scholarly journals On parameter estimation of a replicated linear functional relationship model for circular variables

MATEMATIKA ◽  
2017 ◽  
Vol 33 (2) ◽  
pp. 159
Author(s):  
Nurkhairany Amyra Mokhtar ◽  
Yong Zulina Zubairi ◽  
Abdul Ghapor Hussin ◽  
Rossita Mohamad Yunus
Keyword(s):  
Linear Functional ◽  
Functional Relationship ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Rotation Parameter ◽  
Likelihood Method ◽  
Practical Application ◽  
Data Set ◽  
Relationship Model ◽  
Error Terms

Replicated linear functional relationship model is often used to describe relationships between two circular variables where both variables have error terms and replicate observations are available. We derive the estimate of the rotation parameter of the model using the maximum likelihood method. The performance of the proposed method is studied through simulation, and it is found that the biasness of the estimates is small, thus implying the suitability of the method. Practical application of the method is illustrated by using a real data set.

scholarly journals Parameter Estimation and Covariance Matrix of the Linear Functional Relationship Model for Circular Variables with Unequal Error Concentrations

2020 ◽  
pp. 1-8
Author(s):  
Nurkhairany Amyra Mokhtar ◽  
Yong Zulina Zubairi ◽  
Abdul Ghapor Hussin ◽  
Nor Hafizah Moslim
Keyword(s):  
Parameter Estimation ◽  
Covariance Matrix ◽  
Linear Functional ◽  
Functional Relationship ◽  
Information Matrix ◽  
Estimation Method ◽  
Real Data ◽  
Circular Data ◽  
Data Set ◽  
Relationship Model

Functional relationship model is used to study the data that are subjected to errors. In this paper, we consider the linear functional relationship model with bivariate circular data where the pair of errors is with unequal concentration parameters. The parameter estimation of the model for circular data is different from linear data due to its wrapped around nature. We propose some improvements on the parameter estimation where some iterative procedures are considered. The concentration parameters are estimated based on the Bessel function. Also, we derive the corresponding covariance matrix of the model based on the Fisher Information matrix. Monte Carlo simulation studies were performed to study the suitability of the estimation method. It is found that the biasness of the estimates is small. Practical application of the method is illustrated by using real data set. Keywords: circular data; covariance matrix; Von Mises distribution; simulation study

scholarly journals Extended Odd Fréchet-G Family of Distributions

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Suleman Nasiru
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Data Sets ◽  
Data Set ◽  
New Class ◽  
New Family ◽  
Rate Functions ◽  
The Given ◽  
Family Of Distributions

The need to develop generalizations of existing statistical distributions to make them more flexible in modeling real data sets is vital in parametric statistical modeling and inference. Thus, this study develops a new class of distributions called the extended odd Fréchet family of distributions for modifying existing standard distributions. Two special models named the extended odd Fréchet Nadarajah-Haghighi and extended odd Fréchet Weibull distributions are proposed using the developed family. The densities and the hazard rate functions of the two special distributions exhibit different kinds of monotonic and nonmonotonic shapes. The maximum likelihood method is used to develop estimators for the parameters of the new class of distributions. The application of the special distributions is illustrated by means of a real data set. The results revealed that the special distributions developed from the new family can provide reasonable parametric fit to the given data set compared to other existing distributions.

scholarly journals The Exponentiated Generalized Standardized Half-logistic Distribution

2017 ◽  
Vol 6 (3) ◽  
pp. 24 ◽  
Author(s):  
Gauss M. Cordeiro ◽  
Thiago A. N. De Andrade ◽  
Marcelo Bourguignon ◽  
Frank Gomes-Silva
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Set ◽  
Lorenz Curves ◽  
Lifetime Model ◽  
Two Parameter ◽  
New Distribution

We study a new two-parameter lifetime model called the exponentiated generalized standardized half-logistic distribution, which extends the half-logistic pioneered by Balakrishnan in the eighties. We provide explicit expressions for the moments, generating and quantile functions, mean deviations, Bonferroni and Lorenz curves, and order statistics. The model parameters are estimated by the maximum likelihood method. A simulation study reveals that the estimators have desirable properties such as small biases and variances even in moderate sample sizes. We prove empirically that the new distribution provides a better fit to a real data set than other competitive models.

scholarly journals A New Extension of Lindley Geometric Distribution and its Applications

2019 ◽  
pp. 249-263
Author(s):  
I. Elbatal ◽  
Mohamed G. Khalil
Keyword(s):  
Hazard Rate ◽  
Maximum Likelihood Method ◽  
Geometric Distribution ◽  
Real Data ◽  
Rate Function ◽  
Likelihood Method ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Data Set ◽  
New Distribution

A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.

scholarly journals On the Alpha Power Kumaraswamy Distribution: Properties, Simulation and Application

2020 ◽  
Vol 43 (2) ◽  
pp. 285-313
Author(s):  
Mohamed Ali Ahmed
Keyword(s):  
Maximum Likelihood Method ◽  
Real Data ◽  
Parameters Estimation ◽  
Likelihood Method ◽  
Data Sets ◽  
Alpha Power ◽  
Simulation Studies ◽  
Data Set ◽  
Kumaraswamy Distribution ◽  
Mathematical Properties

