Role of Generalised Linear Model in non-life pricing Phase3

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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 ex…

What is Random Variable?

Random Variable:

When there is a probability associated with a variable that makes it Random Variable.
So a Random variable can take many different values with different probabilities.

Example:

Q.1) No. of Days in a week-: Is this a Random Variable?

A.1)  NO, because no. of days in a week is fixed i.e 7


Q.2) No. of Days in a Month-: Is this a Random  Variable?

A.1)  Yes, because no. of days in a month can be 28,29,30 or 31. So this is Random in nature.


Note:

Suppose X is "Something" now it can take value "0" if 3 comes up on a Dice and "1" if even no. comes up on dice.

So we know that probability of getting a 3 on Dice is 1/6 . So probability of getting a value "0" is 1/6
Similarly the probability of getting an Even no. on dice is 1/2. So probability of getting "1" is 1/2.

so we see that when "something is attached with different values along with different probabilities it becomes a Random variable.


   

Comments

  1. Thankyou for sharing this wonderful article. But I have a doubt~is Random Variable- a variable to which probability is associated? Random variable is a value associated with a random experiment. In that is there really a role of probability? Because in the example you mentioned no. of days in a month can be 28,29,30& 31. There is no probability. It is all about values. Please share your thoughts on this. Thankyou!

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