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

CFM vs UDD vs Balducci

-
Life Tables: It is a computational tool based on a specific survival model. Our task is to generate a survival model and our output will be a life table. Life table is based on Unitary method. lx= Expected no. of lives at age x dx= Expected no. of deaths between exact age x and exact age x+1 NOTE: We call it expected and not actual because most of the values will be in decimal too, so how can it be actual.
But there is a limitation of Life Tables: It is defined only for integer ages. If we have to calculate probability of death/survival at any non-integer age we will use 3 assumptions: 1.CFM= Constant Force of Mortality 2.UDD= Uniform Distribution of death 3.Balducci assumption
1.CFM ·It assumes that the force of mortality is constant, i.e. ux+t = ux ·If the force of mortality of a newborn is constant, it means that the expected future lifetime of this life is 1/μ no matter what age he is in. ·Survival Function in this case will decrease exponentially. ·If 0<s<t<1 then t-spx+s = tpx/spx …
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