scholarly journals Multiple Linear Regressions by Maximizing the Likelihood under Assumption of Generalized Gauss-Laplace Distribution of the Error

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Donatella Bálint ◽  
Sorana D. Bolboacă
Keyword(s):  
Normal Distribution ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Likelihood Estimation ◽  
Real Data ◽  
Multiple Linear Regression Analysis ◽  
Laplace Distribution ◽  
New Approach ◽  
Feature Information ◽  
Linear Regressions

Multiple linear regression analysis is widely used to link an outcome with predictors for better understanding of the behaviour of the outcome of interest. Usually, under the assumption that the errors follow a normal distribution, the coefficients of the model are estimated by minimizing the sum of squared deviations. A new approach based on maximum likelihood estimation is proposed for finding the coefficients on linear models with two predictors without any constrictive assumptions on the distribution of the errors. The algorithm was developed, implemented, and tested as proof-of-concept using fourteen sets of compounds by investigating the link between activity/property (as outcome) and structural feature information incorporated by molecular descriptors (as predictors). The results on real data demonstrated that in all investigated cases the power of the error is significantly different by the convenient value of two when the Gauss-Laplace distribution was used to relax the constrictive assumption of the normal distribution of the error. Therefore, the Gauss-Laplace distribution of the error could not be rejected while the hypothesis that the power of the error from Gauss-Laplace distribution is normal distributed also failed to be rejected.

scholarly journals An improved robust variance inflation factor: Reducing the negative effects of good leverage points

2021 ◽  
Author(s):  
Osman U. Ekiz ◽  
Keyword(s):  
Linear Regression Analysis ◽  
Real Data ◽  
Multiple Linear Regression Analysis ◽  
Coefficient Of Determination ◽  
Negative Effects ◽  
Variance Inflation Factor ◽  
Explanatory Variables ◽  
Robust Variance ◽  
Inflation Factor ◽  
Better Than

In multiple linear regression analysis, the variance inflation factor is a well-known collinearity measure. It is defined as the function of the coefficient of determination between the explanatory variables, and it is based on the maximum likelihood estimator of the regression coefficients. Nevertheless, in addition to outliers, leverage observations can have significant impact on the coefficient of determination, and thereby the variance inflation factor. This study presents an improved robust variance inflation factor estimator that is not affected by these observations. Simulation studies and a real data analysis indicate that the modified robust variance inflation factor estimator performs better than the traditional one.

scholarly journals Using Iterative Reweighting Algorithm and Genetic Algorithm to Calculate The Estimation of The Parameters Of The Maximum Likelihood of The Skew Normal Distribution

2021 ◽  
Vol 27 (127) ◽  
pp. 253-264
Author(s):  
مرتضى علاء الخفاجي ◽  
رباب عبد الرضا البكري
Keyword(s):  
Genetic Algorithm ◽  
Maximum Likelihood ◽  
Normal Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Likelihood Method ◽  
Skew Normal Distribution ◽  
Iterative Reweighting ◽  
Non Linear Equation ◽  
Skew Normal

Excessive skewness which occurs sometimes in the data is represented as an obstacle against normal distribution. So, recent studies have witnessed activity in studying the skew-normal distribution (SND) that matches the skewness data which is regarded as a special case of the normal distribution with additional skewness parameter (α), which gives more flexibility to the normal distribution. When estimating the parameters of (SND), we face the problem of the non-linear equation and by using the method of Maximum Likelihood estimation (ML) their solutions will be inaccurate and unreliable. To solve this problem, two methods can be used that are: the genetic algorithm (GA) and the iterative reweighting algorithm (IR) based on the Maximum Likelihood method. Monte Carlo simulation was used with different skewness levels and sample sizes, and the superiority of the results was compared. It was concluded that (SND) model estimation using (GA) is the best when the samples sizes are small and medium, while large samples indicate that the (IR) algorithm is the best. The study was also done using real data to find the parameter estimation and a comparison between the superiority of the results based on (AIC, BIC, Mse and Def) criteria.

