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The sliding friction of silicon carbide bodies in an aqueous medium is studied using the models that take into account sigmoid changes in the friction force. The dependence of the friction force on the sliding velocity in an aqueous medium is obtained, and the kinetics of the process is determined.

We study the bifurcation curves for a Dirichlet problem with geometrically concave nonlinearity. We give an application to the generalized logistic growth model { u ′ ′ ( x ) + λ f ( u ) = 0 , − 1 > x > 1 , \ u ( − 1 ) = u ( 1 ) = 0 , f ( u ) = u α [ 1 − ( u K ) β ] γ , α , β , γ > 0 . \begin{equation*} \left \{ \begin {array}{l} u^{\prime \prime }(x)+\lambda f(u)=0\text {,}\;-1>x>1\text {, \ }u(-1)=u(1)=0 \text {,} \\ f(u)=u^{\alpha }\left [ 1-\left ( \frac {u}{K}\right ) ^{\beta }\right ] ^{\gamma }\text {, }\alpha ,\beta ,\gamma >0\text {.}\end{array}\right . \end{equation*} There are totally six qualitatively bifurcation curves of order relations for ( α , β , γ ) (\alpha ,\beta ,\gamma ) .

The network of suppliers and, in particular, the allocation of a buyer’s procurement volumes is one of the key issues in supply chain management when following a multiple-sourcing strategy. This paper proposes a buyer–supplier model which considers a supplier quantity–quality trade-off reflecting the responsiveness of quality to changes in volume. The trade-off is based on the assumption that suppliers are not able to maintain the same level of quality, if quantity increases and vice versa. In order to model the relation between quantity and quality, a generalized logistic function is used. Considering heterogeneous suppliers in terms of the quantity–quality trade-off, we analyze, how different procurement volumes for a product affect the supplier structure of a buyer in a multiple-sourcing buyer–supplier network. An agent-based simulation is applied which is an appropriate approach to study systems of heterogeneous and interacting agents (e.g., buyer and suppliers, interactions between suppliers, mutual effects of parameters). The results show that in such a network not only the procurement volume remarkably shapes the supplier structure and, eventually, may lead to instability. Moreover, the results suggest that less advanced quality management systems on the buyer’s side may increase the stability of the supplier structure.

In the present article, we deal with a generalization of the logistic function. Starting from the Riccati differential equation with constant coefficients, we find its analytical form and describe basic properties. Then we use the generalized logistic function for modeling some economic phenomena.

We examine a new form of smooth approximation to the zero one loss in which learning is performed using a reformulation of the widely used logistic function. Our approach is based on using the posterior mean of a novel generalized Beta-Bernoulli formulation. This leads to a generalized logistic function that approximates the zero one loss, but retains a probabilistic formulation conferring a number of useful properties. The approach is easily generalized to kernel logistic regression and easily integrated into methods for structured prediction. We present experiments in which we learn such models using an optimization method consisting of a combination of gradient descent and coordinate descent using localized grid search so as to escape from local minima. Our experiments indicate that optimization quality is improved when learning metaparameters are themselves optimized using a validation set. Our experiments show improved performance relative to widely used logistic and hinge loss methods on a wide variety of problems ranging from standard UC Irvine and libSVM evaluation datasets to product review predictions and a visual information extraction task. We observe that the approach is as follows: (1) more robust to outliers compared to the logistic and hinge losses; (2) outperforms comparable logistic and max margin models on larger scale benchmark problems; (3) when combined with Gaussian–Laplacian mixture prior on parameters the kernelized version of our formulation yields sparser solutions than Support Vector Machine classifiers; and (4) when integrated into a probabilistic structured prediction technique our approach provides more accurate probabilities yielding improved inference and increasing information extraction performance.

