How can you calculate Pure IBNR and IBNER from the IBNR within 5 minutes?

Calculation of IBNER and Pure IBNR This article gives a brief about the different forms of IBNR component and its estimation that we generally come across in the General Insurance industry. Hopefully everyone is already familiar with the other terms of GI before reading this article. It will be useful to familiarize yourself with the following terms before reading this article any further (Ultimate Claims, Reported Claims, Incurred, Accident/Underwriting/Reporting Year Cohort, Chain Ladder Estimate, BF Estimate). Before we get to the estimation, let us first clear our understandings of the various terms. Incurred but not reported (IBNR): For a particular year the actuaries estimate the Ultimate Cost (generally referred as the Ultimate Claims) for all the business that has been written. This ultimate cost can be divided into Incurred Claims (Reported claim amount) and IBNR. IBNR can be further split down to two categories: 1)Incurred but not enough reported (IBNER): This portion of the IB…

What is Bayesian Statistics? Can you explain it to a layman

What is Bayesian Statistics: (I will try to explain in easy terms)
Often researchers investigating an unknown population parameter have information available from other sources in advance of the study that provides a strong indication of what values the parameter is likely to take. This additional information might be in a form that cannot be incorporated directly in the current study. The classical statistical approach offers no scope for the researchers to take this additional information into account. However, the Bayesian statistics is the approach which allows to take this additional information into account while estimating a population parameter.
Let me explain you with the help of an example:
4 championship races had been done between Mr. A and Mr. B. Out of which A has won 3 races and B has won 1 race. SO, on whom are you going to bet your money in the next race?
You will Say Mr. A because P(A) = 0.75 and P(B) = 0.25
So your initial estimate about B is P(B) = 0.25

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Now I will give you additional information say, there was a rain when Mr. B won and there was rain once when Mr. A won. And in the next match there will definitely be a rain.
So now I ask you again on whom will you bet your money?
Let’s decode the answer:
1.  P(R) = 0.50 (Because rain happened twice out of 4 matches)
2. P(R|B) = 1 (Because whenever Mr. B won there was a rain)
So I want to find out that what is probability that in the next race Mr. B will won if it is given that there will be a rain:
P(B|R) = P(R|B)*P(B)/P(R) = 0.50
I hope you know how this formula comes up otherwise you can mention me in comments I will tell you how.
Conclusion: Initially we comes up with an answer that P(B) = 0.25 which is my prior estimate and then I give additional information about rain which we incorporated in the form of conditional probability i.e. P(R|B) = 1 and then ultimately we find P(B|R) which is my posterior probability.
So you see how with the help of Bayesian statistics I incorporated additional information into my current study and how my value changes from 0.25 to 0.50.

Statistics seems easy now. 😊
Its an art and you are an artist.

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