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2 results

  • 6 - Bivariate Regression and Correlation and Statistical Inference

  • Dudley L. Poston, Jr, Texas A&M University, Eugenia Conde, University of North Carolina, Chapel Hill, Layton M. Field, Mount St. Mary’s University
  • Book:
    Applied Regression Models in the Social Sciences
    Published online:
    17 August 2023
    Print publication:
    17 August 2023, pp 88-124

  • Summary

    A major concern in the social sciences is understanding and explaining the relationship between two variables. We showed in Chapter 5 how to address this issue using tabular presentations. In this chapter we show how to address the issue statistically via regression and correlation. We first cover the two concepts of regression and correlation. We then turn to the issue of statistical inference and ways of evaluating the statistical significance of our results. Since most social science research is undertaken using sample data, we need to determine whether the regression and correlation coefficients we calculate using the sample data are statistically significant in the larger population from which the sample data were drawn.

  • ON THE $r\mathcal{B}$ELL FAMILY OF DISTRIBUTIONS WITH ACTUARIAL APPLICATIONS

  • Deepesh Bhati, Enrique Calderín-Ojeda
  • Journal:
    ASTIN Bulletin: The Journal of the IAA / Volume 52 / Issue 1 / January 2022
    Published online by Cambridge University Press:
    18 May 2021, pp. 185-210
    Print publication:
    January 2022

  • In this paper, a new three-parameter discrete family of distributions, the $r{\mathcal B}ell$ family, is introduced. The family is based on series expansion of the r-Bell polynomials. The proposed model generalises the classical Poisson and the recently proposed Bell and Bell–Touchard distributions. It exhibits interesting stochastic properties. Its probabilities can be computed by a recursive formula that allows us to calculate the probability function of the amount of aggregate claims in the collective risk model in terms of an integral equation. Univariate and bivariate regression models are presented. The former regression model is used to explain the number of out-of-use claims in an automobile insurance portfolio, by showing a good out-of-sample performance. The latter is used to describe the number of out-of-use and parking claims jointly. This family provides an alternative to other traditionally used distributions to describe count data such as the negative binomial and Poisson-inverse Gaussian models.