The rapid spread of the COVID-19 pandemic has raised huge concerns about the prospect of a major health disaster that would result in a huge number of deaths. This anxiety was largely fueled by the fact that the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), responsible for the disease, was so far unknown, and therefore an accurate prediction of the number of deaths was particularly difficult. However, this prediction is of the utmost importance for public health authorities to make the most reliable decisions and establish the necessary precautions to protect people’s lives. In this paper, we present an approach for predicting the number of deaths from COVID-19. This approach requires modeling the number of infected cases using a generalized logistic function and using this function for inferring the number of deaths. An estimate of the parameters of the proposed model is obtained using a Particle Swarm Optimization algorithm (PSO) that requires iteratively solving a quadratic programming problem. In addition to the total number of deaths and number of infected cases, the model enables the estimation of the infection fatality rate (IFR). Furthermore, using some mild assumptions, we derive estimates of the number of active cases. The proposed approach was empirically assessed on official data provided by the State of Qatar. The results of our computational study show a good accuracy of the predicted number of deaths.

In the research field of person re-identification, deep metric learning that guides the efficient and effective embedding learning serves as one of the most fundamental tasks. Recent efforts of the loss function based deep metric learning methods mainly focus on the top rank accuracy optimization by minimizing the distance difference between the correctly matching sample pair and wrongly matched sample pair. However, it is more straightforward to count the occurrences of correct top-rank candidates and maximize the counting results for better top rank accuracy. In this paper, we propose a generalized logistic function based metric with effective practicalness in deep learning, namely the“deep top-rank counter metric”, to approximately optimize the counted occurrences of the correct top-rank matches. The properties that qualify the proposed metric as a well-suited deep re-identification metric have been discussed and a progressive hard sample mining strategy is also introduced for effective training and performance boosting. The extensive experiments show that the proposed top-rank counter metric outperforms other loss function based deep metrics and achieves the state-of-the-art accuracies.

Logistic regressions are subject to high uncertainty when the data are not past the inflection point. For example, for logistic regressions estimated with data up to or before inflection point, uncertainties in the upper asymptotic value $K$ can be of the same order of magnitude of the population under analysis. This paper presents a method for uncertainty reduction in logistic regression using data from a surrogate logistic process. We illustrate the procedure using the Richards' growth function (Generalized Logistic Function) to make predictions for COVID-19 evolution in Brazilian cities at stages before and during their epidemic inflection points. We constrain the logistic function regression with $K$ calculated from selected surrogate international cities where the epidemic is clearly past its inflection point. Information gained with this constraint stabilizes the logistic regression, reducing the uncertainty in the curves' parameters, including the rate of growth at the inflection point. The uncertainty is reduced even when the actual surrogate $K$ is used just as an anchor to simulate different epidemic scenarios. Results predicted for COVID-19 trajectories within Brazil agree with actual data. These results suggest that in the absence of big data, a simple logistic regression may provide low uncertainty if surrogate cities have been identified for estimates of $K$, even if the specifics of the evolution in the surrogate cities are different. The method may be used for other logistic models and for other logistic processes in other areas such as economics and biology, if surrogate processes can be identified.

The standard growth model of epidemic evolution such as the Richards generalized logistic function is remarkably successful because it agrees with almost all previous epidemic data. Yet, it fails to explain intervention measures for mitigations of the ongoing coronavirus 2019 disease (COVID-19) pandemic. It also fails to replicate an endemic phase that occurs in many countries epidemic curves (time series data of daily new cases). These discrepancies demonstrate that new epidemic laws are required to understand, predict and mitigate the COVID-19 pandemic. Here we show that almost all COVID-19 evolution can be modeled by three innovative epidemic laws. Specifically, based on the world COVID-19 data, we first divide an epidemic curve into three phases: an exponential growth phase, an exponential decay phase, and a constant endemic phase. We next integrate the growth and the decay phases into the first epidemic law with interventions as a model parameter. This law is completely opposite to the Richards generalized logistic function in terms of intervention measures. We then combine the first epidemic law with the endemic phase to form the second epidemic law, which makes the curve of cumulative cases increase linearly as time tends to infinity. The third epidemic law states if an epidemic is composed of multiple epidemic waves, the superposition principle applies. These laws were confirmed by the COVID-19 data from 18 countries including undeveloped, developing and developed countries. Finally, we pave the way for future research to incorporate the proposed theory into the classic SIR model. We anticipate that the results from this research can provide a scientific base for governments to mitigate the COVID-19 and other epidemic disasters.

