To determine the number of clusters in the clustering analysis that has a broad range of applied sciences, such as physics, chemistry, biology, engineering, economics etc., many methods have been proposed in the literature. The aim of this paper is to determine the number of clusters of a dataset in a model-based clustering by using an Analytic Hierarchy Process (AHP). In this study, the AHP model has been created by using the information criteria Akaike’s Information Criterion (AIC), Approximate Weight of Evidence (AWE), Bayesian Information Criterion (BIC), Classification Likelihood Criterion (CLC), and Kullback Information Criterion (KIC). The achievement of the proposed approach has been tested on common real and synthetic datasets. The proposed approach based on the corresponding information criteria has produced accurate results. The currently produced results have been seen to be more accurate than those corresponding to the information criteria.

The main objective of the present study is to estimate wind power potential using the two Weibull parameters of the wind speed distribution function, the shape parameter k (dimensionless) and the scale parameter c (m/s). In this regard, a methodology that uses three various techniques (maximum likelihood, least squares, and method of moments) for estimating the Weibull parameters was given first. The methodology was then applied to a region in Turkey. Finally, the parameter techniques were compared to Monte-Carlo simulation in different sample sizes, and the best parameter estimation techniques belonging to the sample sizes were also determined.

Clustering analysis based on a mixture of multivariate normal distributions is commonly used in the clustering of multidimensional data sets. Model selection is one of the most important problems in mixture cluster analysis based on the mixture of multivariate normal distributions. Model selection involves the determination of the number of components (clusters) and the selection of an appropriate covariance structure in the mixture cluster analysis. In this study, the efficiency of information criteria that are commonly used in model selection is examined. The effectiveness of information criteria has been determined according to the success in the selection of the number of components and in the selection of an appropriate covariance matrix.

Bimodal mixture Weibull distribution being a special case of mixture Weibull distribution has been used recently as a suitable model for heterogeneous data sets in many practical applications. The bimodal mixture Weibull term represents a mixture of two Weibull distributions. Although many estimation methods have been proposed for the bimodal mixture Weibull distribution, there is not a comprehensive comparison. This paper presents a detailed comparison of five kinds of numerical methods, such as maximum likelihood estimation, least-squares method, method of moments, method of logarithmic moments and percentile method (PM) in terms of several criteria by simulation study. Also parameter estimation methods are applied to real data.

In the context of estimating regression coefficients of an ill-conditioned binary logistic regression model, we develop a new biased estimator having two parameters for estimating the regression vector parameter β when it is subjected to lie in the linear subspace restriction Hβ = h. The matrix mean squared error and mean squared error (MSE) functions of these newly defined estimators are derived. Moreover, a method to choose the two parameters is proposed. Then, the performance of the proposed estimator is compared to that of the restricted maximum likelihood estimator and some other existing estimators in the sense of MSE via a Monte Carlo simulation study. According to the simulation results, the performance of the estimators depends on the sample size, number of explanatory variables, and degree of correlation. The superiority region of our proposed estimator is identified based on the biasing parameters, numerically. It is concluded that the new estimator is superior to the others in most of the situations considered and it is recommended to the researchers.