Posts

Showing posts from November, 2018

Role of Generalised Linear Model in non-life pricing Phase3

Before reading this article, make sure that you read phase1 and phase2. Here are the link:
Phase1: http://www.actuarysense.com/2018/10/role-of-generalised-linear-model-in-non.html
Phase2: http://www.actuarysense.com/2018/11/role-of-generalised-linear-model-in-non.html So we know that the purpose of GLM is to find the relationship between mean of the response variable and covariates.

In this Article we are going to talk about Linear Predictors.
Linear Predictor: Let’s denote it with, “η” (eta). So, linear predictor is actually a function of covariates. For example, in the normal linear model where function is Y = B0 + B1x. So linear predictor will be η = B0 + B1x. Always note that linear predictor has to be linear in its parameter. In this case parameters are B0 and B1. But still the question is how I came up with B0 + B1x as a function? First of all, note that broadly there are two types of Covariates. 1. Variables: It takes the numerical value. For example: age of policyholder, years of…

Role of Generalised Linear Model in Non-Life Pricing - Phase 2

Before reading this article, make sure that you have read the phase 1.
Here is the link for the same:  http://www.actuarysense.com/2018/10/role-of-generalised-linear-model-in-non.html
In this Topic we will talk about Link function and Linear predictors.
We saw in previous topic that exponential family is
f( y; θ, φ) = exp[{(yθ – b(θ))/a(φ)} – c(y, φ)] where θ is your natural parameter and φ is your dispersion parameter.
Response distribution can be Gamma, Binomial, Lognormal, Poisson, Normal or Exponential and then we make it in the form of exponential family.
Now the thing is that relationship between Response and covariates is defined through mean of response distribution i.e. E[Y]
Let’s take the example of linear model where we defined Y = B0 + B1x. (learn about linear model in the previous topic),
Y – N ( µ, σ2) where your µ = B0 + B1x.
Now note one thing always that purpose of GLM is to find the relationship between mean of the response variable and covariates.
Photo credits: baj…