scholarly journals ASYMPTOTIC PROPERTIES IN THE PROBIT-ZERO-INFLATED BINOMIAL REGRESSION MODEL

2021 ◽  
Vol 3 (2) ◽  
pp. 68-81
Author(s):  
LO Fatimata ◽  
BA Demba Bocar ◽  
DIOP Aba
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Probit Model ◽  
Estimation Procedure ◽  
Random Errors ◽  
Restrictive Assumption ◽  
Binomial Regression ◽  
Modeling Data

Zero-inflated regression models have had wide application recently and have provenuseful in modeling data with many zeros. Zero-inflated Binomial (ZIB) regression model is an extension of the ordinary binomial distribution that takes into account the excess of zeros. In comparing the probit model to the logistic model, many authors believe that there is little theoretical justification in choosing one formulation over the other in most circumstances involving binary responses. The logit model is considered to be computationally simpler but it is based on a more restrictive assumption of error independence, although many other generalizations have dealt with that assumption as well. By contrast, the probit model assumes that random errors have a multivariate normal distribution. This assumption makes the probit model attractive because the normal distribution provides a good approximation to many other distributions. In this paper, we develop a maximum likelihood estimation procedure for the parameters of a zero-inflated Binomial regression model with probit link function for both component of the model. We establish the existency, consistency and asymptotic normality of the proposed estimator.

The Odd Log-Logistic Log-Normal Distribution with Theory and Applications

2018 ◽  
Vol 10 (04) ◽  
pp. 1850009 ◽  
Author(s):  
Gamze Ozel ◽  
Emrah Altun ◽  
Morad Alizadeh ◽  
Mahdieh Mozafari
Keyword(s):  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Procedure ◽  
Quantile Function ◽  
Logistic Distribution ◽  
Unknown Parameters ◽  
Heavy Tailed ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, a new heavy-tailed distribution is used to model data with a strong right tail, as often occuring in practical situations. The proposed distribution is derived from the log-normal distribution, by using odd log-logistic distribution. Statistical properties of this distribution, including hazard function, moments, quantile function, and asymptotics, are derived. The unknown parameters are estimated by the maximum likelihood estimation procedure. For different parameter settings and sample sizes, a simulation study is performed and the performance of the new distribution is compared to beta log-normal. The new lifetime model can be very useful and its superiority is illustrated by means of two real data sets.

scholarly journals Statistical analysis based on quaternion normal random variables

1985 ◽  
Vol 4 (3) ◽  
pp. 120-127 ◽  
Author(s):  
H. M. Rautenbach ◽  
J. J. J. Roux
Keyword(s):  
Statistical Analysis ◽  
Maximum Likelihood ◽  
Probability Density Function ◽  
Maximum Likelihood Estimation ◽  
Normal Distribution ◽  
Probability Density ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Unknown Parameters ◽  
Quaternion Case

The quaternion normal distribution is derived and a number of characteristics are highlighted. The maximum likelihood estimation procedure in the quaternion case is examined and the conclusion is reached that the estimation procedure is simplified if the unknown parameters of the associated real probability density function are estimated. The quaternion estimator is then obtained by regarding these estimators as the components of the quaternion estimator. By means of a example attention is given to a test criterium which can be used in the quaternion model.

scholarly journals On the Regression Model for Generalized Normal Distributions

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 173
Author(s):  
Ayman Alzaatreh ◽  
Mohammad Aljarrah ◽  
Ayanna Almagambetova ◽  
Nazgul Zakiyeva
Keyword(s):  
Maximum Likelihood ◽  
Regression Model ◽  
Normal Distribution ◽  
Regression Models ◽  
Likelihood Method ◽  
Normal Distributions ◽  
Normality Assumption ◽  
Normal Regression ◽  
Modeling Data ◽  
Model Residuals

The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generalized normal regression model that assumes a non-normal response. In this paper, we propose regression models based on generalizations of the normal distribution. The proposed regression models can be used effectively in modeling data with a highly skewed response. Furthermore, we study in some details the structural properties of the proposed generalizations of the normal distribution. The maximum likelihood method is used for estimating the parameters of the proposed method. The performance of the maximum likelihood estimators in estimating the distributional parameters is assessed through a small simulation study. Applications to two real datasets are given to illustrate the flexibility and the usefulness of the proposed distributions and their regression models.