Adding  new  parameters to  classical distributions becomes one  of  the most  important methods  for  increasing distributions flexibility,  especially, in  simulation   studies   and real data sets. In this paper, alpha power  transformation (APT) is used  and  applied  to  the Kumaraswamy (K) distribution and a proposed distribution, so called the alpha power Kumaraswamy (AK) distribution, is presented.  Some important mathematical properties are derived, parameters estimation of the AK distribution using maximum likelihood  method  is considered. A simulation study and  a  real  data   set  are  used  to  illustrate the  flexibility of the  AK distribution compared with other  distributions.

scholarly journals On the Omega Distribution: Some Properties and Estimation

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 656
Author(s):  
Abdelaziz Alsubie ◽  
Zuber Akhter ◽  
Haseeb Athar ◽  
Mahfooz Alam ◽  
Abd EL-Baset A. Ahmad ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Order Statistics ◽  
Maximum Likelihood Method ◽  
Real Data ◽  
Likelihood Method ◽  
Type Ii ◽  
Data Set ◽  
Simulation Results ◽  
Censoring Scheme ◽  
Single And Product Moments

We obtain explicit expressions for single and product moments of the order statistics of an omega distribution. We also discuss seven methods to estimate the omega parameters. Various simulation results are performed to compare the performance of the proposed estimators. Furthermore, the maximum likelihood method is adopted to estimate the omega parameters under the type II censoring scheme. The usefulness of the omega distribution is proven using a real data set.

scholarly journals A MIXED BILINEAR INAR(1) MODEL

2021 ◽  
pp. 143
Author(s):  
Predrag M. Popović
Keyword(s):  
Method Of Moments ◽  
Maximum Likelihood Method ◽  
Negative Binomial ◽  
Real Data ◽  
Random Coefficients ◽  
Likelihood Method ◽  
Data Set ◽  
Binomial Thinning ◽  
Conditional Maximum ◽  
Thinning Operator

The paper introduces a new autoregressive model of order one for time seriesof counts. The model is comprised of a linear as well as bilinear autoregressive component. These two components are governed by random coefficients. The autoregression is achieved by using the negative binomial thinning operator. The method of moments and the conditional maximum likelihood method are discussed for the parameter estimation. The practicality of the model is presented on a real data set.

scholarly journals Identification of High Leverage Points in Linear Functional Relationship Model

2020 ◽  
pp. 491-500
Author(s):  
Abu Sayed Md. Al Mamun ◽  
A.H.M. R. Imon ◽  
A. G. Hussin ◽  
Y. Z. Zubairi ◽  
Sohel Rana
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Linear Functional ◽  
Functional Relationship ◽  
Data Set ◽  
Leverage Points ◽  
Explanatory Variables ◽  
Gross Error ◽  
Relationship Model

In a standard linear regression model the explanatory variables, , are considered to be fixed and hence assumed to be free from errors. But in reality, they are variables and consequently can be subjected to errors. In the regression literature there is a clear distinction between outlier in the - space or errors and the outlier in the X-space. The later one is popularly known as high leverage points. If the explanatory variables are subjected to gross error or any unusual pattern we call these observations as outliers in the - space or high leverage points. High leverage points often exert too much influence and consequently become responsible for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers etc. Although a good number of works has been done on the identification of high leverage points in linear regression model, this is still a new and unsolved problem in linear functional relationship model. In this paper, we suggest a procedure for the identification of high leverage points based on deletion of a group of observations. The usefulness of the proposed method for the detection of multiple high leverage points is studied by some well-known data set and Monte Carlo simulations.

The co-responsibility of mass and environment in the formation of lenticular galaxies

2020 ◽  
Vol 15 (S359) ◽  
pp. 173-174
Author(s):  
A. Cortesi ◽  
L. Coccato ◽  
M. L. Buzzo ◽  
K. Menéndez-Delmestre ◽  
T. Goncalves ◽  
...  
Keyword(s):  
Active Galactic Nuclei ◽  
Maximum Likelihood Method ◽  
Spiral Galaxies ◽  
Galactic Nuclei ◽  
Rotation Velocity ◽  
Elliptical Galaxies ◽  
Likelihood Method ◽  
Data Set ◽  
Lenticular Galaxies ◽  
Galaxies Kinematics

AbstractWe present the latest data release of the Planetary Nebulae Spectrograph Survey (PNS) of ten lenticular galaxies and two spiral galaxies. With this data set we are able to recover the galaxies’ kinematics out to several effective radii. We use a maximum likelihood method to decompose the disk and spheroid kinematics and we compare it with the kinematics of spiral and elliptical galaxies. We build the Tully- Fisher (TF) relation for these galaxies and we compare with data from the literature and simulations. We find that the disks of lenticular galaxies are hotter than the disks of spiral galaxies at low redshifts, but still dominated by rotation velocity. The mechanism responsible for the formation of these lenticular galaxies is neither major mergers, nor a gentle quenching driven by stripping or Active Galactic Nuclei (AGN) feedback.

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