1. GLM, GNM and GAM Approaches on MTPL Pricing

    Claudio Giorgio Giancaterino

    Abstract:

    This work has the aim to compare different statistics modelling approaches both used and could be second-hand used in motor third party liability pricing.
    Generalized Linear Models are made up by a systematic component ηi = Σnj=1 xijβj linked with a random component Yi = EF(b(θi); φi/ωi) by a link function g(μi). A Generalized Non-linear Model is the same as the GLM model except the link function g(μi) = ηi(xij; βj) where the systematic component is non linear in the parameters βj. Generalized Additive Models extend Generalized Linear Models in the predictor ηi = Σnp=1 xipβp + Σnj=1 fj(xij) made up by one parametric linear part and one non parametric part built by the sum of unknown “smoothing” functions of the covariates.

    Mean commercial tariff Tariff requirement Loss Ratio Residuals degrees of freedom Expected Losses Actual Losses Explained Deviance Risk coefficients
    Uni- GLM 234,4587 1,000490 1,447822 27.501 9.337.547 9.342.125 96,96% 20
    Variate GNM 234,4647 1,000476 1,447785 27.501 9.337.683 9.342.125 96,96% 20
    Analysis GAM 232,8702 1,001729 1,457698 27.476 9.325.999 9.342.125 96,20% 45
    Multi- GLM 234,6486 0,9981246 1,446650 27.505 9.359.678 9.342.125 87,64% 16
    Variate GNM 234,6165 0,9979703 1,446848 27.505 9.361.125 9.342.125 87,04% 16
    Analysis GAM 248,5732 0,8596438 1,365612 27.265 10.867.438 9.342.125 84,80% 256

    GAM approach is flexible to fit data, with realistic values and low level of residual deviance, but quite complex to realize. GLM is easier to use, but sometimes with overestimated coefficients and high values about residual deviance. GNM is an upgrade of GLM model, it grants some elaborations that GLM can’t replicate and with lower values compared to it.
    From these three models GAM is able to personalize a premium with more risk coefficients.

    Keywords: Actuarial Sciences, Non-Life Insurance Pricing, Statistical Modelling.

    Pages: 427 – 481 | Full PDF Paper

  2. Le-MATH: Learning Mathematics Through New Communication Factors

    Gr. Makrides and project Le-MATH partners

    Introduction: Many students claim that mathematics is often too abstract and therefore difficult to understand. As a result, this project developed different and innovative approaches by inviting teachers and pupils together to apply new communication methods in the learning of mathematics, which could be fun and enjoyable at the same time. An approach, that brings new ideas in the context of “play and learn.”This European project developed a new methodology for the learning and teaching of mathematics to students aged between 9 and 18, which subsequently can be used in any school environment. It will also make learning more attractive and enjoyable for all students and it will strengthen their skills for creative thinking. These methods could be used in other subjects of the education curricula, as well as for other age groups. The consortium comprises partners from universities, schools, mathematics associations, foundations, theatre schools, art schools and enterprises.The project activities contribute to the Education and Training 2020 as it is enhancing creativity and innovation among youth. It also contributes to the benchmark for decreasing low-achievers in basic skills (mathematics and science) to 15%. It promotes the European Cooperation on schools in fundamental aptitudes, by supporting the key competence for mathematics.

    Pages: 482 – 489 | Full PDF Paper

  3. Comparison of Parameter Estimation in the Exponentiated Gumbel Distribution based on Ranked Set Sampling and Simple Random Sampling

    Hossein Jabbari Khamnei, Sanaz Ravandeh Mayan

    Abstract:

    Various parametric families of distribution in lifetime data analysis and failure models are used. In this condition, the gamma distribution, Weibull and log-normal named because of the shape and scale parameters flexible high plasticity analysis of different types of data, especially lifetime data are skew.

    Recently, a new distributed Exponential Gumbel distribution by Mudholkarand Srivastava (1993) and Nadarajah (2006) presented and analyzed the characteristics to estimate the parameters of the distributions. In this paper, we estimate the parameters of Gumbel distribution based on Simple Random Sampling, and Ranked Set Sampling, also we will compare these two methods.

    Keywords: Exponentiated Gumbel distribution, Order Statistics, Simple Random Sampling, Ranked Set Sampling, Maximum Likelihood Estimation.

    Pages: 490 – 497 | Full PDF Paper

  4. Performance of T2 Chart over 𝑥̅ Chart for Monitoring the Process Mean: A Simulation Study

    Md. Belal Hossain and Mohammad Shahed Masud

    Abstract: In real life we observe that there are many situations in which the simultaneous monitoring or control of two or more related quality characteristics is necessary. In such situations we can use univariate control charts to each individual quality characteristics but these control charts can lead to erroneous conclusions. Multivariate methods that consider the quality characteristics jointly are required. The most familiar multivariate process monitoring and control procedure is the Hotelling T2 control chart for monitoring the process mean simultaneously. It is a direct analog of the univariate Shewhart  control chart. In this paper, using simulation study we show that if the quality characteristics are related then for monitoring the mean of the process Hotelling T2 control chart performs better than Shewhart  control chart.

    Keywords: Quality characteristics; Shewhart control chart; multivariate control chart; detection rate of out of control signal.

    Pages: 498 – 512 | Full PDF Paper