scholarly journals A Bayesian Approach to Heavy-Tailed Finite Mixture Autoregressive Models

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 929
Author(s):  
Mohammad Reza Mahmoudi ◽  
Mohsen Maleki ◽  
Dumitru Baleanu ◽  
Vu-Thanh Nguyen ◽  
Kim-Hung Pho
Keyword(s):  
Bayesian Analysis ◽  
Heavy Tails ◽  
Linear Time ◽  
Real Data ◽  
Finite Mixture ◽  
Stochastic Representation ◽  
Bayesian Approaches ◽  
Proposed Model ◽  
Heavy Tailed ◽  
Informative Prior Distributions

In this paper, a Bayesian analysis of finite mixture autoregressive (MAR) models based on the assumption of scale mixtures of skew-normal (SMSN) innovations (called SMSN–MAR) is considered. This model is not simultaneously sensitive to outliers, as the celebrated SMSN distributions, because the proposed MAR model covers the lightly/heavily-tailed symmetric and asymmetric innovations. This model allows us to have robust inferences on some non-linear time series with skewness and heavy tails. Classical inferences about the mixture models have some problematic issues that can be solved using Bayesian approaches. The stochastic representation of the SMSN family allows us to develop a Bayesian analysis considering the informative prior distributions in the proposed model. Some simulations and real data are also presented to illustrate the usefulness of the proposed models.

scholarly journals A Generalized Rayleigh Family of Distributions Based on the Modified Slash Model

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1226
Author(s):  
Inmaculada Barranco-Chamorro ◽  
Yuri A. Iriarte ◽  
Yolanda M. Gómez ◽  
Juan M. Astorga ◽  
Héctor W. Gómez
Keyword(s):  
Heavy Tails ◽  
Real Data ◽  
Rate Function ◽  
Data Sets ◽  
Estimation Of Parameters ◽  
Stochastic Representation ◽  
Likelihood Methods ◽  
Chi Square ◽  
Maximum Likelihood Methods ◽  
Family Of Distributions

Specifying a proper statistical model to represent asymmetric lifetime data with high kurtosis is an open problem. In this paper, the three-parameter, modified, slashed, generalized Rayleigh family of distributions is proposed. Its structural properties are studied: stochastic representation, probability density function, hazard rate function, moments and estimation of parameters via maximum likelihood methods. As merits of our proposal, we highlight as particular cases a plethora of lifetime models, such as Rayleigh, Maxwell, half-normal and chi-square, among others, which are able to accommodate heavy tails. A simulation study and applications to real data sets are included to illustrate the use of our results.

scholarly journals A New Right-Skewed Upside Down Bathtub Shaped Heavy-tailed Distribution and its Applications

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Sandeep Kumar Maurya ◽  
Sanjay K Singh ◽  
Umesh Singh
Keyword(s):  
Maximum Likelihood ◽  
Real Data ◽  
Statistical Properties ◽  
New Right ◽  
Data Sets ◽  
Proposed Model ◽  
Heavy Tailed Distribution ◽  
Heavy Tailed

A one parameter right skewed, upside down bathtub type, heavy-tailed distribution is derived. Various statistical properties and maximum likelihood approaches for estimation purpose are studied. Five different real data sets with four different models are considered to illustrate the suitability of the proposed model.

scholarly journals Robust Mixture Modeling Based on Two-Piece Scale Mixtures of Normal Family

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 38 ◽  
Author(s):  
Mohsen Maleki ◽  
Javier Contreras-Reyes ◽  
Mohammad Mahmoudi
Keyword(s):  
Real Data ◽  
Finite Mixture ◽  
Maximum Likelihood Estimates ◽  
Model Parameters ◽  
Normal Distributions ◽  
Scale Mixtures ◽  
Robust Model ◽  
Heavy Tailed Distributions ◽  
The Family ◽  
Heavy Tailed

In this paper, we examine the finite mixture (FM) model with a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family components. This family allows the development of a robust estimation of FM models. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and light/heavy tailed distributions. It represents an alternative family to the well-known scale mixtures of the skew normal (SMSN) family studied by Branco and Dey (2001). Also, the TP-SMN covers the SMN (normal, t, slash, and contaminated normal distributions) as the symmetric members and two-piece versions of them as asymmetric members. A key feature of this study is using a suitable hierarchical representation of the family to obtain maximum likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and real data, and then compared to other finite mixture of SMSN models.

