• Title/Summary/Keyword: Gompertz 곡선

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Determination of starting values in estimating growth curves by using non-linear least squares (비선형 최소자승법을 이용한 성장곡선 모형의 매개변수 추정시 초기값 설정 방법에 관한 연구)

  • Youm, Se-Kyoung;Hong, Seung-Pyo;Kang, Hoe-Il;Kim, Ji-Soo;Jun, Chi-Hyuck
    • IE interfaces
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    • v.14 no.2
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    • pp.190-197
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    • 2001
  • Growth curves including Logistic and Gompertz functions are widely used in forecasting the market demand. To estimated the parameters of those functions, we use the non-linear least square method. However, it is difficult to set up the starting points for each parameter. If a wrong starting point is selected, the result reveals the local optimum or does not converge to a certain value. The purpose of this paper is to resolve the problem of selecting a starting point. Especially, rescaling the market data using the national economic index make it possible to figure out the range of parameters and to utilize the grid search method. Applications to some real data are also included.

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Development of Market Growth Pattern Map Based on Growth Model and Self-organizing Map Algorithm: Focusing on ICT products (자기조직화 지도를 활용한 성장모형 기반의 시장 성장패턴 지도 구축: ICT제품을 중심으로)

  • Park, Do-Hyung;Chung, Jaekwon;Chung, Yeo Jin;Lee, Dongwon
    • Journal of Intelligence and Information Systems
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    • v.20 no.4
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    • pp.1-23
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    • 2014
  • Market forecasting aims to estimate the sales volume of a product or service that is sold to consumers for a specific selling period. From the perspective of the enterprise, accurate market forecasting assists in determining the timing of new product introduction, product design, and establishing production plans and marketing strategies that enable a more efficient decision-making process. Moreover, accurate market forecasting enables governments to efficiently establish a national budget organization. This study aims to generate a market growth curve for ICT (information and communication technology) goods using past time series data; categorize products showing similar growth patterns; understand markets in the industry; and forecast the future outlook of such products. This study suggests the useful and meaningful process (or methodology) to identify the market growth pattern with quantitative growth model and data mining algorithm. The study employs the following methodology. At the first stage, past time series data are collected based on the target products or services of categorized industry. The data, such as the volume of sales and domestic consumption for a specific product or service, are collected from the relevant government ministry, the National Statistical Office, and other relevant government organizations. For collected data that may not be analyzed due to the lack of past data and the alteration of code names, data pre-processing work should be performed. At the second stage of this process, an optimal model for market forecasting should be selected. This model can be varied on the basis of the characteristics of each categorized industry. As this study is focused on the ICT industry, which has more frequent new technology appearances resulting in changes of the market structure, Logistic model, Gompertz model, and Bass model are selected. A hybrid model that combines different models can also be considered. The hybrid model considered for use in this study analyzes the size of the market potential through the Logistic and Gompertz models, and then the figures are used for the Bass model. The third stage of this process is to evaluate which model most accurately explains the data. In order to do this, the parameter should be estimated on the basis of the collected past time series data to generate the models' predictive value and calculate the root-mean squared error (RMSE). The model that shows the lowest average RMSE value for every product type is considered as the best model. At the fourth stage of this process, based on the estimated parameter value generated by the best model, a market growth pattern map is constructed with self-organizing map algorithm. A self-organizing map is learning with market pattern parameters for all products or services as input data, and the products or services are organized into an $N{\times}N$ map. The number of clusters increase from 2 to M, depending on the characteristics of the nodes on the map. The clusters are divided into zones, and the clusters with the ability to provide the most meaningful explanation are selected. Based on the final selection of clusters, the boundaries between the nodes are selected and, ultimately, the market growth pattern map is completed. The last step is to determine the final characteristics of the clusters as well as the market growth curve. The average of the market growth pattern parameters in the clusters is taken to be a representative figure. Using this figure, a growth curve is drawn for each cluster, and their characteristics are analyzed. Also, taking into consideration the product types in each cluster, their characteristics can be qualitatively generated. We expect that the process and system that this paper suggests can be used as a tool for forecasting demand in the ICT and other industries.

Characteristics of Individual Growth Curve by Porcine LEPR-derived Microsatellite Polymorphisms (돼지의 Leptin receptor 유전자내 초위성체 다형성에 따른 개체별 성장곡선 특성)

  • Cho, Y.M.;Choi, B.H.;Kim, T.H.;Lee, J.W.;Cheong, I.C.
    • Journal of Animal Science and Technology
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    • v.45 no.6
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    • pp.885-890
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    • 2003
  • This study was conducted to estimate the growth curve parameters of 253 heads of F2 population produced by inter-crossing F1 from Korean Native boars and Landrace sows, and to estimate the effects of Leptin receptor gene(LEPR) on their growth characteristics. Growth curve parameters were estimated from nonlinear regression using Gompertz model individually. Average mature weight and average maturing rate estimated were 179.69${\pm}$4.40kg and 0.3103${\pm}$0.0043, respectively. The effect of sex was insignificant for all the parameters estimated from Gempertz model(p〉.05), and the effect of calving group was significant for mature weight and maximum growth rate at inflection point (p〈.05). The effect of LEPR genotype were significant for all the growth curve parameters(p〈.05). According from the results of the least squares means of growth curve parameters by LEPR genotypes, mature weight and point of inflection were highest in genotype AA in which the maturing rate was the lowest, and were lowest in genotype DD in which maturing rate was the highest, reversely.

