For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characteri...For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.展开更多
In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the...In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14<sup>th</sup> March 2020 to 1<sup>st</sup> February 2021. The first wave was experienced from 14<sup>th</sup> March 2020 to 15<sup>th</sup> September 2020, the second wave from around 15<sup>th</sup> September 2020 to 1<sup>st</sup> February 2021 and the third wave was experienced from 1<sup>st</sup> February 2021 to 3<sup>rd</sup> June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.展开更多
基金Supported by Nature Science Foundation of Hainan Province (Grant No. 118MS040,2018CXTD338)NSF of Higher Education Institutions of Hainan Province (Grant No. Hnky2018ZD-6)National Natural Science Foundation of China (Grant No. 11861029)。
文摘For multi-dimensional integer-valued sequence, a new proof of the upper-bound and lower-bound estimations on the product of all its components is given in this paper. Those estimations are very important to characterize the Kondratiev space of random test function, in which space it is convenient to study random distribution,random partial differential equation and other problems.
文摘In this paper, a Negative Binomial (NB) Integer-valued Autoregressive model of order 1, INAR (1), is used to model and forecast the cumulative number of confirmed COVID-19 infected cases in Kenya independently for the three waves starting from 14<sup>th</sup> March 2020 to 1<sup>st</sup> February 2021. The first wave was experienced from 14<sup>th</sup> March 2020 to 15<sup>th</sup> September 2020, the second wave from around 15<sup>th</sup> September 2020 to 1<sup>st</sup> February 2021 and the third wave was experienced from 1<sup>st</sup> February 2021 to 3<sup>rd</sup> June 2021. 5, 10, and 15-day-ahead forecasts are obtained for these three waves and the performance of the NB-INAR (1) model analysed.