Bayesian Analysis of the Brown–Proschan Model

2015 ◽  
Vol 30 (1) ◽  
Author(s):  
Dinh Tuan Nguyen ◽  
Yann Dijoux ◽  
Mitra Fouladirad
Keyword(s):  
Weibull Distribution ◽  
Bayesian Analysis ◽  
Failure Rate ◽  
Bayesian Approach ◽  
Real Data ◽  
Posterior Distributions ◽  
Imperfect Maintenance ◽  
Maintenance Model ◽  
Informative Prior Distributions

AbstractThe paper presents a Bayesian approach of the Brown–Proschan imperfect maintenance model. The initial failure rate is assumed to follow a Weibull distribution. A discussion of the choice of informative and non-informative prior distributions is provided. The implementation of the posterior distributions requires the Metropolis-within-Gibbs algorithm. A study on the quality of the estimators of the model obtained from Bayesian and frequentist inference is proposed. An application to real data is finally developed.

Erlang mixture distribution with application on COVID-19 cases in egypt

2021 ◽  
pp. 2150015
Author(s):  
M. M. E. Abd El-Monsef
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Finite Mixture ◽  
Erlang Distribution ◽  
Parameter Estimates ◽  
Proposed Model ◽  
Shape Characteristics ◽  
Erlang Distributions ◽  
Special Case

In this paper, a finite mixture of m-Erlang distributions is proposed. Different moments, shape characteristics and parameter estimates of the proposed model are also provided. The proposed mixture has the property that it has a bounded hazard function. A special case of the mixed Erlang distribution is introduced and discussed. In addition, a predictive technique is introduced to estimate the needed number of mixture components to fit a certain data. A real data concerning the confirmed COVID-19 cases in Egypt is introduced to utilize the predictive estimation technique. Two more real datasets are used to examine the flexibility of the proposed model.

scholarly journals Bayesian Analysis of Competing Risks Models with Masked Causes of Failure and Incomplete Failure Times

2017 ◽  
Author(s):  
Yosra Yousif ◽  
Faiz A. M. Elfaki ◽  
Meftah Hrairi
Keyword(s):  
Bayesian Analysis ◽  
Failure Time ◽  
Real Data ◽  
Data Sets ◽  
Hazard Functions ◽  
Periodic Inspection ◽  
Proposed Model ◽  
Interval Censored ◽  
Gamma Processes ◽  
The Impact

Bayesian analysis for masked data under competing risk frameworks is studied for the purpose of assessing the impact of covariates on the hazard functions when the failure time is exactly observed for some subjects but only known to lie in an interval of time for the remaining subjects. Such data, known as partly interval-censored data, usually result from periodic inspection. Dirichlet and Gamma processes are assumed as priors for masking probabilities and baseline hazards. The Markov Chain Monte Carlo (MCMC) technique is employed for the implementation of the Bayesian approach. The effectiveness of the proposed model is tested through numerical studies, including simulated and real data sets.

scholarly journals Robust functional regression model for marginal mean and subject-specific inferences

2017 ◽  
Vol 27 (11) ◽  
pp. 3236-3254 ◽  
Author(s):  
Chunzheng Cao ◽  
Jian Qing Shi ◽  
Youngjo Lee
Keyword(s):  
Real Data ◽  
Functional Regression ◽  
Conditional Mean ◽  
Data Contamination ◽  
Data Application ◽  
Proposed Model ◽  
Subject Specific ◽  
Heavy Tailed ◽  
Conditional Means ◽  
Functional Regression Models

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student t-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting conditional means as well as interpolation and extrapolation for the subject-specific inferences. We develop bootstrap prediction intervals (PIs) for conditional mean curves. Numerical studies show that the proposed model provides a robust approach against data contamination or distribution misspecification, and the proposed PIs maintain the nominal confidence levels. A real data application is presented as an illustrative example.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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 MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

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