STUDY OF INACCURACY IN THE OPERATION OF THE MAIN CONTROLLER OF STB MACHINE

2019 ◽  
Keyword(s):  
Normal Distribution ◽  
Stable Process ◽  
Random Errors ◽  
Actual Length ◽  
Experimental Data Processing ◽  
Set Up ◽  
Main Regulator ◽  
Transmission Gear ◽  
Selection Of

At production of fabrics, including fabrics for agricultural purpose, an important role is played by the cor-rect adjustment of operation of machine main regulator. The quality of setup of machine main controller is determined by the proper selection of rotation angle of warp beam weaving per one filling thread. In the pro-cess of using the regulator as a result of mistakes in adjustment, wear of transmission gear and backlashes in connections of details there are random changes in threads length. The purpose of the article is the research of property of random errors of basis giving by STB machine regulator. Mistakes can be both negative, and positive. In case of emergence only negative or only positive mistakes operation of the machine becomes im-possible as there will be a consecutive accumulation of mistakes. As a result of experimental data processing for stable process of weaving and the invariable diameter of basis threads winding of threads it is revealed that the random error of giving is set up as linear function of the accidental length having normal distribution. Measurements of accidental deviations in giving of a basis by the main regulator allowed to construct a curve of normal distribution of its actual length for one pass of weft thread. The presented curve of distribution of random errors in giving of a basis is the displaced curve of normal distribution of the accidental sizes. Also we define the density of probability of normal distribution of basis giving errors connected with a margin er-ror operation of the main regulator knowing of which allows to plan ways of their decrease that is important for improvement of quality of the produced fabrics.

scholarly journals Statistical models for analyzing count data: predictors of length of stay among HIV patients in Portugal using a multilevel model

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Ahmed Nabil Shaaban ◽  
Bárbara Peleteiro ◽  
Maria Rosario O. Martins
Keyword(s):  
Length Of Stay ◽  
Regression Model ◽  
Random Effects ◽  
Count Data ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Comprehensive Approach ◽  
Negative Binomial Regression Model ◽  
Hiv Patients ◽  
Binomial Regression

Abstract Background This study offers a comprehensive approach to precisely analyze the complexly distributed length of stay among HIV admissions in Portugal. Objective To provide an illustration of statistical techniques for analysing count data using longitudinal predictors of length of stay among HIV hospitalizations in Portugal. Method Registered discharges in the Portuguese National Health Service (NHS) facilities Between January 2009 and December 2017, a total of 26,505 classified under Major Diagnostic Category (MDC) created for patients with HIV infection, with HIV/AIDS as a main or secondary cause of admission, were used to predict length of stay among HIV hospitalizations in Portugal. Several strategies were applied to select the best count fit model that includes the Poisson regression model, zero-inflated Poisson, the negative binomial regression model, and zero-inflated negative binomial regression model. A random hospital effects term has been incorporated into the negative binomial model to examine the dependence between observations within the same hospital. A multivariable analysis has been performed to assess the effect of covariates on length of stay. Results The median length of stay in our study was 11 days (interquartile range: 6–22). Statistical comparisons among the count models revealed that the random-effects negative binomial models provided the best fit with observed data. Admissions among males or admissions associated with TB infection, pneumocystis, cytomegalovirus, candidiasis, toxoplasmosis, or mycobacterium disease exhibit a highly significant increase in length of stay. Perfect trends were observed in which a higher number of diagnoses or procedures lead to significantly higher length of stay. The random-effects term included in our model and refers to unexplained factors specific to each hospital revealed obvious differences in quality among the hospitals included in our study. Conclusions This study provides a comprehensive approach to address unique problems associated with the prediction of length of stay among HIV patients in Portugal.

A Bayesian regression model for circular data based on the projected normal distribution

2011 ◽  
Vol 11 (3) ◽  
pp. 185-201 ◽  
Author(s):  
Gabriel Nuñez-Antonio ◽  
Eduardo Gutiérrez-Peña ◽  
Gabriel Escarela
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Bayesian Regression ◽  
Circular Data ◽  
Projected Normal Distribution
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