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 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 Bivariate Model based on Compound Negative Binomial Distribution

2018 ◽  
Vol 41 (1) ◽  
pp. 87-108 ◽  
Author(s):  
Maha Ahmad Omair ◽  
Fatimah E AlMuhayfith ◽  
Abdulhamid A Alzaid
Keyword(s):  
Maximum Likelihood ◽  
Method Of Moments ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Traffic Accidents ◽  
Negative Binomial ◽  
Conditional Distributions ◽  
Bivariate Model ◽  
Distributional Properties ◽  
Parameter Estimators

A new bivariate model is introduced by compounding negative binomial and geometric distributions. Distributional properties, including joint, marginal and conditional distributions are discussed. Expressions for the product moments, covariance and correlation coefficient are obtained. Some properties such as ordering, unimodality, monotonicity and self-decomposability are studied. Parameter estimators using the method of moments and maximum likelihood are derived. Applications to traffic accidents data are illustrated.

scholarly journals Estimation for random coefficient integer-valued autoregressive model under random environment

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yan Cui ◽  
Yun Y. Wang
Keyword(s):  
Random Environment ◽  
Autoregressive Model ◽  
Strong Consistency ◽  
Negative Binomial ◽  
Random Coefficient ◽  
Model Parameters ◽  
Binomial Thinning ◽  
First Order ◽  
Proposed Model ◽  
Thinning Operator

AbstractA first-order random coefficient integer-valued autoregressive model based on the negative binomial thinning operator under r states random environment is introduced. This paper derives numerical characteristics of the proposed model, establishes Yule–Walker estimators of model parameters, and discusses the strong consistency of the obtained estimators. Finally, a simulation is carried out to verify the feasibility of parameter estimation.

A seasonal geometric INAR process based on negative binomial thinning operator

2018 ◽  
Vol 61 (6) ◽  
pp. 2561-2581 ◽  
Author(s):  
Shengqi Tian ◽  
Dehui Wang ◽  
Shuai Cui
Keyword(s):  
Negative Binomial ◽  
Binomial Thinning ◽  
Thinning Operator

scholarly journals An INAR(1) Model Based on Negative Binomial Thinning Operator with Serially Dependent Noise.

2020 ◽  
Vol 14 (1) ◽  
pp. 217-234
Author(s):  
Mehrnaz Mohammadpour ◽  
Masoumeh Shirozhan ◽  
◽  
Keyword(s):  
Negative Binomial ◽  
Binomial Thinning ◽  
Model Based ◽  
Thinning Operator

scholarly journals Delta Boosting Implementation of Negative Binomial Regression in Actuarial Pricing

Risks ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 19 ◽  
Author(s):  
Simon CK Lee
Keyword(s):  
Parameter Estimation ◽  
Negative Binomial ◽  
Real Life ◽  
Negative Binomial Regression ◽  
Interaction Patterns ◽  
Customer Base ◽  
Novel Approach ◽  
Binomial Regression ◽  
Two Parameters ◽  
Two Parameter

This study proposes an efficacious approach to analyze the over-dispersed insurance frequency data as it is imperative for the insurers to have decisive informative insights for precisely underwriting and pricing insurance products, retaining existing customer base and gaining an edge in the highly competitive retail insurance market. The delta boosting implementation of the negative binomial regression, both by one-parameter estimation and a novel two-parameter estimation, was tested on the empirical data. Accurate parameter estimation of the negative binomial regression is complicated with considerations of incomplete insurance exposures, negative convexity, and co-linearity. The issues mainly originate from the unique nature of insurance operations and the adoption of distribution outside the exponential family. We studied how the issues could significantly impact the quality of estimation. In addition to a novel approach to simultaneously estimate two parameters in regression through boosting, we further enrich the study by proposing an alteration of the base algorithm to address the problems. The algorithm was able to withstand the competition against popular regression methodologies in a real-life dataset. Common diagnostics were applied to compare the performance of the relevant candidates, leading to our conclusion to move from light-tail Poisson to negative binomial for over-dispersed data, from generalized linear model (GLM) to boosting for non-linear and interaction patterns, from one-parameter to two-parameter estimation to reflect more closely the reality.

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.

Characterization of the water flow through concrete based on parameter estimation from infiltration tests

2006 ◽  
Vol 36 (9) ◽  
pp. 1575-1582 ◽  
Author(s):  
Vicente Navarro ◽  
Ángel Yustres ◽  
Luís Cea ◽  
Miguel Candel ◽  
Ricardo Juncosa ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Water Flow ◽  
Flow Through ◽  
Infiltration Tests

scholarly journals Parameter estimation approach to the thermal characterization of intumescent fire retardant paints

2015 ◽  
Vol 655 ◽  
pp. 012048 ◽  
Author(s):  
L Calabrese ◽  
F Bozzoli ◽  
G Bochicchio ◽  
B Tessadri ◽  
P Vocale ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Fire Retardant ◽  
Thermal Characterization
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