COVID-19 was declared as a pandemic by the World Health Organization on March 11, 2020. Here, the dynamics of this epidemic is studied by using a generalized logistic function model and extended compartmental models with and without delays. For a chosen population, it is shown as to how forecasting may be done on the spreading of the infection by using a generalized logistic function model, which can be interpreted as a basic compartmental model. In an extended compartmental model, which is a modified form of the SEIQR model, the population is divided into susceptible, exposed, infectious, quarantined, and removed (recovered or dead) compartments, and a set of delay integral equations is used to describe the system dynamics. Time-varying infection rates are allowed in the model to capture the responses to control measures taken, and distributed delay distributions are used to capture variability in individual responses to an infection. The constructed extended compartmental model is a nonlinear dynamical system with distributed delays and time-varying parameters. The critical role of data is elucidated, and it is discussed as to how the compartmental model can be used to capture responses to various measures including quarantining. Data for different parts of the world are considered, and comparisons are also made in terms of the reproductive number. The obtained results can be useful for furthering the understanding of disease dynamics as well as for planning purposes.

Many analytical approaches to single-case data assume either linear effects (regression-based methods) or instant effects (mean-based methods). Neither assumption is realistic; therefore, these approaches’ assumptions are often violated. In this article, we propose modeling curvilinear effects to appropriately parametrize the characteristics of singe-case data. Specifically, we introduce the generalized logistic function as adequate function for this situation. The merits of the proposed procedure are demonstrated using data previously used in single case research that represent typical single case data. We provide the function with auxiliary graphical options to demonstrate the model parameters. The function is freely available in the R package “userfriendlyscience.” The proposed procedure is a new way to analyze single case data, which may provide applied single case researchers with a new tool to better understand their data and avoid applying methods with violated assumptions.

The logistic regression model constitutes a natural and simple tool to understand how covariates (when available) contribute to explain the topology of a binary network. After estimating the logistic parameters, one of the main questions which arises in practice is to assess the goodness of fit of the corresponding model. To address this problem, we add a general term, related to the graphon function of W-graph models, to the logistic function. Such an extra term aims at characterizing the residual structure of the network, that is not explained by the covariates. We approximate this new generic logistic model using a class of models with blockwise constant residual structure. This framework allows to derive a Bayesian procedure from a model based selection context using goodness-of-fit criteria. All these criteria depend on marginal likelihood terms for which we do provide estimates relying on two series of variational approximations. Experiments on toy data are carried out to assess the inference procedure. Finally, six networks from social sciences and ecology are studied to illustrate the proposed methodology. Logistic regression is a natural and simple tool to understand how covariates contribute to explain the topology of a binary network. Once the model is fitted, the practitioner is interested in the goodness-of-fit of the regression in order to check if the covariates are sufficient to explain the whole topology of the network and, if they are not, to analyze the residual structure. To address this problem, we introduce a generic model that combines logistic regression with a network-oriented residual term. This residual term takes the form of the graphon function of a W-graph. Using a variational Bayes framework, we infer the residual graphon by averaging over a series of blockwise constant functions. This approach allows us to define a generic goodness-of-fit criterion, which corresponds to the posterior probability for the residual graphon to be constant. Experiments on toy data are carried out to assess the accuracy of the procedure. Several networks from social sciences and ecology are studied to illustrate the proposed methodology.

A new method to model the probability of detection (PoD) of flaws that takes into consideration the correlation between the flaw features as a function of the correlated flaw dimensions, the length and depth, is proposed in this work. Boundary element method was used to efficiently obtain the required flaw features. The features used are the maximum change in the amplitudes of the three components of the scattered magnetic flux density ( B x , B y and B z ). Firstly, the magnetic-electric Green's function, for a finite thickness plate, is formulated. On knowing the distribution of the dipole density, the scattered fields at the axial center of the coil are computed. Experiments were conducted in a controlled environment to validate the predictions of the BEM. The features, from the BEM, computed for several flaw lengths and depths, were fit to a trivariate Gaussian distribution. The discrete form of the PoD was determined after identifying the sensor threshold. A continuous function is later obtained by linking the discrete PoD with a generalized logistic function.

