• Management Science and Financial Engineering
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• v.14 no.2
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• pp.89-104
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• 2008

Growth curves including Bass, Logistic and Gompertz functions are widely used in forecasting the market demand. Nonlinear least square method is often adopted for estimating the model parameters but it is difficult to set up the starting value for each parameter. If a wrong starting point is selected, the result may lead to erroneous forecasts. This paper proposes a method of selecting starting values for model parameters in estimating some growth curves by nonlinear least square method through grid search and transformation into linear regression model. Resealing the market data using the national economic index makes it possible to figure out the range of parameters and to utilize the grid search method. Application to some real data is also included, where the performance of our method is demonstrated.

• Computers and Concrete
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• v.5 no.3
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• pp.261-277
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• 2008

This paper presents methodologies for remaining life prediction of plain concrete structural components considering tension softening effect. Non-linear fracture mechanics principles (NLFM) have been used for crack growth analysis and remaining life prediction. Various tension softening models such as linear, bi-linear, tri-linear, exponential and power curve have been presented with appropriate expressions. A methodology to account for tension softening effects in the computation of SIF and remaining life prediction of concrete structural components has been presented. The tension softening effects has been represented by using any one of the models mentioned above. Numerical studies have been conducted on three point bending concrete structural component under constant amplitude loading. Remaining life has been predicted for different loading cases and for various tension softening models. The predicted values have been compared with the corresponding experimental observations. It is observed that the predicted life using bi-linear model and power curve model is in close agreement with the experimental values. Parametric studies on remaining life prediction have also been conducted by using modified bilinear model. A suitable value for constant of modified bilinear model is suggested based on parametric studies.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.12
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• pp.295-303
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• 2021

The aim of this study is to analyze the effects of oil prices on economic growth and exchange rate in Saudi Arabia during the period 1980-2020. For this purpose, the linear and nonlinear ARDL models are estimated. The linear ARDL model shows that the oil price and economic growth are cointegrated. Moreover, the two variables have a significant positive association in the long run. However, the oil price has no significant impact on the exchange rate. When estimating the nonlinear ARDL model, it has been shown that oil price is only cointegrated with economic growth but not with the exchange rate. The estimation of nonlinear effects using the nonlinear ARDL model shows that economic growth is affected by both positive and negative oil shocks in the long run. However, the impact of positive shocks is higher than those of negative shocks. Moreover, results show that the short-run effects of positive and negative oil shocks are not statistically significant. Regarding the exchange rate, our results show that the effects of positive and negative oil shocks are not statistically significant. Consequently, this study concludes that the oil price has an asymmetric effect on economic growth in Saudi Arabia, but not on the exchange rate.

• Asia pacific journal of information systems
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• v.25 no.3
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• pp.563-578
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• 2015

Forecasting daily box-office performance is critical for planning the distribution of marketing resources, and by extension, maximizing profits. For certain movies, the number of viewers increases rapidly at the beginning of their theatrical run, and the increments slow down later. Other movies are not popular in the beginning, but the audience sizes grow rapidly afterward. Thus, the audience attendance of movies grow in different trajectories, which are influenced by various factors including marketing budget, distributors, directors, actors, and word of mouth. In this paper, we propose a method for predicting the daily performance trajectory of running movies based on the hierarchical linear model. More specifically, we focus on the effect of online word of mouth on the shape of the growth curves. We fitted the mean trajectory of the cumulative audience size as a cubic function of time, and allowed the intercept and slope to vary movie-to-movie. Moreover, we fitted the linear slope with a function of online word of mouth predictors to help determine the shape of the trajectories. Finally, we provide performance predictions for individual movies.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.81-94
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• 1996

This paper suggests a new criterion for testing the general linear hypothesis about coefficients in multivariate growth curve model. It is developed from a Bayesian point of view using the highest posterior density region methodology. Likelihood ratio test criterion(LRTC) by Khatri(1966) results as an approximate special case. It is shown that under the simple case of vague prior distribution for the multivariate normal parameters a LRTC-like criterion results; but the degrees of freedom are lower, so the suggested test criterion yields more conservative test than is warranted by the classical LRTC, a result analogous to that of Berger and Sellke(1987). Moreover, more general(non-vague) prior distributions will generate a richer class of tests than were previously available.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.479-484
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• 2000

A Navier-stokes based finite volume method has been developed to analyze an incompressible, steady state, turbulent wall-jet flow. The standard k-e model, the RNG ${\kappa}-{\varepsilon}$ model and their nonlinear counterparts are adopted as a closure relationship. Comparison with the experimental data shows that a linear ${\kappa}-{\varepsilon}$ model performs satisfatorily for two-dimensional wall-jet flows. However, as the flow becomes three dimensional, the linear model fails to predict the spanwise jet growth accurately and the nonlinear model needs to be adopted to capture three-dimensional flow characteristics.

