A novel unit exponential regression model with improved estimation method under multicollinearity

An improved method for estimating capillary pressure from 3D microtomography images and its application to the study of disconnected nonwetting phase

This paper considered a long term electric power load forecast for twenty years (20 years) projection, in Nigeria power system using least-square regression and exponential regression model. The model is implemented in Matlab platform with a plot in residential load demand, commercial load demand and industrial load demand in (MW). In the quest for analysis and predicting the energy (power) demand (MW) requirement for a projection period of (2013 - 2032), data are collected between (2000 - 2012), from the Central Bank of Nigeria (CBN), and National Bureau of statistics (NBS). The results obtained shows that energy generated from the respective generating station including Egbin thermal power station Lagos, Sapele thermal power station etc. are grossly inadequate. This mismatch is a major problem in power system planning and operation. The result also shows that there is deviation between predicted energy demand (MW) and available power (or capacity allocated). The predicted energy demand into the projected future of 20years is 45 5,870.2MW. The paper work also extended the prediction form into: least-square, exponential regression model. Evidently, the comparism plot for linear and exponential model which shows similar predicting pattern: particularly least-square exhibit linear behavior, while exponential shows non-linear behaviour, the linear model gives more accurate result as compared to the exponential.

In this paper, we will rely on a probability distribution, which is the exponential distribution, to build a parametric survival regression model, which is the exponential survival regression model, relying on the Cox regression model to be used in forming this model. The data used in this research were obtained through the Cancer Council in Iraq, which is affiliated with the Ministry of Health. The data was represented by a figure of patients with stomach cancer for a period of two years (2021-2022), who were registered from the onset of symptoms to hospitalization and then death or recovery., and they numbered 200 sick, the data represents the length of stay of patients in the hospital in months. This aims to study the effect of some explanatory variables on the length of survival of stomach cancer patients. The model was used to analyze the data and estimate the parameters of this model using the Bayesian method, and using goodness-of-fit tests provided by the statistical program. The ready-made Easy Fit 5.6 test is the Kolmokrov-Smirnov test, the Anderson-Darlink test, and the Chi-Squared test. It turns out that the exponential survival regression model is the most appropriate model for the data of this research, use a program (R 4.3.1), one of the most important conclusions reached was the great convergence between the exponential survival regression model for the estimated values Use a Bayesian method and the exponential survival regression model for the original values. This indicates the effectiveness of the Bayesian method in estimating parameters and its ability to approach the real data. Accurately based on the available data, and when the estimated values of the model are close to the true values of the model, this means that the Bayesian method that was used for estimation is highly accurate and that the model that was used for estimation has estimated it well and reflects the facts accurately.

Monopulse estimation is an angle measurement method with high data rate, measurement precision and anti-jamming ability, since the angle information of target is obtained by comparing echoes received in two or more simultaneous antenna beams. However, the data rate of this method decreases due to coherent integration when applied in pulse Doppler (PD) radar. This paper presents an improved method of monopulse estimation in PD radar. In this method, the received echoes are selected by shift before coherent integration, detection and angle measurement. It can increase data rate while maintain angle measurement precision. And the validity of this method is verified by theoretical analysis and simulation results.

The intracranial pressure (ICP) is usually continuously monitored in the management of patients with increased ICP. The aim of this study was to discover a mathematic equation to express the intracranial pressure-volume (P-V) curve and a single indicator to reflect the status of the curve. Patients with severe brain damage who had bilateral external ventricular drainage (EVD) from December 2008 to February 2010 were included in this study. The EVD was used as drainage of CSF and ICP monitor. The successive volume pressure response [6] values were obtained by successive drainage of CSF from ICP 20-25 to 10 mmHg. Parabolic, exponential, and linear regression models were designed to have a single parameter as the indicator to determine the P-V curves. The mean of parameter "a" in the exponential equation is 1.473 ± 0.054; in the parabolic equation, it is 0.332 ± 0.061; and in the linear equation, it is 1.717 ± 0.209. All regression equations of P-V curves had statistical significance (p < 0.005). Parabolic and exponential equations are closer to the original ICP curve than linear equation (p < 0.005). There is no statistically significant difference between parabolic and exponential regressions. The P-V curve can be expressed with linear, parabolic, and exponential regression models in increased ICP patients. The parabolic and exponential equations are more accurate methods to represent the P-V curve. The single parameter in the three regression equations can be compared in different conditions of one patient in clinical practice.

