scholarly journals A New First-Order Integer-Valued Autoregressive Model with Bell Innovations

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 713
Author(s):  
Jie Huang ◽  
Fukang Zhu
Keyword(s):  
Poisson Distribution ◽  
Autoregressive Model ◽  
Real Data ◽  
Good Alternative ◽  
Distribution Functions ◽  
Infinitely Divisible ◽  
First Order ◽  
The Mean ◽  
Conditional Maximum ◽  
Mean Variance

A Poisson distribution is commonly used as the innovation distribution for integer-valued autoregressive models, but its mean is equal to its variance, which limits flexibility, so a flexible, one-parameter, infinitely divisible Bell distribution may be a good alternative. In addition, for a parameter with a small value, the Bell distribution approaches the Poisson distribution. In this paper, we introduce a new first-order, non-negative, integer-valued autoregressive model with Bell innovations based on the binomial thinning operator. Compared with other models, the new model is not only simple but also particularly suitable for time series of counts exhibiting overdispersion. Some properties of the model are established here, such as the mean, variance, joint distribution functions, and multi-step-ahead conditional measures. Conditional least squares, Yule–Walker, and conditional maximum likelihood are used for estimating the parameters. Some simulation results are presented to access these estimates’ performances. Real data examples are provided.

scholarly journals Interval Estimation of Random Coefficient Integer-Valued Autoregressive Model Based on Mean Empirical Likelihood Method

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Xianghong Xu ◽  
Dehui Wang ◽  
Zhiwen Zhao
Keyword(s):  
Data Analysis ◽  
Empirical Likelihood ◽  
Autoregressive Model ◽  
Interval Estimation ◽  
Real Data ◽  
Confidence Regions ◽  
Random Coefficient ◽  
Likelihood Method ◽  
First Order ◽  
The Mean

In this paper, we study the use of the mean empirical likelihood (MEL) method in a first-order random coefficient integer-valued autoregressive model. The MEL ratio statistic is established, its limiting properties are discussed, and the confidence regions for the parameter of interest are derived. Furthermore, a simulation study is presented to demonstrate the performance of the proposed method. Finally, a real data analysis of dengue fever is performed.

scholarly journals The concept of stochastic dominance in ranking investment alternatives

2005 ◽  
Vol 50 (164) ◽  
pp. 135-149
Author(s):  
Dejan Trifunovic
Keyword(s):  
Stochastic Dominance ◽  
Distribution Functions ◽  
Third Order ◽  
Ranking Problem ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Arbitrage Opportunities ◽  
Second Order Stochastic Dominance ◽  
Mean Variance ◽  
Almost Stochastic Dominance

In order to rank investments under uncertainty, the most widely used method is mean variance analysis. Stochastic dominance is an alternative concept which ranks investments by using the whole distribution function. There exist three models: first-order stochastic dominance is used when the distribution functions do not intersect, second-order stochastic dominance is applied to situations where the distribution functions intersect only once, while third-order stochastic dominance solves the ranking problem in the case of double intersection. Almost stochastic dominance is a special model. Finally we show that the existence of arbitrage opportunities implies the existence of stochastic dominance, while the reverse does not hold.

scholarly journals Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mursala Khan ◽  
Rajesh Singh
Keyword(s):  
Finite Population ◽  
Real Data ◽  
Survey Sampling ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Data Set ◽  
Population Mean ◽  
First Order ◽  
The Mean ◽  
A Chain

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

scholarly journals On two extensions of the canonical Feller–Spitzer distribution

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Vladimir Vladimirovich Vinogradov ◽  
Richard Bruce Paris
Keyword(s):  
Hypergeometric Functions ◽  
Exponential Family ◽  
Special Functions ◽  
Natural Exponential Family ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Absolutely Continuous ◽  
The Mean ◽  
Monotone Densities ◽  
Mean Variance

AbstractWe introduce two extensions of the canonical Feller–Spitzer distribution from the class of Bessel densities, which comprise two distinct stochastically decreasing one-parameter families of positive absolutely continuous infinitely divisible distributions with monotone densities, whose upper tails exhibit a power decay. The densities of the members of the first class are expressed in terms of the modified Bessel function of the first kind, whereas the members of the second class have the densities of their Lévy measure given by virtue of the same function. The Laplace transforms for both these families possess closed–form representations in terms of specific hypergeometric functions. We obtain the explicit expressions by virtue of the particular parameter value for the moments of the distributions considered and establish the monotonicity of the mean, variance, skewness and excess kurtosis within the families. We derive numerous properties of members of these classes by employing both new and previously known properties of the special functions involved and determine the variance function for the natural exponential family generated by a member of the second class.

