scholarly journals On stability Conditions of Burr X Autoregressive model

2019 ◽  
Vol 24 (5) ◽  
pp. 91
Author(s):  
Zena. S. Khalaf ◽  
, Azher. A. Mohammad
Keyword(s):  
Limit Cycle ◽  
Autoregressive Model ◽  
Cumulative Distribution Function ◽  
Linearization Method ◽  
Cumulative Distribution ◽  
Stability Conditions ◽  
Proposed Model ◽  
Nonlinear Autoregressive Model ◽  
Nonlinear Autoregressive ◽  
Local Linearization Method

This article deals with proposed nonlinear autoregressive model based on Burr X cumulative distribution function known as Burr X AR (p), we demonstrate stability conditions of the proposed model in terms of its parameters by using dynamical approach known as local linearization method to find stability conditions of a nonzero fixed point of the proposed model, in addition the study demonstrate stability condition of a limit cycle if Burr X AR (1) model have a limit cycle of period greater than one.   http://dx.doi.org/10.25130/tjps.24.2019.096

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

scholarly journals On the Analysis of New COVID-19 Cases in Pakistan Using an Exponentiated Version of the M Family of Distributions

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 953
Author(s):  
Rashad A. R. Bantan ◽  
Christophe Chesneau ◽  
Farrukh Jamal ◽  
Mohammed Elgarhy
Keyword(s):  
Statistical Models ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Exponential Distributions ◽  
New Family ◽  
Proposed Model ◽  
Complete Study ◽  
Probability And Statistics ◽  
Definition Of ◽  
Analyze Data

This paper develops the exponentiated Mfamily of continuous distributions, aiming to provide new statistical models for data fitting purposes. It stands out from the other families, as it depends on two baseline distributions, with the use of ratio and power transforms in the definition of the main cumulative distribution function. Thanks to the joint action of the possibly different baseline distributions, flexible statistical models can be created, motivating a complete study in this regard. Thus, we discuss the theoretical properties of the new family, with emphasis on those of potential interest to the overall probability and statistics. Then, a new three-parameter lifetime distribution is derived, with the choices of the inverse exponential and exponential distributions as baselines. After pointing out the great flexibility of the related model, we apply it to analyze an actual dataset of current interest: the daily COVID-19 cases observed in Pakistan from 21 March to 29 May 2020 (inclusive). As notable results, we demonstrate that the proposed model is the best among the 15 top ranked models in the literature, including the inverse exponential and exponential models, several modern extensions of them depending on more parameters, and the “unexponentiated” version of the proposed model as well. As future perspectives, the proposed model can be of interest to analyze data on COVID-19 cases in other countries, for possible comparison studies.

scholarly journals A Load-Share Reliability Model under the Changeable Piecewise Smooth Load

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Sergey V. Gurov ◽  
Lev V. Utkin
Keyword(s):  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Continuous Functions ◽  
Piecewise Smooth ◽  
Cumulative Distribution ◽  
Residual Lifetime ◽  
Time To Failure ◽  
Reliability Model ◽  
Piecewise Constant ◽  
Proposed Model

A new load-share reliability model of systems under the changeable load is proposed in the paper. It is assumed that the load is a piecewise smooth function which can be regarded as an extension of the piecewise constant and continuous functions. The condition of the residual lifetime conservation, which means continuity of a cumulative distribution function of time to failure, is accepted in the proposed model. A general algorithm for computing reliability measures is provided. Simple expressions for determining the survivor functions under assumption of the Weibull probability distribution of time to failure are given. Various numerical examples illustrate the proposed model by different forms of the system load and different probability distributions of time to failure.

scholarly journals Geomorphology-Wavelet based approach to rainfall runoff modeling for data scarce semi-arid regions, Kolar River catchment, India

2021 ◽  
Author(s):  
Deepak Kumar Tiwari ◽  
◽  
Tiwari H. L. ◽  
Raman Nateriya ◽  
◽  
...  
Keyword(s):  
Autoregressive Model ◽  
Water Resource Management ◽  
Kendall Test ◽  
Rainfall Runoff ◽  
Ungauged Catchments ◽  
Slope Test ◽  
Runoff Modeling ◽  
Nonlinear Autoregressive Model ◽  
Nonlinear Autoregressive ◽  
Semi Arid

The conceptual and physical mathematical model of rainfall-runoff modeling uses various parameters such as land use land cover, soil type classification, rainfall, atmospheric data such as temperature, evapotranspiration, solar radiation and wind speed, etc. But these data may not be available for developing countries and data scares semi-arid watershed. Also, the problem is even more critical for ungauged catchments and where manual record is maintained of water level and rainfall data. To address this issue, trend analysis is performed using Mann-Kendall test and Sen’s slope test which shows significant trend change stressing the need for new method for runoff prediction for better water resource management. In this study, a total of four models namely nonlinear autoregressive model with exogenous inputs lumped (LNARX), nonlinear autoregressive model with exogenous geomorphometrically processed inputs (GNARX), wavelet nonlinear autoregressive model with exogenous inputs (WLNARX) and nonlinear autoregressive model with exogenous geomorphometrically processed inputs (WGNARX). Ten models with different input combinations were selected based on their performance are analyzed for all the four networks. The best performing model for these networks is model no. 6 with WGNARX network with NSE 0.97 and RMSE 0.97 and with least value of RMSE. This method can be applied to data scarce region where data available are available for shorter duration and helpful for ungauged catchments also.

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