The study of the dependence of response-time data on a multivariate regressor variable in the presence of arbitrary censoring has been approached in a number of ways. The exponential regression model proposed byr Feigl and Zelen [1965] and extended by Zippin and Armitage [1966] and by Mantel and Myers [1971] to the case of arbitrarily right censored data relates the reciprocal of the exponential parameter, i.e. the expected survival time, to a linear function of the regressor variables. Later, Glasser [1967] proposed an exponential model in which the logarithm of the exponential parameter was assumed to be a linear function of the regressor variables. In both formulations the rather stringent assumption of a constant hazard may be dropped by the assumption of a more general response-time distribution such as the Weibull, gamma or Gompertz, each of which contains the exponential as a special case. The nonparametric model proposed by Cox [1972] admits an arbitrary response-time distribution and, for discrete data, becomes a logistic regression model. An alternative version of Cox's discrete model has beenl proposed by Kalbfleisch and Prentice [1973]. These approaches have the advantage of not specifying the hazard function in advance and, as such, are more robust than the above parametric methods. Their major drawback, however, is the computational difficulties in the presence of tied response times. In many practical situations the data are recorded in such a way as to make this a very real problem and serious enough to implv that an alternative procedure may be desirable. This logistic regression model was also used by Myers et al. [1973] in conjunction with the assumption of a constant hazard. The model they considered incorporated concomitant information by assuming that the probability of responding within a unit time period followed a logistic regression function, while the actual time to response followed a particular distributional form. They chose a form which assumed a time-independent risk of responding-the exponential for a continuous time process or geometric for discrete time. This approach was extended by Hankey and Mantel [1974] by the addition of a time function to the logistic regression function. This tinme function was approximated by a low order polynomial. Inherent in these exponential and logistic regression models is the assumption that the effects of the covariates are independent of time. The exponential model of Feigl and Zelen relates the expected survival time to the concomitant information and, since the exponential distribution is without memory, the expected remaining survival timne given survival up to some time point T has the same relationship to the concomitant information no matter what the value of T. The logistic regression methods that have been proposed allow the underlying hazard to be a function of time but the relative effects of the covariates

The relationship between migration and fertility has vexed demographers for years. One issue missing in the literature is the lack of careful temporal consideration of when women migrate and specifically, the extent to which they do either before or after live births. Here, we opt for a more appropriate methodological approach to help remedy the complexity of the temporal aspect of migration and childbirth processes: regression models using the episode-splitting method. This paper applies a rarely used methodological approach (episode-splitting) in the literature of migration-fertility relationship to investigate how internal in-migration is associated with inter-birth intervals among women in Cotonou, the largest city of Benin. Data comes from the 2017-2018 Benin Demographic and Health Survey (DHS) of women aged 15-49. Estimates from exponential regression models with episode-splitting were compared to estimates from exponential regression models without episode-splitting approach. Sensitivity analysis was also conducted to determine the robustness of the comparison between the two methods. Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) were used to identify the method that provides models with best fit. The results from (standard) exponential regression models without episode-splitting show that there is no significant association between migration and interbirth transition rate. However, significant associations between migration and interbirth transition rate emerge after applying the episode splitting method. The hazard ratios (HR) of the transition to the next live birth are higher among migrant women than among nonmigrant women. This trend is persistent even after 10 years spent in Cotonou by migrant women. Exponential regression models with episode-splitting were of better fit than exponential regression models without episode-splitting. Sensitivity analysis conducted seems to confirm that models with episode-splitting produce estimates that are accurate, reliable and superior to models without episode-splitting. The results suggest a long-run process adaptation of migrants to lower fertility behaviours in Cotonou and are therefore consistent with the socialization hypothesis.

Heat supply is socially and economically important in our country. In this regard, high-quality monitoring and planning of the development of heat supply systems are a strategic vector of scientific research. This paper is focused on the studies demonstrating how to choose a methodological approach to describe changes in heat consumption in the retrospective. The change in heat consumption is described using multiple regression models. In the first part of the paper, the parameters for the regression model are determined and a statistical analysis of the obtained model is performed. In the second part of the paper, to eliminate the multicollinearity of the regression equation, the number of dependent variables in the model is reduced. A statistical analysis of the new regression model and the exponential regression model are carried out. The heat consumption values obtained using these models are compared with the statistical data. The conclusions about the quality of the obtained regression models are made. In the third part of the article, we make a forecast of heat consumption in the medium term by using a linear regression model and an exponential model.