• Korean Journal of Environmental Agriculture
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• v.39 no.3
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• pp.204-213
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• 2020

BACKGROUND: Since the number of crops cultivated in reclaimed land is huge, it is very difficult to quantify the total crop production. Therefore, a non-destructive method for predicting crop production is needed. Salt tolerant root vegetables such as red beets and sugar beet are suitable for cultivation in reclaimed land. If their underground biomass can be predicted, it helps to estimate crop productivity. Objectives of this study are to investigate maximum leaf length and weight of red beet, sugar beet, and turnips grown in reclaimed land, and to determine optimal model with regression analysis for linear and allometric growth models. METHODS AND RESULTS: Maximum leaf length, width, and root fresh weight of red beets, sugar beets, and turnips were measured. Ten linear models and six allometric growth models were selected for estimation of root fresh weight and non-linear regression analysis was conducted. The allometric growth model, which have a variable multiplied by square of maximum leaf length and maximum leaf width, showed highest R² values of 0.67, 0.70, and 0.49 for red beets, sugar beets, and turnips, respectively. Validation results of the models for red beets and sugar beets showed the R² values of 0.63 and 0.65, respectively. However, the model for turnips showed the R² value of 0.48. The allometric growth model was suitable for estimating the root fresh weight of red beets and sugar beets, but the accuracy for turnips was relatively low. CONCLUSION: The regression models established in this study may be useful to estimate the total production of root vegetables cultivated in reclaimed land, and it will be used as a non-destructive method for prediction of crop information.

• Journal of The Korean Society of Agricultural Engineers
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• v.52 no.6
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• pp.19-26
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• 2010

Batch experiments were conducted to investigate growth and nutrient removal performance of microalgae Chlorella vulgaris by using piggery wastewater in different concentration of pollutants and the common growth models (logistic, Gompertz and Richards) were applied to compare microalgal growth parameters. Removal of nitrogen (N) and phosphorus (P) by Chlorella vulgaris showed correlation with biomass increase, implying nutrient uptake coupled with microalgae growth. The higher the levels of suspended solids (SS), COD and ammonia nitrogen were in the wastewater, the worse growth of Chlorella vulgaris was observed, showing the occurrence of growth inhibition in higher concentration of those pollutants. The growth parameters were estimated by non-linear regression of three growth curves for comparative analyses. Determination of growth parameters were more accurate with population as a variable than the logarithm of population in terms of R square. Richards model represented better fit comparing with logistic and Gompertz model. However, Richards model showed some complexity and sensitivity in calculation. In the cases tested, both logistic and Gompertz equation were proper to describe the growth of microalgae on piggery wastewater as well as easy to application.

• The KIPS Transactions:PartD
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• v.11D no.7 s.96
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• pp.1451-1458
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• 2004

Current software reliability growth models based on Gompertz growth curve are all logarithmic type. Software reliability growth models based on logarithmic type Gompertz growth curve has difficulties in parameter estimation. Therefore this paper proposes a software reliability growth model based on the logistic type Gompertz growth curie. Its usefulness is empirically verified by analyzing the failure data sets obtained from 13 different software projects. The parameters of model are estimated by linear regression through variable transformation or Virene's method. The proposed model is compared with respect to the average relative prediction error criterion. Experimental results show that the pro-posed model performs better the models based on the logarithmic type Gompertz growth curve.

• Journal of the Korean Society of Combustion
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• v.17 no.2
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• pp.17-23
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• 2012

In this study, thermoacoustic analysis model was developed in order to predict both eigenfrequencies and initial growth rate of combustion instabilities for lean premixed gas turbine combustors. As a first step, a model combustor and nozzle were selected and analytical linear equations for thermoacoustic waves were derived for a given combustion system. Then, methods showing how the equations can be used for analysis of the combustion instability were suggested. It was found that the prediction results showed a good agreement with the measurements. However, there were some limitation in growth rate predictions, which were related with over-simplification of flame structure, acoustic boundary conditions, and temperature distribution in the combustor.