مجله بین المللی محاسبات و مدل سازی ریاضی
سال دوازدهم شماره 3 (Summer 2022)

This paper presents a mechanism for insurance companies to assess the most effective features to classify the risk of their customers for third party liability (TPL) car insurance. Basically, the process of underwriting is carried out based on the expert experiences and the industry suffers from lack of a systematic method to categorize their policyholders with respect to the risk level. We analyzed 13,388 observations of an insurance claim dataset from body injury reports provided by an Iranian insurance company. The main challenge is the imbalanced dataset. Here we employ logistic regression and random forest with different resampling of the original data in order to increase the performance of models. Results indicate that the random forest with the hybrid resampling methods is the best classifier and furthermore, victim age, premium, car age and insured age are the most important factors for claims prediction.

In this work, an iterative method under the umbrella of inverse-free methods which do not rely on the calculation of the inverse matrix per loop is proposed for finding the maximal solution of a well-known nonlinear matrix equation (NME) in the form of Hermitian positive definite (HPD) matrices. The computational of the minimal solution is discussed as well. The iterative scheme is constructed based on methods for finding generalized matrix inverse. We illustrate some estimations for obtaining the solution, and its convergence. To ensure its validity and usefulness, some experiments are run which reveal the superiority of the proposed method.

In this paper, we present several numerical radius and norm inequalities for sum of Hilbert space operators. These inequalities improve some earlier related inequalities. For $A,B\in B\left( H \right)$, we prove that\[\omega \left( {{B}^{*}}A \right)\le \sqrt{\frac{1}{2}{{\left\| A \right\|}^{2}}{{\left\| B \right\|}^{2}}+\frac{1}{2}\omega \left( {{\left| B \right|}^{2}}{{\left| A \right|}^{2}} \right)}\le 4\omega \left( A \right)\omega \left( B \right).\]

In today's world, with the advancement of science and technology, data is generated at high speeds, and with the increase in the size and volume of data, we often face a lot of extensions and redundant data and noise data that make the task of analysis difficult. Therefore, dimension reduction of the data without losing useful information in the data is very important to prepare the data for data mining and can increase the speed and even accuracy of the analysis. In this research, we present a dimensional reduction method using a copula function that reduces the dimensions of the data by identifying the relationships between the data. The copula function provides a good pattern of dependence for comparing multivariate distributions to better identify the relationship between data. In fact, by fitting the appropriate copula function to the data and estimating the copula function parameter, we measure the structural correlation of the variables and eliminate variables that are highly structurally correlated with each other. As a result, in the method presented in this study, using the copula function, we identify noise data and data with many common features and remove them from the original data.

Given any graph G, its square graph G^2 has the same vertex set V (G), with two vertices adjacent in G^2 whenever they are at distance 1 or 2 in G. A set S ⊆ V (G) is a 2-distance independent set of a graph G if the distance between every two vertices of S is greater than 2. The 2-distance independence number α_2(G) of G is the maximum cardinality over all 2-distance independent sets in G. In this paper, we establish the 2-distance independence number and 2-distance chromatic number for C_3□C_6□C_m, C_n□P_3□P_3 and C_4□C_7□C_n where m ≡ 0 (mod 3) and n,m ⩾ 3.

The purpose of the present study is to consider the estimation of the PDF and CDF of the three-parameter inverse Weibull (IWD) distribution. To do so, we propose the following well-known methods moment (MM) estimation, maximum likelihood (ML) estimation, and a developed method entitled the location and scale parameters free maximum likelihood (LSPF) derived from Nagatsuka et al. (2013). Having estimated the parameters, we would consider estimating the PDF and the CDF of the IWD distribution with these three methods. Then, analytical expressions are derived for the mean integrated squared error (MISE) to compare the estimators. According to the results of simulation and two real data for estimation of the PDF and CDF, when the shape parameter is greater than 1, the LSPF method performs better than the others, and when the shape parameter is equal to or smaller than 1, the ML method is better than the others.