This paper proposes a new color fringe correction method that preserves the object color well by the color difference prediction using the logistic function. We observe two characteristics between normal edge (NE) and degraded edge (DE) due to color fringe: 1) the DE has relatively smaller R-G and B-G correlations than the NE and 2) the color difference in the NE can be fitted by the logistic function. The proposed method adjusts the color difference of the DE to the logistic function by maximizing the R-G and B-G correlations in the corrected color fringe image. The generalized logistic function with four parameters requires a high computational load to select the optimal parameters. In experiments, a one-parameter optimization can correct color fringe gracefully with a reduced computational load. Experimental results show that the proposed method restores well the original object color in the DE, whereas existing methods give monochromatic or distorted color.

Let P(x) be a polynomial monotone increasing on ( − ∞, +∞). The probability distribution possessing the distribution function is called the polynomial logistic distribution with associated polynomial P. This has recently been introduced by Koutras et al., who have also demonstrated its importance for modeling financial data. In this article, the properties of the polynomial logistic distribution with an associated polynomial of degree 3 have been investigated in detail. An example of polynomial logistic distribution describing daily exchange rate fluctuations for the US dollar versus the Turkish lira is provided.

A general diagnostic approach to the evaluation of asymptotic approximation in likelihood based models is developed and applied to logistic regression. The expected asymptotic and observed log-likelihood functions are compared using a chi distribution in a directional Bayesian setting. This provides a general approach to assessing and visualizing non-convergence in higher dimensional models. Several well-known examples from the logistic regression literature are discussed.

The problems of existence and uniqueness of maximum likelihood estimates for logistic regression were completely solved by Silvapulle in 1981 and Albert and Anderson in 1984. In this paper, we extend the well-known results by Silvapulle and by Albert and Anderson to weighted logistic regression. We analytically prove the equivalence between the overlap condition used by Albert and Anderson and that used by Silvapulle. We show that the maximum likelihood estimate of weighted logistic regression does not exist if there is a complete separation or a quasicomplete separation of the data points, and exists and is unique if there is an overlap of data points. Our proofs and results for weighted logistic apply to unweighted logistic regression.

The univariate logistic distribution and its properties and applications have been studied quite extensively in the literature. Some generalizations as well as multivariate extensions of it have also been proposed for greater flexibility in modeling univariate and multivariate data. In this paper, we construct three different types of generalized bivariate logistic type distributions through conditional specification, and discuss some of their properties. Finally, we use a data set to fit the proposed models for the purpose of illustration.

The growth characteristics of the recently derived Trans-Gompertz function are compared to those of the Generalized Logistic function. Both functions are defined by one shaping parameter and one rate parameter. The functions are matched at a specified point on the growth curve by equating both the first and second derivatives. Analysis shows that the matched Trans-Gompertz function will have grown at a faster rate with a larger inflection point ratio.

A generalized logistic function has been proposed as a kinetic analysis method that is superior to traditional methods. In fact, the parameter τ in the generalized logistic function has an effect on the reaction profile similar to the parameter n in the extended Prout–Tompkins model for autocatalytic reactions. Furthermore, the comparisons made in some papers to traditional methods were made by using the discredited method of determining kinetic parameters from a single heating rate, so they are misleading compared to proper kinetic analysis methods that simultaneously analyze multiple thermal histories. In addition, the current implementation of the generalized logistic function of fitting each experiment individually is prone to introduce errors in the kinetic parameters. Guidance is given on how the generalized logistic function might be used for proper chemical kinetic analysis.

A generalization of the fractional logistic equation by using k-Caputo derivative is introduced. Also a solution that can be expressed en terms of the k-Mittag-Le er function is obtained. The development of this paper has been done on the basis what has been done by Camargo and Bruno-Alfonso. Fil: Cerutti, Rubén A. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura; Argentina.

