One of the most widely used statistical topics in research fields is REGRESSION problems. In these models, the basic assumption of model errors is their normality, which, in some cases, is different due to asymmetry features or break points in the data. PIECEWISE REGRESSION models have been widely used in various fields, and it is essential to detect the breakpoint. The break points in PIECEWISE REGRESSION models are necessary to know when and how the pattern of the data structure changes. One of the major problems is that there is a heavy tail in these data, which has been solved by using some distributions that generalize the normal distribution. In this paper, the PIECEWISE REGRESSION model will be investigated based on the scale mixture of the normal distribution. Also, this model will be compared with the standard PIECEWISE REGRESSION model derived from normal errors.

Estimation of formation water saturation (Sw) using log data is an important approach in the seismic exploration and characterization of a hydrocarbon reservoir. Therefore, it seems that the proper prediction/simulation of Sw is essential. The first objective of this study was to develop a predictive model for Sw estimation based on hybrid cluster analysis with PIECEWISE nonlinear REGRESSION, and after that, using the developed model, Sw was simulated by the Monte Carlo simulation (MCS). In order to achieve objectives of this study, a group of 909 data points was used for model construction and 302 data points were employed for assessment of model. The obtained results of MCS modeling indicated that this approach is capable of simulating Sw ranges with a good level of accuracy. The mean of simulated Sw by MCS was obtained as 0.28 m, while this value was achieved as 0.29 m for the measured one. Furthermore, a sensitivity analysis was also conducted to investigate the effects of model inputs on the output of the system. The analysis demonstrated that RHOB is the most influential parameter on Sw among all model inputs. It is noticeable that the proposed hybrid cluster analysis with PIECEWISE nonlinear REGRESSION and MCS models should be utilized only in the studied area and the direct use of them in the other conditions is not recommended.

In this work we prove that for any measurable admissible control w (.) and for any e>0 there exists PIECEWISE constant admissible control w¯ (.) such that for fuzzy solutions of control fuzzy linear system are e-closed.

The problem of finding the minimum cost multi-commodity flow in an undirected and complete network is studied when the link costs are PIECEWISE linear and convex. The arc-path model and overflow model are presented to formulate the problem. The results suggest that the new overflow model outperforms the classical arc-path model for this problem. The classical revised simplex, Frank and Wolf and a heuristic method are compared for the problem.

Background: Diabetes mellitus is a metabolic disorder and its subsequent complications such as retinopathy, nephropathy, ulcers, disability, and amputation increase the burden of the disease. Patient knowledge-improving programs are employed to prevent disease progression and to improve the quality of life of the patients. In this way, we need to characterize the groups of patients in urgent need for more and rich-in-content programs. In the present study, we used PIECEWISE REGRESSION to evaluate the trends of diabetic nephropathy prevalence in patients registered in the Sedigheh-Tahereh Research Center and to identify patients who were in need of more attention. Materials and Methods: PIECEWISE REGRESSION, used in this study, is a statistical method to identify change points, if any, in the trends of mortality rates, prevalence of a disease, or any other trends. Available information for 1, 935 patients were retrieved from the database. Joinpoint program 3.5.3 and Statistical Package for the Social Sciences (SPSS) 20 was used to fit PIECEWISE REGRESSION and obtain descriptive statistics, respectively.Results: We assessed the trend of diabetic nephropathy in different groups of diabetic patients with respect to sex, blood pressure status, education, family history of diabetes, and age. The results showed an increasing trend in females, patients without family history of diabetes, and eover th recent years. The prevalence of diabetic nephropathy in patients with academic education was high.Conclusion: The groups with high prevalence or increasing trends need more preventive intervention and detailed assessment of the present trends. Exploring high-risk groups is beneficial for better policy-making in the future. However, discovering the reasons for the increased trend of the disease is really helpful in controlling diabetes complications.

This paper presents a new approach to estimate and to enlarge the domain of attraction for a planar continuous-time PIECEWISE affine system. Various continuous Lyapunov functions have been proposed to estimate and to enlarge the system’s domain of attraction. In the proposed method with a new vision and with the aids of a discontinuous PIECEWISE quadratic Lyapunov function, the domain of attraction at the origin is enlarged by designing a state feedback controller. This paper shows that the continuity of the Lyapunov function on the boundaries, increases the conservativeness in estimating the domain of attraction, and gives more powerful search ability to the domain of attraction estimation algorithm by relaxing this continuity condition. The simulation results show the superiority of the proposed method so that using this method the larger estimation of the domain of attraction is obtained than continuous one.

The present study investigates whether the basic assumption in the Jones model, which normal accruals are a linear function of change in sales, is empirically valid. It also discusses and addresses the implications of the assumption violation in the earnings management detection tests. The research employs a sample of 2832 observations of the annual information of firms listed in Tehran Stock Exchange and Iran Fara Bource for the period of 2002 to 2017. The findings suggest that normal accruals follow a PIECEWISE linear function with respect to sales changes. The results also suggest that the Jones model generates predictable systematic measurement error, which is consistent with its failure in capturing the accruals nonlinear behavior. The results of a Monte Carlo simulation of the type I error show that the level of abnormal accruals are understated for extreme sales growth and overstated for medium sales growth. The research highlights the importance of controlling the asymmetric behavior of normal accruals, especially in studies where earnings management incentives are correlated with sales growth.