scholarly journals The Impact of Discipline and Motivation Towards Employee Performance in The Permata Pamulang Hospital

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Lucia Maduningtias
Keyword(s):  
Employee Performance ◽  
Linear Regression Analysis ◽  
Multiple Linear Regression Analysis ◽  
Primary Data ◽  
Simple Correlation ◽  
Hospital Employees ◽  
Simultaneous Test ◽  
Constant Determination ◽  
The Impact ◽  
Linear Regressions

The purpose of this study is to figure out the impact of motivation and discipline toward the employee performance in The Permata Pamulang Hospital both partially and simultaneously. This study used saturated samples, so all of 55 hospital employees in The Permata Pamulang Hospital be respondents from this study. The data-collecting tool that was used is a questionnaire, and the data used is primary data. Data collected was analyzed by multiple linear regression analysis with hypothetical test, with partial test (t) and simultaneous test (F). The analysis results of the disciplinary and motivational impact towards employee performance in Permata Pamulang Hospital with simple correlation number = 0,857, it means that discipline and motivation have a moderate level of relation towards employee performance. In equations of multiple linear regressions, it was obtained Y = 4,097 + 0.48 X1 + 0.53 X2, which means that when X variable is increased to 1 unit, thus Y variable will increase to 0.48 + 0.53 units at 4,907 constant. Determination coefficient values of 72% show that the amount of disciplinary and motivational variables in the effort to increase the employee performance, the other 28% were affected by other unstudied variables in this study. After significant testing by using the "t test", it was obtained that t-count > t-table where 4,320 > 2,007 which means Ho was rejected and Ha is accepted, this means there is a significant influence between discipline and motivation toward employee performance in The Permata Pamulang Hospital.

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.

PERFORMANCE OF MIXED EFFECTS FOR CLUSTERED COUNTING DATA MODELS

2020 ◽  
Vol 3 (2) ◽  
pp. 34-41
Author(s):  
Intesar N. El-Saeiti ◽  
Khalil Mostafa ALsawi
Keyword(s):  
Generalized Linear Models ◽  
Standard Error ◽  
Mixed Models ◽  
Linear Models ◽  
Generalized Linear Mixed Models ◽  
Linear Mixed Models ◽  
Likelihood Estimation ◽  
Real Data ◽  
Estimation Technique ◽  
Counting Data

This article is concerned with hierarchical generalized linear models. It includes generalized linear models and generalized linear mixed models, which are related to linear models. In generalized linear mixed models, the dependent variable and the standard error follow any distribution from the exponential family, e.g. normal, Poisson, binomial, gamma, etc. We studied counting data, and then use the Poisson-gamma model,where the dependentvariable follows the Poisson distribution and the standard error follow the gamma distribution. Several estimation techniques can be used for generalized linear mixed model. In this paperthe hierarchical likelihood estimation technique was used to prove the performance of H-likelihood methodwhen thecounting data were balanced or unbalanced. Real data were used to test the performance of Poisson-gamma H-likelihood estimation method in case of balanced and unbalanced counting data.When real data used in the past research for another problem, it was noticed that the performance of the hierarchical likelihood estimation technique gave a close approximations in the event of balanced and unbalanced counting data, and the output of the technique was approximately equivalent in both instances.

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 ANALISIS FAKTOR-FAKTOR FUNDAMENTAL YANG BERPENGARUH TERHADAP RETURN SAHAM SYARIAH PADA PERUSAHAAN YANG TERGABUNG DALAM JAKARTA ISLAMIC INDEX (JII)

2018 ◽  
Vol 5 (2) ◽  
pp. 18-36
Author(s):  
Fitri .
Keyword(s):  
Stock Returns ◽  
Linear Regression Analysis ◽  
Real Data ◽  
Multiple Linear Regression Analysis ◽  
Fundamental Analysis ◽  
Current Ratio ◽  
Test Analysis ◽  
Equity Ratio ◽  
Consistent Performance ◽  
Turn Over

