Is the geometric mean an unbiased estimator?

Is the geometric mean an unbiased estimator?

Blume (1974) shows that the arithmetic mean, A, is an unbiased estimate of the true expecta- tion M, and the compounded geometric mean G’ is an unbiased estimate of the compounded wealth relative M’. As the geometric mean is always below the arithmetic mean, it is always the more biased of the two estimates.

Is the geometric mean consistent?

Note: the geometric mean will not always equal the median, only in cases where there is an exact consistent multiplicative relationship between all numbers (e.g. multiplying each previous number by 3, as we did).

Which is the unbiased estimator for geometric distribution?

Let X 1, …, X n to be sample distributed geometric with parameter p. Find MLE. Is it unbiased? L ( p) = ∏ i = 1 n p ( 1 − p) X i − 1. ( 1 − p). I derivatied and found maximum in p m = n n + ∑ i = 1 n ( X i − 1). Now I need to calculate E [ p m]:

Which is the best definition of a geometric mean?

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the product of n numbers, i.e.,…

Which is an unbiased estimator of the parameter θ?

If the following holds: then the statistic u ( X 1, X 2, …, X n) is an unbiased estimator of the parameter θ. Otherwise, u ( X 1, X 2, …, X n) is a biased estimator of θ. If X i is a Bernoulli random variable with parameter p, then: is the maximum likelihood estimator (MLE) of p.

How to calculate the geometric mean of a program?

Application to normalized values Computer A Computer B Computer C Program 1 0.05 0.5 1 Program 2 50 5 1 Arithmetic mean 25.025 2.75 1 Geometric mean 1.581 . . . 1.581 . . . 1