A Study on forecasting the long-run path of the Korean bioindustry based on the experiences of the U.S. BT and the Korean ICT industries (미국 BT와 한국 ICT 산업 연구를 통한 한국 바이오산업 장기전망에 관한 연구)

  • Moon, Sunung;Kim, Minseong;Jeon, Yongil
    • International Area Studies Review
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    • v.13 no.3
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    • pp.331-359
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    • 2009
  • We forecast the performance of the Korean biotechnology industry by adopting similar development paths taken by the U.S. biotechnology and Korean ICT industries. Our long-term forecasting techniques predict that Korean BT market size will increase from 3.7 billion to 10.8 billion U.S. dollars by year 2030. The pharmaceutical industry, one of major bio-subindustries, is expected to dominate Korean BT market in the long-run. Also, the relative portion of the exports in the Korean BT industry will be larger and thus the export-oriented government policy is required for the long-run growth of the Korean BT industry. Since the Korean ICT industry has already slowed down in the development, Korean BT industry is likely to catch up with ICT industry in the near future.

Anaerobic Co-Digestion Characteristics of Food Waste Leachate and Sewage Sludge (BMP test를 통한 음폐수와 하수슬러지의 병합소화 특성 평가)

  • Lee, Suyoung;Yoon, Young-Sam;Kang, Jun-Gu;Kim, Ki-Heon;Shin, Sun Kyoung
    • Journal of the Korea Organic Resources Recycling Association
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    • v.24 no.1
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    • pp.21-29
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    • 2016
  • We mix food waste leachate and sewage sludge by the proportion of 1:9, 3:7 and 5:5. It turns out that they produced 233, 298 and 344 $CH_4{\cdot}mL/g{\cdot}VS$ of methane gas. The result suggests that as the mixing rate of food waste leachate rises, the methane gas productions increases as well. And more methane gas is made when co-digesting sewage sludge and food waste leachate based on the mixing ratio, rather than digesting only sewage sludge alone. Modified Gompertz and Exponential Model describe the BMP test results that show how methane gas are produced from organic waste. According to the test, higher the mixing rate of food waste leachate is, higher the methane gas productions is. The mixing ratio of food waste leachate that produces the largest volume of methane gas is 3:7. Modified Gompertz model and Exponential model describe the test results very well. The correlation values($R^2$) that show how the results of model prediction and experiment are close is 0.92 to 0.98.

Study on the Optimum Range of Weight-Age Data for Estimation of Growth Curve Parameters of Hanwoo (한우의 체중 성장곡선 모수 추정을 위한 체중 측정 자료의 최적 범위에 관한 연구)

  • Cho, Y.M.;Yoon, H.B.;Park, B.H.;Ahn, B.S.;Jeon, B.S.;Park, Y.I.
    • Journal of Animal Science and Technology
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    • v.44 no.2
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    • pp.165-170
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    • 2002
  • Mature weight (A) and rate of maturing (k) estimated by nonlinear regression were studied to determine the optimum age range over which the estimate of growth curve parameters can be estimated. The weight-age data from 1,133 Hanwoo bulls at Hanwoo Improvement Center of N.A.C.F. were used to fit the growth curve using Gompertz model. All available weight data from birth to the specific age of months were used for the estimation of parameters: the six specific ages used were 12, 14, 16, 18, 20 22 and 24 months of age. The mean estimates of mature weight (A) were 966.5, 1,255.9, 1,126.2, 916.5, 842.2, 780.9 and 767.0kg for ages 12 through 24 months, respectively. The mean estimates of mature weight (A) to 22 and 24 months of age were not different from each other. However, they were different from the estimates based on the data to other ages. Mean estimates of rate of maturing (k) were 3.362, 3.595, 3.536, 3.421, 3.403, 3.409 and 3.411 for ages 12 through 24 months, respectively. The mean estimates of maturing rate (k) for ages 18 through 24 months of age were not significantly different from each other. However, they were different from the estimates based on the data to other ages. Correlations among estimates of A at various ages showed the highest value of 0.93 between 22 and 24 months. Correlations among estimates of k at various ages were highest ranging from 0.91 to 0.99 among 18 to 24 months. The correlations between A and k were positive and tended to decrease with the increase of the age from 0.84 for the age of 12 months to 0.10 for the age of 24 months. Thus, the estimates of growth curve parameters, A and k, suitable for genetic studies can be derived from accumulated Hanwoo bulls after 22 months of age.

