Statistics Phase 6-: Skewness

-

SKEWNESS
Skewness means lack of symmetry.
Data can be skewed meaning that it tends to have a long tail on one side or the other.
POSITIVE SKEWNESS
Let’s take an example of the number of accident claims by an insurance customer in a sample of 50 people.
NUMBER OF CLAIMS
FREQUENCY
0
30
1
15
2
5
3
3
4
2
5 or more
1
TOTAL
50

Mean=8.33
Mode=0
Median=4
Here we can see that MEAN > MEDIAN
After plotting, this looks like this

From the graph, its clear that there is no symmetry in this as most of the data is concentrated towards the left of the graph and the tail is towards its right. So it is called positively skewed or right skewed.
NEGATIVE SKEWNESS
Lets take an example of 20 students obtaining CGPAs at the end of the semester exams.
CGPA
NO. OF STUDENTS
0-2
0
2-4
1
4-6
5
6-8
6
8-10
8
TOTAL
20

Mean = 4
Median = 5
Mode = 8-10 CGPA
Here, Mean < Median

NO SKEWNESS
When mean=median=mode, there is 0 skewness or it is normally distributed.









Comments

Post a Comment

Popular posts from this blog

Role of Generalised Linear Model in Non Life Pricing - Phase1

-
We will cover a series of topics relating to how Non Life Pricing is done through GLM.
But first let's see what is GLM

Generalised Linear Model Before Jumping on to what is GLM, let’s see what is Linear models 1.Linear Models:
Let’s take the example of Weight (Y) and Height (X). The aim of linear models is to find the line of best fit through the data points.



      Here is your X axis is Height and Y axis is your Weight. Y = B0­ + B1x
Line of Best Fit is B0­ + B1x where B0 is intercept on Y axis and B1 is the gradient.
Now the question is how that line comes?
Well, line is chosen in such a way to minimize the sum of squared error terms where error terms are distances from data points to straight line, error terms are normally distributed with mean 0 and variance σ2.


2.Multiple Linear Regression:
We can extend our model to allow for other predictive variables. For example, we can decide that Weight can depend on height and calories consumed per day both. So here we cannot find the line…
Read more

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…
Read more

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…
Read more