INAR(1) Processes with Inflated-parameter Generalized Power Series Innovations

2020 ◽  
Vol 12 (2) ◽  
Author(s):  
Tito Lívio ◽  
Marcelo Bourguignon ◽  
Fernando Nascimento
Keyword(s):  
Power Series ◽  
Transition Probability ◽  
Innovation Process ◽  
Real Data ◽  
Generalized Power Series ◽  
The Family ◽  
New Models ◽  
Power Series Distributions ◽  
Conditional Maximum ◽  
Mean Variance

AbstractIn this paper, new models are studied by proposing the family of generalized power series distributions with inflated parameter (IGPSD) for the innovation process of the INAR(1) model. The main properties of the process were established, such as mean, variance, autocorrelation and transition probability. The methods of estimation by Yule–Walker and the conditional maximum likelihood were used to estimate the parameters of the models. Two particular cases of the INAR$\left(1\right)$ model with IGPSD innovation were studied, named IPoINAR$\left(1\right)$ and IGeoINAR$\left(1\right)$. Finally, in the real data example, a good performance of the proposed new models was observed.

scholarly journals Phenotype Classification Using Moment Features of Single-Cell Data

2018 ◽  
Vol 17 ◽  
pp. 117693511877170 ◽  
Author(s):  
Chao Sima ◽  
Jianping Hua ◽  
Michael L Bittner ◽  
Seungchan Kim ◽  
Edward R Dougherty
Keyword(s):  
Single Cell ◽  
Tissue Sample ◽  
Synthetic Data ◽  
Real Data ◽  
Higher Order ◽  
The Real ◽  
Phenotype Classification ◽  
The Mean ◽  
Mean Variance ◽  
Cell Data

Features for standard expression microarray and RNA-Seq classification are expression averages over collections of cells. Single cell provides expression measurements for individual cells in a collection of cells from a particular tissue sample. Hence, it can yield feature vectors consisting of higher order and mixed moments. This article demonstrates the advantage of using these expression moments in cancer-related classification. We use synthetic data generated from 2 real networks, the mammalian cell cycle network and a melanoma-related pathway network, and real single-cell data generated via fluorescent protein reporters from 2 cell lines, HT-29 and HCT-116. The networks consist of hidden binary regulatory networks with Gaussian observations. The steady-state distributions of both the original and mutated networks are found, and data are drawn from these for moment-based classification using the mean, variance, skewness, and mixed moments. For the real data, we only observe 1 gene at a time, so that only the mean, variance, and skewness are considered, the analysis being done for 2 genes, EGFR and ERRB2. For the synthetic data, classification improves as we move from just the mean to mean, variance, and skewness and then to these plus the mixed moments. Comparisons are done with 3, 4, or 5 features, using feature selection. Sample size effects are considered. For the real data, we only consider mean, variance, and skewness, with results improving when the higher order moments are used as features.

scholarly journals Parameterization of the COM-Poisson Distribution through the Mean Using Spectral Algorithms for Solving Nonlinear Equations

2019 ◽  
pp. 701-712
Author(s):  
Isaac Adeola Adeniyi ◽  
Dolapo Abidemi Shobanke ◽  
Helen Olaronke Edogbanya
Keyword(s):  
Poisson Distribution ◽  
Nonlinear Equations ◽  
Negative Binomial ◽  
Likelihood Function ◽  
Real Life ◽  
Location Parameter ◽  
Real Data ◽  
Probability Models ◽  
Spectral Algorithm ◽  
The Mean

The Poisson regression is popularly used to model count data. However, real data often do not satisfy the assumption of equality of the mean and variance which is an important property of the Poisson distribution. The Poisson – Gamma (Negative binomial) distribution and the recent Conway-Maxwell-Poisson (COM-Poisson) distributions are some of the proposed models for over- and under-dispersion respectively. Nevertheless, the parameterization of the COM-Poisson distribution still remains a major challenge in practice as the location parameter of the original COM-Poisson distribution rarely represents the mean of the distribution. As a result, this paper proposes a new parameterization of the COM-Poisson distribution via the central location (mean) so that more easily-interpretable models and results can be obtained.  The parameterization involves solving nonlinear equations which do not have analytical solutions. The nonlinear equations are solved using the efficient and fast derivative free spectral algorithm. Implementation of the parameterization in R (R Core Team, 2018) is used to present useful numerical results concerning the relationship between the mean of the COM-Poisson distribution and the location parameter in the original COM-Poisson parameterization. The proposed technique is further used to fit COM-Poisson probability models to real life datasets. It was found that obtaining estimates via this parameterization makes the estimation easier and faster compared to directly maximizing the likelihood function of the standard COM-Poisson distribution.

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