IFER—Institute of Forest Ecosystem Research, Cs. armady 655,Jilove u Prahy 254 01, Czech RepublicAbstract. Automatic mapping of tree crown size (radius, diameter, or width) from remote sens-ing can provide a major benefit for practical and scientific purposes, but requires the develop-ment of accurate methods. This study presents an improved method for average tree crowndiameter estimation at a forest plot level from high-resolution airborne data. The improvedmethod consists of the combination of a window binarization procedure and a granulometricalgorithm, and avoids the complicated crown delineation procedure that is currently used toestimate crown size. The systematic error in average crown diameter estimates is correctedwith the improved method. The improved method is tested with coniferous, beech, andmixed-species forest plots based on airborne images of various spatial resolutions. The absolute(quantitative) accuracy of the improved crown diameter estimates is comparable or higher forboth monospecies plots and mixed-species plots than the current methods. The ability of theimproved method to produce good estimates for average crown diameters for monocultureand mixed species, to use remote sensing data of various spatial resolution and to operate inautomatic mode promisingly suggests its applicability to a wide range of forest systems.

For the characterisation of influencing factors on chronic endothelial cell loss after penetrating keratoplasty by means of multivariate statistics, a mathematical description of the course of the individual postoperative endothelial cell density is a prerequisite. This mathematical description should result in a standardized index value describing course and amount of the postoperative endothelial cell loss over time in a canonical way. The slopes of the linear regression lines for each individual scatter plot of a) the endothelial cell density values plotted against the respective postoperative time directly (linear regression), and b) after logarithmic transformation (exponential regression) are evaluated, respectively. 58 patients after normal-risk keratoplasty (26x keratokonus, 22x Fuchs-dystrophy and 10 cases of corneal decompensation after cataract surgery) with 5 or more postoperatively acquired endothelial density values and without any episodes of graft rejection were included in this study. Mean follow up was 2.9 +/- 1.1 years. The postoperative endothelial cell density values were plotted against the respective time for each patient individually. The coefficients of variation (R2) derived from the linear and the exponential regression models were calculated for each of these scatter plots. The pairs of R2 values (linear vs. exponential) were compared statistically. A dependence of the difference of linear and exponential R2-values on the ophthalmologic diagnosis was tested as well. The linear model is able to declare 83% the total variance of the course of the endothelial cell density. The exponential model even declares 86%. This small difference was statistically significant. Since both methods of regression describe the course of the cell density well, intra/and extrapolation of missing endothelial values is possible with both models. No dependence of the difference of linear and exponential R2-values on the ophthalmologic diagnosis could be demonstrated. Both, the intuitively understandable slope of the linear regression line and the constant of decay of the exponential regression curve, are suitable for describing the amount of the postoperative loss of endothelial cells after normal-risk keratoplasty independent of the ophthalmologic diagnosis. Both can thus be used as target variable in forthcoming statistical analyses for chronic endothelial cell loss.

Enhancing sediment transport predictions through machine learning-based multi-scenario regression models