The development of the sharia capital market in Indonesia until 2016 shows that Islamic stock shares do not yet have optimal and consistent performance in terms of the returns given. Fundamental analysis is a study that studies matters relating to the finances of a business with a view to better understanding the basic nature and operational characteristics of public companies that issue shares. Accounting information or company financial statements can be used as a factor of fundamental analysis based on real data that is useful for evaluating and projecting the value of a stock. The purpose of this study was to determine the effect of return on assets (ROA), Debt to Equity Ratio (DER), Current Ratio (CR), Earning per share (EPS), Total asset turn over (TATO) on Islamic stock returns. The research method used is descriptive verification. The unit of analysis in this study is Islamic stocks that are members of the Jakarta Islamic Index (JII). Statistical test analysis in this study using multiple linear regression analysis, t test and F test. The results showed that the variables ROA, CR, EPS and TATO have a positive and significant effect on Islamic stock returns, but the DER variable does not have a significant effect on stock returns. sharia.   Keywords: return on asset (ROA), Debt to Equity Ratio (DER), Current  Ratio (CR), Earning per share (EPS), Total assets turn over (TATO),

scholarly journals A New Class of Distributions Generated by the Extended Bimodal-Normal Distribution

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Milton A. Cortés ◽  
David Elal-Olivero ◽  
Juan F. Olivares-Pacheco
Keyword(s):  
Monte Carlo Simulation ◽  
Normal Distribution ◽  
Real Data ◽  
Laplace Distribution ◽  
Data Sets ◽  
Stochastic Representation ◽  
New Class ◽  
New Family ◽  
Special Cases ◽  
Family Of Distributions

In this study, we present a new family of distributions through generalization of the extended bimodal-normal distribution. This family includes several special cases, like the normal, Birnbaum-Saunders, Student’s t, and Laplace distribution, that are developed and defined using stochastic representation. The theoretical properties are derived, and easily implemented Monte Carlo simulation schemes are presented. An inferential study is performed for the Laplace distribution. We end with an illustration of two real data sets.

scholarly journals PENGARUH PENGALAMAN, KEAHLIAN, DAN SKEPTISISME PROFESIONAL TERHADAP PENDETEKSIAN KECURANGAN (STUDI EMPIRIS PADA BPK RI PERWAKILAN SUMATERA SELATAN)

AKUNTABILITAS ◽  
2019 ◽  
Vol 12 (2) ◽  
pp. 113-124
Author(s):  
Indri Ningtyas ◽  
Harun Delamat ◽  
Emylia Yuniartie
Keyword(s):  
Regression Analysis ◽  
Data Analysis ◽  
Linear Regression ◽  
Linear Regression Analysis ◽  
Fraud Detection ◽  
Multiple Linear Regression Analysis ◽  
Multiple Linear Regressions ◽  
Professional Skepticism ◽  
Independent Variables ◽  
Linear Regressions

This research was aimed to examine the effect of experience, expertise,and professional skepticism toward fraud detection empirical study in BPK RI South Sumatra Representative. The research uses independent variables is experience, expertise and professional skepticism. The dependent variabels are fraud detection. The population of this study is all of the auditors working at BPK RI South Sumatra Respresentative. The samples was conducted by total sampling. For collecting data, the writer uses questionnaires.The Data Analysis uses a multiple linear regressions using the Statistical Packages for Social Science (SPSS) version 21. The statistical method which is used to test the hypothesis is multiple linear regression analysis. The result showed that experience and expertise have a influence on fraud detection. Variable professional skepticism have no influence on fraud detection.

scholarly journals A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

2020 ◽  
Vol 8 (5) ◽  
pp. 183-198
Author(s):  
Marcus Pinto da Costa da Rocha ◽  
Lucelia M. Lima ◽  
Valcir J. C. Farias ◽  
Benjamin Bedregal ◽  
Heliton R. Tavares
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Portfolio Selection ◽  
Real Data ◽  
Laplace Distribution ◽  
Fuzzy Probability ◽  
Variance Model ◽  
Risk Rate ◽  
Mean Variance ◽  
Fuzzy Normal Distribution

The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution.

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