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Paulo Roberto Prezotti Filho  One of the best experts on this subject based on the ideXlab platform.

a periodic and seasonal statistical model for non Negative Integer valued time series with an application to dispensed medications in respiratory diseases
Applied Mathematical Modelling, 2021CoAuthors: Paulo Roberto Prezotti Filho, Valderio Anselmo Reisen, Pascal Bondon, Marton Ispany, Milena M Melo, Faradiba Sarquis SerpaAbstract:Abstract This paper introduces a new class of models for nonNegative Integervalued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasimaximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitoria, Brazil.
Faradiba Sarquis Serpa  One of the best experts on this subject based on the ideXlab platform.

a periodic and seasonal statistical model for non Negative Integer valued time series with an application to dispensed medications in respiratory diseases
Applied Mathematical Modelling, 2021CoAuthors: Paulo Roberto Prezotti Filho, Valderio Anselmo Reisen, Pascal Bondon, Marton Ispany, Milena M Melo, Faradiba Sarquis SerpaAbstract:Abstract This paper introduces a new class of models for nonNegative Integervalued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasimaximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitoria, Brazil.
Valderio Anselmo Reisen  One of the best experts on this subject based on the ideXlab platform.

a periodic and seasonal statistical model for non Negative Integer valued time series with an application to dispensed medications in respiratory diseases
Applied Mathematical Modelling, 2021CoAuthors: Paulo Roberto Prezotti Filho, Valderio Anselmo Reisen, Pascal Bondon, Marton Ispany, Milena M Melo, Faradiba Sarquis SerpaAbstract:Abstract This paper introduces a new class of models for nonNegative Integervalued time series with a periodic and seasonal autoregressive structure. Some properties of the model are discussed and the conditional quasimaximum likelihood method is used to estimate the parameters. The consistency and asymptotic normality of the estimators are established. Their performances are investigated for finite sample sizes and the empirical results indicate that the method gives accurate estimates. The proposed model is applied to analyse the daily number of antibiotic dispensing medication for the treatment of respiratory diseases, registered in a health center of Vitoria, Brazil.
Apoloniusz Tyszka  One of the best experts on this subject based on the ideXlab platform.

a function f n 0 n 0 that cannot be bounded by a computable function and an infinite loop in mupad such that it takes as input a positive Integer n returns non Negative Integers g n m m 1 2 3 and f n g n m for any m f n
2013CoAuthors: Apoloniusz TyszkaAbstract:For a positive Integer n, let f(n) denote the smallest nonNegative Integer b such that for each system S \subseteq {x_k=1,x_i+x_j=x_k,x_i*x_j=x_k: i,j,k \in {1,...,n}} with a solution in nonNegative Integers x_1,...,x_n, there exists a solution of S in {0,...,b}^n. We prove that the function f is strictly increasing and dominates all computable functions. We present an infinite loop in MuPAD which takes as input a positive Integer n and returns a nonNegative Integer on each iteration. Let g(n,m) denote the number returned on the mth iteration, if n is taken as input. Then, g(n,m) \leq m1, 0=g(n,1) N that cannot be bounded by any computable function. This code takes as input a nonNegative Integer n, immediately returns 0, and computes a system S of polynomial equations. If the loop terminates for S, then the next instruction is executed and returns \xi(n).

mupad codes which implement limit computable functions that cannot be bounded by any computable function
arXiv: Computational Complexity, 2013CoAuthors: Apoloniusz TyszkaAbstract:For a positive Integer n, let f(n) denote the smallest nonNegative Integer b such that for each system S \subseteq {x_k=1,x_i+x_j=x_k,x_i*x_j=x_k: i,j,k \in {1,...,n}} with a solution in nonNegative Integers x_1,...,x_n, there exists a solution of S in {0,...,b}^n. We prove that the function f is strictly increasing and dominates all computable functions. We present an infinite loop in MuPAD which takes as input a positive Integer n and returns a nonNegative Integer on each iteration. Let g(n,m) denote the number returned on the mth iteration, if n is taken as input. Then, g(n,m) \leq m1, 0=g(n,1)<1=g(n,2) \leq g(n,3) \leq g(n,4) \leq ... and g(n,f(n))
N that cannot be bounded by any computable function. This code takes as input a nonNegative Integer n, immediately returns 0, and computes a system S of polynomial equations. If the loop terminates for S, then the next instruction is executed and returns \xi(n).
Klaus L P Vasconcellos  One of the best experts on this subject based on the ideXlab platform.

first order non Negative Integer valued autoregressive processes with power series innovations
Brazilian Journal of Probability and Statistics, 2015CoAuthors: Marcelo Bourguignon, Klaus L P VasconcellosAbstract:In this paper, we introduce a first order nonNegative Integer valued autoregressive process with power series innovations based on the binomial thinning. This new model contains, as particular cases, several models such as the Poisson INAR(1) model (AlOsh and Alzaid (J. Time Series Anal. 8 (1987) 261–275)), the geometric INAR(1) model (Jazi, Jones and Lai (J. Iran. Stat. Soc. (JIRSS) 11 (2012) 173–190)) and many others. The main properties of the model are derived, such as mean, variance and the autocorrelation function. Yule–Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Special submodels are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new model.