# Unbiased estimator for The exponential

1. Dec 23, 2011

### srhjnmrg

Looking at obtaining the unbiased estimator of σ^2, i know how to do it for σ, to obtain
1/x(bar), was wondering how to obtain for σ^2, i guess you just dont square bot sides. It should tale the form of kƩ(x_i)^2.
many thanks any help would be much appreciated.

2. Dec 23, 2011

### mathman

Try to clarify what you are doing. Usually estimations are made for σ2 and σ is just the square root.

3. Dec 23, 2011

### SW VandeCarr

Note, the rate parameter estimate is $\hat \lambda = 1/\bar x$. The mean is therefore $1/\lambda$ and the variance is $1/\lambda^2$. The standard deviation is not really defined for the exponential distribution because it is not symmetrical around the mean. The usual maximum likelihood estimate of the mean $\bar x = (\sum_{i=1}^{i=n} x_i)/n$ is unbiased, and therefore so is the estimate of lambda.

Last edited: Dec 24, 2011