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 A New Extension of Thinning-Based Integer-Valued Autoregressive Models for Count Data

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 62
Author(s):  
Zhengwei Liu ◽  
Fukang Zhu
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Autoregressive Models ◽  
Superior Performance ◽  
Data Sets ◽  
Binomial Thinning ◽  
Free Case ◽  
Two Parameters ◽  
Conditional Maximum ◽  
Thinning Operator

The thinning operators play an important role in the analysis of integer-valued autoregressive models, and the most widely used is the binomial thinning. Inspired by the theory about extended Pascal triangles, a new thinning operator named extended binomial is introduced, which is a general case of the binomial thinning. Compared to the binomial thinning operator, the extended binomial thinning operator has two parameters and is more flexible in modeling. Based on the proposed operator, a new integer-valued autoregressive model is introduced, which can accurately and flexibly capture the dispersed features of counting time series. Two-step conditional least squares (CLS) estimation is investigated for the innovation-free case and the conditional maximum likelihood estimation is also discussed. We have also obtained the asymptotic property of the two-step CLS estimator. Finally, three overdispersed or underdispersed real data sets are considered to illustrate a superior performance of the proposed model.

scholarly journals A mixed thinning based geometric INAR(1) model

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4009-4022 ◽  
Author(s):  
Aleksandar Nastic ◽  
Miroslav Ristic ◽  
Ana Janjic
Keyword(s):  
Parameter Estimation ◽  
Method Of Moments ◽  
Negative Binomial ◽  
Real Life ◽  
Binomial Thinning ◽  
Conditional Least Squares ◽  
Counting Data ◽  
Parameter Estimators ◽  
Thinning Operator

In this article a geometrically distributed integer-valued autoregressive model of order one based on the mixed thinning operator is introduced. This new thinning operator is defined as a probability mixture of two well known thinning operators, binomial and negative binomial thinning. Some model properties are discussed. Method of moments and the conditional least squares are considered as possible approaches in model parameter estimation. Asymptotic characterization of the obtained parameter estimators is presented. The adequacy of the introduced model is verified by its application on a certain kind of real-life counting data, while its performance is evaluated by comparison with two other INAR(1) models that can be also used over the observed data.

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 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 Inverted Beta Lindley Distribution

2017 ◽  
Vol 13 (1) ◽  
pp. 7074-7086
Author(s):  
Neveen Kilany ◽  
H M Atallah
Keyword(s):  
Method Of Moments ◽  
Maximum Likelihood Method ◽  
Information Matrix ◽  
Continuous Distribution ◽  
Real Data ◽  
Point Estimation ◽  
Likelihood Method ◽  
New Model ◽  
Positive Data ◽  
Rate Functions

In this paper, a three-parameter continuous distribution, namely, Inverted Beta-Lindley (IBL) distribution is proposed and studied. The new model turns out to be quite flexible for analyzing positive data and has various shapes of density and hazard rate functions. Several statistical properties associated with this distribution are derived. Moreover, point estimation via method of moments and maximum likelihood method are studied and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models.

A Latent Factor Model for Forecasting Realized Variances

2020 ◽  
Author(s):  
Giorgio Calzolari ◽  
Roxana Halbleib ◽  
Aygul Zagidullina
Keyword(s):  
Method Of Moments ◽  
Maximum Likelihood Method ◽  
Factor Model ◽  
Real Data ◽  
Likelihood Method ◽  
Latent Factors ◽  
Latent Factor ◽  
Efficient Method Of Moments ◽  
Standard Models ◽  
Parsimonious Model

Abstract This article proposes a parsimonious model to forecast large vectors of realized variances (RVar) by exploiting their common dynamics within a latent factor structure. Their long persistence is captured by aggregating latent factors with AR(1) dynamics. The model has obvious advantages over standard autoregressive models not only in terms of parametrization, but also in terms of efficiency, when increasing the dimension of the vector, as it provides more information on the commonality of the series’ dynamics. The model easily accommodates further empirical features of RVars, such as conditional heteroskedasticity. For estimation purposes, we use the maximum likelihood method based on Kalman filter and the efficient method of moments, both being easy to implement and providing accurate estimates. Our empirical illustration on real data shows that the model we propose often outperforms standard models, most of which are, for vectors of RVar series, only implementable under heavy parametric restrictions.

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