Baseline correction methods based on penalized least squares are successfully applied to various spectral analyses. The methods change the weights iteratively by estimating a baseline. If a signal is below a previously fitted baseline, large weight is given. On the other hand, no weight or small weight is given when a signal is above a fitted baseline as it could be assumed to be a part of the peak. As noise is distributed above the baseline as well as below the baseline, however, it is desirable to give the same or similar weights in either case. For the purpose, we propose a new weighting scheme based on the generalized logistic function. The proposed method estimates the noise level iteratively and adjusts the weights correspondingly. According to the experimental results with simulated spectra and measured Raman spectra, the proposed method outperforms the existing methods for baseline correction and peak height estimation.

In this article, I present three commands that perform adjacent-category logistic regression (adjcatlogit), constrained continuation-ratio logistic regression (ccrlogit), and unconstrained continuation-ratio logistic regression (ucrlogit) for ordered response data.

The usage of mixed methods approach on qualitative data has been exemplified in this chapter. The chapter presents the relevance of using multinomial regression approach in the study and discusses its results. The chapter is insightful for readers looking forward to learning practical applications of quantitative techniques on qualitative data.

Objectives The Extended Mechanistic Growth Function (EMGF) method (Clementi et al. [1999]: Am J Med Genet 87:317–323) is a possible alternative to the Cole and Green LMS method ([1992] Stat Med 11:1305-1319) to construct cross-sectional anthropometric charts. It differs from the technique used by Kuczmarski et al. ([2002]: Vital Health Stat 11:1–190) to trace the CDC growth charts in that all centiles are simultaneously fitted with a single function. The aim of this study is to show how an EMGF model can be designed. Methods To illustrate the structure and properties of the EMGF method, the data of the Italian Neonatal Study (Bertino et al. [2010]: J Pediatr Gastroenterol Nutr 51:353–361) were analyzed. The dataset included the birth weight of 45,272 single liveborn babies with gestational ages ranging from 23 to 42 weeks. The EMGF method consists of three steps. In the preliminary step, selected age-dependent raw centiles of the anthropometric trait are computed. In the smoothing step, all centiles are simultaneously fitted with a growth function extended with the inclusion of a few extra parameters. In the transformation step, estimates of the age-dependent L (skewness), M (median), and S (coefficient of variation) parameters are derived. Results A four-parameter generalized logistic function, extended with five parameters to model between-sex differences, distance between centiles and their slope, was found to fit the raw centiles of birth weight distribution with a residual standard deviation of 51.3 g. Conclusions The EMGF method represents a bridge to link cross-sectional and longitudinal studies and allows us to identify milestones of the median growth in a population in the same way used for individual profiles. Am. J. Hum. Biol. 27:175–183, 2015. © 2014 Wiley Periodicals, Inc.

This paper proposes a simple model selection test between the Gompertz and the Logistic growth models based on parameter significance testing in a comprehensive linear regression. Simulations studies are provided to show the accuracy of the method. Two real-data examples are also provided to illustrate the implementation of the proposed method in practice.

A logistic regression method can be applied to regressing the [Formula: see text]-year survival probability to covariates, if there are no censored observations before time [Formula: see text]. But if some observations are incomplete due to censoring before time [Formula: see text], then the logistic regression cannot be applied. Jung (1996) proposed to modify the score function for logistic regression to accommodate the right-censored observations. His modified score function, motivated for a consistent estimation of regression parameters, becomes a regular logistic score function if no observations are censored before time [Formula: see text]. In this article, we propose a modification of Jung's estimating function for an optimal estimation for the regression parameters in addition to consistency. We prove that the optimal estimator is more efficient than Jung's estimator. This theoretical comparison is illustrated with a real example data analysis and simulations.

In the present paper, we propose a new approach to investigate the logistic function, which is commonly used in mathematical models in economics and management. The approach is based on indicating in a given time series, having a logistic trend, some characteristic points corresponding to zeroes of successive derivatives of the logistic function. We also give examples of application of this method.

We modeled binary count data with categorical predictors, using logistic regression to develop a statistical method. We found that ANOVA-type analyses often performed unsatisfactorily, even when using different transformations. The logistic transformation of fraction data could be an alternative, but it is not desirable in the statistical sense. We concluded that such methods are not appropriate, especially in cases where the fractions were close to 0 or 1. The major purpose of this paper is to demonstrate that logistic regression with an ANOVA-model like parameterization aids our understanding and provides a somewhat different, but sound, statistical background. We examined a simple real world example to show that we can efficiently test the significance of regression parameters, look for interactions, estimate related confidence intervals, and calculate the difference between the mean values of the referent and experimental subgroups. This paper demonstrates that precise confidence interval estimates can be obtained using the proposed ANOVA-model like approach. The method discussed here can be extended to any type of experimental fraction data analysis, particularly for experimental design.

