# Approximate with a Normal distribution (Bayesian statistics)

• Jan 3rd 2010, 11:42 AM
JrShohin
Approximate with a Normal distribution (Bayesian statistics)
Dear users,

I am solving an exercise.
Here, assume a Gamma distribution with a parameter lambda I have a priori:
Pr(lambda is (belongs) [10,20])=0.95

I have to approximate the priori with a Normal distribution.

When I saw the solution, it says:

after approximation with a normal distribution, we obtain the confidence interval: lambda belongs [15+-5]
Which results in:
E[lambda]=15
V[lambda]=(5/1.96)^2=6.5.

Please, could you explain me, how to approximate with a Normal distribution. And could you give me the formula itself. I cannot understand how to get the confidence interval [15+-5].

What about the mean and the variance, I understood.

Thank you in advance, I highly appreciate.
• Jan 4th 2010, 06:42 AM
CaptainBlack
Quote:

Originally Posted by JrShohin
Dear users,

I am solving an exercise.
Here, assume a Gamma distribution with a parameter lambda I have a priori:
Pr(lambda is (belongs) [10,20])=0.95

I have to approximate the priori with a Normal distribution.

When I saw the solution, it says:

after approximation with a normal distribution, we obtain the confidence interval: lambda belongs [15+-5]
Which results in:
E[lambda]=15
V[lambda]=(5/1.96)^2=6.5.

Please, could you explain me, how to approximate with a Normal distribution. And could you give me the formula itself. I cannot understand how to get the confidence interval [15+-5].

What about the mean and the variance, I understood.

Thank you in advance, I highly appreciate.

All that is happening here is that your gamma distribution has a 95% interval [10,20] and you are modelling this with a symmetric normal 95% interval which has its mean at the centre of the interval and extends from (mean-1.96 sigma) to (mean + 1.96 sigma).

CB