A Study on Estimation of Individual Growth Curve Parameters and their Relationships with Meat Quality Traits of Crossbred between Korean Native Boars and Landrace Sows (재래돼지와 랜드레이스 교잡종의 개체별 성장곡선 추정 및 육질형질과의 상관관계 추정에 관한 연구)

  • Cho, Y.M.;Choi, B.H.;Kim, T.H.;Lee,, J.W.;Lee, J.E.;Oh, S.J.;Cheong, I.C.
    • Journal of Animal Science and Technology
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    • v.46 no.4
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    • pp.503-508
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    • 2004
  • This study was conducted to estimate the growth curve parameters of crossbreds between Korean native boars and Landrace sows and their relationships with meat qualities. The data used were weight-age data and carcass data from 131 males and 122 females raised at N.L.R.I in Korea. Growth curve parameters were estimated from nonlinear regression using Gompertz model individually. Average mature weight(A), average maturing rate(k), and average inflection point(u) showing maximum growth rate estimated were 179.54${\pm}$6.06kg, 0.3154${\pm}$0.0059, and 5.50${\pm}$0.11 months in females, and 179.84${\pm}$6.33kg, 0.3049${\pm}$0.0061, and 5.24${\pm}$0.13 months in males, respectively. For the growth curve parameters and derived statistics, the phenotypic correlations of maturing rate with gain rate at inflection, mature weight, and inflection point were - .30, - .77, and - .93 in male, and - .31, - .78 and - .94 in female, respectively. Matrure weight was positively correlated to the inflection point as + .89 in both male and female, indicating that late maturing pigs with lower k had longer maturing period with increasing gain rate and reached point of inflection later than early maturing pigs with higher k, and grew to larger mature weight. Backfat thickness and erode fat contents were correlated with mature weight positively in male and negatively in female, and correlated with gain rate at inflection point positively in both male and female, of which coefficients were as high as .42 and .50 in male, respectively.

Forecasting for the Demand on Water Amenity Zones in the Large Rivers Based on Regional Characteristics and Monthly Variation (지역 특성 및 월간 변화를 고려한 대하천 수변 친수지구 이용수요 예측)

  • Suh, Myong-kyo;Rhee, Dong Sop
    • Journal of Wetlands Research
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    • v.17 no.4
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    • pp.436-446
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    • 2015
  • It is suggested investigating method about the existing state of demand in this study. The total demand of 357 water amenity zones in 2014 is estimated based on the growth curve models. The effects of population density and distances between water amenity zones and metropolises populated over 1 million are investigated on each river system. The suitability like RMSE and MAPE of logistic and gompertz models are considered to select more suitable model for each water amenity zone. Demand for water amenity zones in 2014 is seemed to be rather high at Han Gang river system and Chungcheongbukdo after analyzing. The influence of population density is rarely effective except Geum Gang river system. The influence of metropolis on the demand for water amenity zones is higher at Geum Gang river system than others.

The Growth-Curve Analysis of Tobacco in Various Cultivation Types (잎담배의 재배방법에 따른 생장 분석에 대하여)

  • 김윤동;김용암
    • Journal of the Korean Society of Tobacco Science
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    • v.2 no.2
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    • pp.44-50
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    • 1980
  • The growth of flue-cured tobacco was analyzed with the mathematical treatment. The results are summarized as followings: 1. The growth curve was fitted to the quadratic polynomial equation in improved-mulching cultivation, blot to the Gompertz equation in the other cultivations. 2. The initial point of the maximum growth phase for dry weight was about 50 days after transplanting in improved-mulching cultivation, but about 40 days in the other cultivations, and the maximum growth period was for 25 days in all cultivations. 3. The growth rate of the maximum growth period in dry weight decreased in the order of improved-mulching cultivation, mulching cultivation, and non-mulching cultivation. 4. A relative growth amount in the maximum growth period was higher in later sowing. 5. The length of maximum growth was 5 days shorter in leaf area than in dry weight. The maximum growth phase was 7 days earlier in leaf area than in dry weight.

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Re-estimation of Model Parameters in Growth Curves When Adjusting Market Potential and Time of Maximum Sales (성장곡선 예측 모형의 특성치 보정에 따른 매개변수의 재추정)

  • Park, Ju-Seok;Ko, Young-Hyun;Jun, Chi-Hyuck;Lee, Jae-Hwan;Hong, Seung-Pyo;Moon, Hyung-Don
    • IE interfaces
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    • v.16 no.1
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    • pp.103-110
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    • 2003
  • Growth curves are widely used in forecasting the market demand. When there are only a few data points available, the estimated model parameters have a low confidence. In this case, if some expert opinions are available, it would be better for predicting future demand to adjust the model parameters using these information. This paper proposes the methodology for re-estimation of model parameters in growth curves when adjusting market potential and/or time of maximum sales. We also provide the detailed procedures for five growth curves including Bass, Logistic, Gompertz, Weibull and Cumulative Lognormal models. Applications to real data are also included.