em algorithm

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.

Model-based clustering is the most widely used statistical clustering method, in which heterogeneous data are divided into homogeneous groups using inference based on mixture models. The presence of measurement error in the data can reduce the quality of clustering and, for example, cause overfitting and produce spurious clusters. To solve this problem, model-based clustering assuming a normal distribution for measurement errors has been introduced. However, too large or too small (outlier) values ​​of measurement errors cause poor performance of existing clustering methods. To tackle this problem {and build a stable model against the presence of outlier measurement errors in the data}, in this article, a symmetric $alpha$-stable distribution is proposed as a replacement for the normal distribution for measurement errors, and the model parameters are estimated using the EM algorithm and numerical methods. Through simulation and real data analysis, the new model is compared with the MCLUST-based model, considering cases with and without measurement errors, and the performance of the proposed model  for data clustering in the presence of various outlier measurement errors is shown.

As application of compound distributions in the study of longevity data, in this paper the compound distribution of inverse Weibull Geometric is investigated. The presence of parameters of scale, shape and failure rate in this distribution, their study in terms of estimation and hypothesis testing is of particular importance. However, since the phenomenon of censorship is also considered in the study of lifetime data, so the parameters under the type-II of censorship are estimated using the maximum likelihood and Bayesian estimation. In Bayesian estimation, the parameters under different loss functions are estimated based on appropriate prior distributions, then the symmetric confidence interval and HPD are presented by simulation and the estimators are compared using statistical criteria. Finally, the goodness of fit of model is presented by the real data.

The common ways for analyzing the nonlinear autoregressive models are based on normality assumption of errors, whereas in many practical situations, the residuals show a nonnormal structure. The use of these methods leads to misleading and unreliable forecasts. Also, in these conditions, parametric and nonparametric methods do not have the necessary efficiency in estimating the nonlinear regression function. In this paper, a first-order nonlinear autoregressive model with dependent skew normal errors is introduced and a semiparametric method is proposed to estimate the nonlinear part of model. The parameters are estimated by the maximum likelihood (ML) method using Expectation-Maximization (EM) algorithm. The performance of the proposed model is investigated by a simulation study and analysis of a real data set of daily data on the exchange rate of the euro to the dollar.

Joint models use in follow-up studies to investigate the relationship between longitudinal markers and survival outcomes
and have been generalized to multiple markers or competing risks data. Many statistical achievements in the field of joint
modeling focuse on shared random effects models which include characteristics of longitudinal markers as explanatory variables
in the survival model. A less-known approach is the joint latent class model, assuming that a latent class structure
fully captures the relationship between the longitudinal marker and the event risk. The latent class model may be appropriate
because of the flexibility in modeling the relationship between the longitudinal marker and the time of event, as well as the
ability to include explanatory variables, especially for predictive problems. In this paper, we provide an overview of the joint
latent class model and its generalizations. In this regard, first a review of the discussed models is introduced and then the
estimation of the model parameters is discussed. In the application section, two real data sets are analyzed.

Profile monitoring is usually faced by control charts and mostly the response variable is observable in those problems‎. ‎We confront here with a similar problem where the values of the reward function are observed instead of the response variable vector and we use the dart model to make it easier to understand‎. ‎Supposing there exists at most one change-point‎, ‎a sequence of independent points resulted by darts throws is observed and the estimation of parameters and the change-point (if there exists any) are presented using the‎ ‎frequentist and Bayesian approaches‎. ‎In both the approaches‎, ‎two possible precision scalar and matrix are studied separately‎. ‎The results are examined through a simulation study and the methods applied on a real data‎.

In this article, a mixture of multivariate normal and standard exponential distributions is investigated. It is shown that the range of skewness and kurtosis coefficients for this distribution is wider than that of the skew-normal distribution. Some properties of this distribution, such as characteristic function, moment generating function, four first moments, skewness and kurtosis of distribution are presented. Also, the distribution of offine transformations and canonical forms of distribution are derived. The maximum likelihood estimation of parameters of the model is computed by using an EM algorithm. To investigate the suitability and efficiency of the model, a simulation study is presented. Finally, two numerical examples with real data sets are studied.

‎The class of α-stable distributions incorporates both heavy tails and skewness and so are the most widely used class of distributions in several fields of study which incorporates both the skewness and heavy tails‎. ‎Unfortunately‎, ‎there is no closed-form expression for the density function of almost all of the members of this class‎, ‎and so finding the maximum likelihood estimator for the parameters of this distribution is a challenging problem‎. ‎In this paper‎, ‎in order to tackle this issue‎, ‎we propose some type of EM algorithm‎. ‎The performance of the proposed EM algorithm is demonstrated via simulation and analyzing three sets of real data‎.

Breast cancer is the most prevalent cause of cancer mortality among women. Early diagnosis of breast cancer gives patients greater survival time. The present study aims to provide an algorithm for more accurate prediction and more effective decision-making in the treatment of patients with breast cancer.

The present study was applied, descriptive-analytical, based on the use of computerized methods. We obtained 699 independent records containing nine clinical variables from the UCI machine learning. The EM algorithm was used to analyze the data before normalizing them. Following that, a combination of neural network model based on multilayer perceptron structure with the Whale Optimization Algorithm (WOA) was used to predict the breast tumor malignancy.

After preprocessing the disease data set and reducing data dimensions, the accuracy of the proposed algorithm for training and testing data was 99.6% and 99%, respectively. The prediction accuracy of the proposed model was 99.4%, which would be a satisfying result compared to different methods of machine learning in other studies.

Considering the importance of early diagnosis of breast cancer, the results of this study may have highly useful implications for health care providers and planners so as to achieve the early diagnosis of the disease.