In this note we construct a family of recurrence generated sigmoidal logistic functions based on the Verhulst logistic function.We prove estimates for the Hausdorff approximation of the Heaviside step function by means of this family. Numerical examples, illustrating our results are given.

Summary Logistic regression is a popular tool for risk analysis in medical and population health science. With continuous response data, it is common to create a dichotomous outcome for logistic regression analysis by specifying a threshold for positivity. Fitting a linear regression to the nondichotomized response variable assuming a logistic sampling model for the data has been empirically shown to yield more efficient estimates of odds ratios than ordinary logistic regression of the dichotomized endpoint. We illustrate that risk inference is not robust to departures from the parametric logistic distribution. Moreover, the model assumption of proportional odds is generally not satisfied when the condition of a logistic distribution for the data is violated, leading to biased inference from a parametric logistic analysis. We develop novel Bayesian semiparametric methodology for testing goodness of fit of parametric logistic regression with continuous measurement data. The testing procedures hold for any cutoff threshold and our approach simultaneously provides the ability to perform semiparametric risk estimation. Bayes factors are calculated using the Savage–Dickey ratio for testing the null hypothesis of logistic regression versus a semiparametric generalization. We propose a fully Bayesian and a computationally efficient empirical Bayesian approach to testing, and we present methods for semiparametric estimation of risks, relative risks, and odds ratios when parametric logistic regression fails. Theoretical results establish the consistency of the empirical Bayes test. Results from simulated data show that the proposed approach provides accurate inference irrespective of whether parametric assumptions hold or not. Evaluation of risk factors for obesity shows that different inferences are derived from an analysis of a real data set when deviations from a logistic distribution are permissible in a flexible semiparametric framework.

D-optimal designs for nonlinear models are often minimally supported. They have been frequently criticized for their inability to test for lack of fit. We construct alternative designs to address this issue for some commonly used sigmoid curves, including logistic, probit, and Gompertz models with two, three, or four parameters. For each model, we compare five nonminimally supported designs in terms of their efficiency, and propose designs that are both statistically efficient and practically convenient for practitioners.

In this paper, we present a generalization of the commonly used growth models. We introduce Koya-Goshu biological growth model, as a more general solution of the rate-state ordinary differential equation. It is shown that the commonly used growth models such as Brody, Von Bertalanffy, Richards, Weibull, Monomolecular, Mitscherlich, Gompertz, Logistic, and generalized Logistic functions are its special cases. We have constructed growth and relative growth functions as solutions of the rate-state equation. The generalized growth function is the most flexible so that it can be useful in model selection problems. It is also capable of generating new useful models that have never been used so far. The function incorporates two parameters with one influencing growth pattern and the other influencing asymptotic behaviors. The relationships among these growth models are studies in details and provided in a flow chart.

In the paper an experiment is described, that was designed and conducted to verify hypothesis that artificial neuron with sigmoidal activation function can efficiently solve the task of logistic regression in the case when the explaining variable is one-dimensional, and the explained variable is binomial. Computations were performed with 12 sets of statistical parameters, assumed for the generation of 65356 sets of data in each case. Comparative analysis of the obtained results with use of the reference values for the regression coefficients indicated that the investigated neuron can satisfactory perform the task, with efficiency similar to that obtained with classical logistic regression algorithm, when the teaching sets of input data, corresponding with output values 0 and 1, do not allow for simple separation. Moreover, it has been discovered that the simple formulas estimating the statistical distributions parameters from the samples, offer statistically superior assessment of the regression coefficient parameters.

