Predicting the trend of non-seasonal data is a difficult task in Social Science. In this research work, we used time series analysis of 144 observations on monthly basis for record of reported cases of tuberculosis pa...Predicting the trend of non-seasonal data is a difficult task in Social Science. In this research work, we used time series analysis of 144 observations on monthly basis for record of reported cases of tuberculosis patients in Minna General Hospital, Niger State from the period of 2007-2018. Exploratory Data Analysis (EDA: Time Plot and Descriptive Statistics), Stationarity Test (ADF), Trend estimation (<i><span style="font-family:Verdana;">T</span><sub><span style="font-family:Verdana;">t</span></sub></i><span style="font-family:Verdana;">), Normality Test, and Forecast evaluation were carried out. The Augmented Dickey Fuller test for stationarity was conducted and the result revealed that the series are not stationary but became stationary after first difference. The correlogram established that the ARIMA (2, 1, 3) was the best model this was further confirmed from the result of L-jung Box. Equation for ARIMA (2, 1, 3) was given as </span><i><span style="font-family:Verdana;">X</span><sub><span style="font-family:Verdana;">t</span></sub></i><span style="font-family:Verdana;"> + 0.6867</span><i><span style="font-family:Verdana;">X</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> – 0.8859</span><i><span style="font-family:Verdana;">X</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;"> = </span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t</span></sub></i><span style="font-family:Verdana;"> + 1.3077</span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">1</span></sub> -<span><span><span style="font-family:;" "=""><span><span style="font-family:Verdana;"> 1.2328</span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;"> + 0.5788</span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">3</span></sub><span style="font-family:Verdana;">. Which was used to predict five years likely cases of tuberculosis in Minna for the period of 2019-2023. It was clearly shown from the projection that the reported cases of tuberculosis reduce year by year by 7% over the period under consideration which could be as a result of intervention from government, health worker, and individuals. In line with these findings, we recommend that the management of general hospital to increase awareness campaign to the public on the causes and dangers of tuberculosis.</span></span></span></span></span>展开更多
This paper addresses the problem of the interpretation of the stochastic differential equations (SDE). Even if from a theoretical point of view, there are infinite ways of interpreting them, in practice only Stratonov...This paper addresses the problem of the interpretation of the stochastic differential equations (SDE). Even if from a theoretical point of view, there are infinite ways of interpreting them, in practice only Stratonovich’s and Itô’s interpretations and the kinetic form are important. Restricting the attention to the first two, they give rise to two different Fokker-Planck-Kolmogorov equations for the transition probability density function (PDF) of the solution. According to Stratonovich’s interpretation, there is one more term in the drift, which is not present in the physical equation, the so-called spurious drift. This term is not present in Itô’s interpretation so that the transition PDF’s of the two interpretations are different. Several examples are shown in which the two solutions are strongly different. Thus, caution is needed when a physical phenomenon is modelled by a SDE. However, the meaning of the spurious drift remains unclear.展开更多
文摘Predicting the trend of non-seasonal data is a difficult task in Social Science. In this research work, we used time series analysis of 144 observations on monthly basis for record of reported cases of tuberculosis patients in Minna General Hospital, Niger State from the period of 2007-2018. Exploratory Data Analysis (EDA: Time Plot and Descriptive Statistics), Stationarity Test (ADF), Trend estimation (<i><span style="font-family:Verdana;">T</span><sub><span style="font-family:Verdana;">t</span></sub></i><span style="font-family:Verdana;">), Normality Test, and Forecast evaluation were carried out. The Augmented Dickey Fuller test for stationarity was conducted and the result revealed that the series are not stationary but became stationary after first difference. The correlogram established that the ARIMA (2, 1, 3) was the best model this was further confirmed from the result of L-jung Box. Equation for ARIMA (2, 1, 3) was given as </span><i><span style="font-family:Verdana;">X</span><sub><span style="font-family:Verdana;">t</span></sub></i><span style="font-family:Verdana;"> + 0.6867</span><i><span style="font-family:Verdana;">X</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> – 0.8859</span><i><span style="font-family:Verdana;">X</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;"> = </span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t</span></sub></i><span style="font-family:Verdana;"> + 1.3077</span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">1</span></sub> -<span><span><span style="font-family:;" "=""><span><span style="font-family:Verdana;"> 1.2328</span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;"> + 0.5788</span><i><span style="font-family:Verdana;">E</span><sub><span style="font-family:Verdana;">t-</span></sub></i><sub><span style="font-family:Verdana;">3</span></sub><span style="font-family:Verdana;">. Which was used to predict five years likely cases of tuberculosis in Minna for the period of 2019-2023. It was clearly shown from the projection that the reported cases of tuberculosis reduce year by year by 7% over the period under consideration which could be as a result of intervention from government, health worker, and individuals. In line with these findings, we recommend that the management of general hospital to increase awareness campaign to the public on the causes and dangers of tuberculosis.</span></span></span></span></span>
文摘This paper addresses the problem of the interpretation of the stochastic differential equations (SDE). Even if from a theoretical point of view, there are infinite ways of interpreting them, in practice only Stratonovich’s and Itô’s interpretations and the kinetic form are important. Restricting the attention to the first two, they give rise to two different Fokker-Planck-Kolmogorov equations for the transition probability density function (PDF) of the solution. According to Stratonovich’s interpretation, there is one more term in the drift, which is not present in the physical equation, the so-called spurious drift. This term is not present in Itô’s interpretation so that the transition PDF’s of the two interpretations are different. Several examples are shown in which the two solutions are strongly different. Thus, caution is needed when a physical phenomenon is modelled by a SDE. However, the meaning of the spurious drift remains unclear.