Assessing the limits of human athletic performance has been a very attractive topic not only to scientists but also to common people. Human being has been running faster and faster and jumping higher and higher through the world from east to west. Especially in last two decades, the best track and field performances in the Far East countries such as China and Korea have been improving dramatically. One is always wondering whether this trend would continue and when is the end. Is sky the limit for improving the track and field performances? There is little research in the literature to assess the trend of the track and field performances of the east and west countries. A suitable procedure is real demand for the assessment of the limits of human athletic performances. PURPOSE (1) to find an appropriate procedure to assess the limits of human track and field performances, (2) to examine the trend of the best track and field performances in Far East (China and Korea) and to compare the Far East best performances with the world best performances, and to investigate whether sky is really the limit. METHODS Both the male and female best annual performance data of the four selected events over the last three decades (800 meters, 1500 meters, Marathon, and high jump) were used. The annual best performances were recorded based on Chinese, Korean, and world athletes' competitions in national and international levels. Different nonlinear regression models (polynomial and exponential models) and the autoregressive integrated moving average model (ARIMA) in time-series analysis were used to fit the male and female data separately. In the nonlinear model, the best performance is dependent variable and the chronicle year is the independent variable. The best fitting models were identified to explain whether the selected track and field events at Chinese, Korean and international levels have reached an asymptotic level (a stationary time series). RESULTS For both male and female performances, the exponential model was the best fitting model in all the selected events. An asymptotic level has been achieved in all the selected events at both the east country (China and Korea) and international competitions. An ARIMA(0.0.0) model was identified for the last two decades data. CONCLUSION (1) Using the exponential nonlinear regression model and ARIMA time series model is a valid procedure to assess the track and field best performance data. (2) The waiting time to establish new records would be considerably longer in future, and it may show a random phenomenon.

BackgroundThe relationship between migration and fertility has vexed demographers for years. One issue missing in the literature is the lack of careful temporal consideration of when women migrate and specifically, the extent to which they do either before or after live births.ObjectiveHere, we opt for a more appropriate methodological approach to help remedy the complexity of the temporal aspect of migration and childbirth processes: regression models using the episode-splitting method.MethodsThis paper applies a rarely used methodological approach (episode-splitting) in the literature of migration-fertility relationship to investigate how internal in-migration is associated with inter-birth intervals among women in Cotonou, the largest city of Benin. Data comes from the 2017–2018 Benin Demographic and Health Survey (DHS) of women aged 15–49. Estimates from exponential regression models with episode-splitting were compared to estimates from exponential regression models without episode-splitting approach. Sensitivity analysis was also conducted to determine the robustness of the comparison between the two methods. Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) were used to identify the method that provides models with best fit.ResultsThe results from (standard) exponential regression models without episode-splitting show that there is no significant association between migration and interbirth transition rate. However, significant associations between migration and interbirth transition rate emerge after applying the episode splitting method. The hazard ratios (HR) of the transition to the next live birth are higher among migrant women than among nonmigrant women. This trend is persistent even after 10 years spent in Cotonou by migrant women.ConclusionExponential regression models with episode-splitting were of better fit than exponential regression models without episode-splitting. Sensitivity analysis conducted seems to confirm that models with episode-splitting produce estimates that are accurate, reliable and superior to models without episode-splitting. The results suggest a long-run process adaptation of migrants to lower fertility behaviours in Cotonou and are therefore consistent with the socialization hypothesis.

Introduction: Probiotics are well-defined as live microorganisms that usefully affect the host and probiotic bacteria have been used intensely. For years to target gastrointestinal disease by rebalancing the compound microflora. Besides the gastrointestinal tract also the oral cavity is highly colonized by bacteria and many different bacterial species are part of the microbiota in the mouth, as it offers ideal conditions for bacteria with a stable temperature, moist surface with a relatively stable pH and regular supply of nutrients. Probiotic bacteria like Lactobacillus are a promising treatment strategy for oral disease with a microbiological etiology. To gain better results, many researchers that study and emphasize specific methods been tried to build a new or improved methodology.&#x0D; Objectives: The aimed of this study is to improve the performance of exponential growth by adding bootstrap and fuzzy techniques (Integrated exponential regression method). The aim of the research work is to develop a comprehensive framework for an integrated exponential regression model.&#x0D; Material and Methods: The data were taken from the present data available from the recently done by a researcher for nurturing selected microorganisms. The gathered data will be used for the exponential modeling and the efficiency of the model will be compared accordingly due to the predicted interval from the exponential regression method and an integrated exponential regression method. This paper also provides the algorithm for the prediction of cell growth and inferences.&#x0D; Results: The result shows that the average width for the exponential regression model was 19.2228 while an integrated exponential regression method was 0.0075. The average width of integrated exponential regression was smaller than the exponential regression. This clearly shows that the integrated exponential regression method is more efficient than exponential regression technique.&#x0D; Conclusion: This proposed method can be applied to small sample size data, especially when limited data is obtained.&#x0D; Bangladesh Journal of Medical Science Vol.19(3) 2020 p.552-557

Ten-year trends in vertical distribution of radiocesium in Fukushima forest soils, Japan