Fuzzy Cognitive Maps is an important representation tool that has the ability to model complicated systems. Based on linear influence relations between concepts, FCMs can be trained to lead a system to a desired state. This work proposes a generalized flexible nonlinear function as an alternative way of estimating that influence. Its adjustable character offers the ability to lead a FCM into a large set of different equilibrium states, where the conventional approach constitutes only one instance. Experimental studies present the properties of the proposed methodology in two benchmarks and other synthetic data. The examination of a system under different considerations of influence offers a more complete understanding of a system behavior.

This paper discusses the Bayesian approach as an alternative to the classical analysis of nonlinear models for growth curve data in Japanese quail. A Bayesian nonlinear modeling method is introduced and compared with the classical nonlinear least squares (NLS) method using three non-linear models that are widely used in modeling the growth data of poultry. The Gompertz, Richards and Logistic models were fitted to 499 Japanese quail weekly averaged body weight data. Normal prior was assumed for all growth curve parameters of the models with assuming Jeffreys' non-informative prior for residual variances. Models were compared based on the Bayesian measure of fit, deviance information criterion (DIC), and our results indicated the better fit of Gompertz and Richards models than the Logistic model to our data. Moreover, the parameter estimates of the models fitted by both approaches showed only small differences. Akdeniz University Scientific Research Projects Management UnitAkdeniz University [2005.02.0121.005] We would like to express our gratitude to Dr. Tulin Aksoy (Akdeniz University, Faculty of Agriculture, Department of Animal Science, Antalya-TURKEY) for supplying the data, which was collected as part of a research project supported by Akdeniz University Scientific Research Projects Management Unit (project number: 2005.02.0121.005).

We present an EM algorithm for Maximum Likelihood estimation of the location, scale, and skew, and shape parameters of the z distribution, also known as the generalized logistic function (type IV). We use the Barndorff-Nielsen, Kent, and Sorensen representation of the z distribution as a Gaussian location-scale mixture to derive an EM algorithm for estimating the location, scale, skew, and shape parameters. We use a variational bound on the likelihood function to determine a monotonically converging closed form update for the skew (or drift) parameter. The algorithm also extends naturally to multivariate GLSM estimation using the Kolmogorov-Smirnov mixing density in odd dimensions.

Background/Objectives: Different methods can be applied to create predictive models for the clinical data with binary outcome variable. This research aims to explore the process of constructing the modified predictive model of Logistic Regression (LR). Method/Statistical Analysis: To improve the accuracy of prediction, the Distance based Outlier Detection (DBOD) is used for pre-processing and Bipolar Sigmoid Function calculated using Neuro based Weight Activation Function is used in Logistic Regression instead of Sigmoid Function. Datasets were collected from clinical laboratory of AR Hospital in Madurai for the three years 2012, 2013 and 2014 are used for analysis. Data pre-processing is done to avoid the existence of insignificant data in the dataset. The detected outliers, using DBOD method are treated using a method closest to the normal range. A comparative study among different distance measures likes Euclidean and Manhattan etc. are done for DBOD method. The pre-processed data finally is fed as input to the Logistic Regression model. Maximum likelihood estimation is used to fit the model. Logistic Model is built from the Sigmoid Function using the Regression Coefficients. The accuracy of the model is evaluated by 10 fold cross validation. Findings: Logistic Model is built from the Sigmoid Function using the Regression Coefficients, produces the accuracy of 79%. The Sigmoid Function calculated using Random Weight Function provides the prediction accuracy of 84.2% and the Bipolar Sigmoid Function calculated using Neuro based Weight Activation function provides the prediction accuracy of 90.4%. On comparison, Bipolar Sigmoid Function calculated using Neuro weight activation function outperforms well than the Sigmoid Function calculated using regression coefficients. Improvements/Applications: The accuracy of Logistic Regression is improved from 79% to 90.4%. The most important factors: Erythrocyte Sedimentation Rate (ESR) and Estimation of Mean blood Glucose are identified from positive subjects of Diabetes Mellitus. The analysis is done for the 31 Diabetes Disease attributes of three years dataset.

The traditional logistic regression model is always used binary classification tasks, such as a person’s gender (male or female). In this paper, we introduce how to adapt the traditional logistic regression model to multiple classification task. To validate our proposed method, we conduct an experiment on a open dataset, and the experimental results show that our proposed method is promising in multiple classification task.