Author(s):  
Leili Tapak ◽  
Omid Hamidi ◽  
Majid Sadeghifar ◽  
Hassan Doosti ◽  
Ghobad Moradi
Keyword(s):  
Regression Model ◽  
Simulation Study ◽  
Real Data ◽  
P Value ◽  
Parameter Estimates ◽  
Beta Regression ◽  
Rate Data ◽  
Data Set ◽  
Proposed Model ◽  
Beta Regression Model

Abstract Objectives Zero-inflated proportion or rate data nested in clusters due to the sampling structure can be found in many disciplines. Sometimes, the rate response may not be observed for some study units because of some limitations (false negative) like failure in recording data and the zeros are observed instead of the actual value of the rate/proportions (low incidence). In this study, we proposed a multilevel zero-inflated censored Beta regression model that can address zero-inflation rate data with low incidence.Methods We assumed that the random effects are independent and normally distributed. The performance of the proposed approach was evaluated by application on a three level real data set and a simulation study. We applied the proposed model to analyze brucellosis diagnosis rate data and investigate the effects of climatic and geographical position. For comparison, we also applied the standard zero-inflated censored Beta regression model that does not account for correlation.Results Results showed the proposed model performed better than zero-inflated censored Beta based on AIC criterion. Height (p-value <0.0001), temperature (p-value <0.0001) and precipitation (p-value = 0.0006) significantly affected brucellosis rates. While, precipitation in ZICBETA model was not statistically significant (p-value =0.385). Simulation study also showed that the estimations obtained by maximum likelihood approach had reasonable in terms of mean square error.Conclusions The results showed that the proposed method can capture the correlations in the real data set and yields accurate parameter estimates.

scholarly journals A Mixture of Inverse Weibull and Inverse Burr Distributions: Properties, Estimation, and Fitting

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
A. S. Al-Moisheer ◽  
K. S. Sultan ◽  
M. A. Al-Shehri
Keyword(s):  
Mixture Model ◽  
Classical Method ◽  
Likelihood Estimation ◽  
Real Data ◽  
Probability Density Functions ◽  
Density Functions ◽  
Data Set ◽  
Burr Distributions ◽  
Lindley’S Approximation ◽  
Rate Functions

The new mixture model of the two components of the inverse Weibull and inverse Burr distributions (MIWIBD) is proposed. First, the properties of the investigated mixture model are introduced and the behaviors of the probability density functions and hazard rate functions are displayed. Then, the estimates of the five-dimensional vector of parameters by using the classical method such as the maximum likelihood estimation (MLEs) and the approximation method by using Lindley’s approximation are obtained. Finally, a real data set for the proposed mixture model is applied to illustrate the proposed mixture model.

scholarly journals General Results for the Transmuted Family of Distributions and New Models

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Marcelo Bourguignon ◽  
Indranil Ghosh ◽  
Gauss M. Cordeiro
Keyword(s):  
Maximum Likelihood ◽  
Generating Functions ◽  
Real Data ◽  
Model Parameters ◽  
Data Set ◽  
Proposed Model ◽  
Method Of Maximum Likelihood ◽  
The Family ◽  
New Models ◽  
Family Of Distributions

The transmuted family of distributions has been receiving increased attention over the last few years. For a baselineGdistribution, we derive a simple representation for the transmuted-Gfamily density function as a linear mixture of theGand exponentiated-Gdensities. We investigate the asymptotes and shapes and obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, mean deviations, Rényi and Shannon entropies, and order statistics and their moments. We estimate the model parameters of the family by the method of maximum likelihood. We prove empirically the flexibility of the proposed model by means of an application to a real data set.

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