MLB Betting

[jelly]

[ QUOTE ]
crockpot, where could one get further reading on this topic? If the statement is incorrect, then I'd like to know why the authors are incorrectly stating it this way.

[/ QUOTE ]

Distribution is not a number, it cannot lie within an interval. Most likely, the author just slipped wrong word in.

[rjp]

Here is exactly what the author's state:

... we can assert that if we repeatedly obtain independent random samples of size n from the population and calculate the [confidence] bands every time, then in the long run XX% of these bands will enclose the unknown distribution entirely. In the remaining cases, the true distribution may fall partly or wholly outside.

From Statistical Analysis of Nonnormal Data.

[rjp]

jelly, they're actually referring to a distribution function, such that for any given number a confidence band is made for the entire function.

In the case of a single number, as is the case here, they say to exploit the binomial distribution, which is where the above interval comes from.

[jelly]

[ QUOTE ]
Here is exactly what the author's state:

... we can assert that if we repeatedly obtain independent random samples of size n from the population and calculate the [confidence] bands every time, then in the long run XX% of these bands will enclose the unknown distribution entirely. In the remaining cases, the true distribution may fall partly or wholly outside.

From Statistical Analysis of Nonnormal Data.

[/ QUOTE ]

That is fine, but it deals with a different situation. You do not deal with all distributions as you restrict yourself to binomic distribution family. Once you make this assumption it is enough to work with its parameter p that you are trying to work out from the sample mean.
You use too general statement for a precise situation. In the original statement, interval does not stand for say 47.64% - 52.22% but for a 2-dimensional interval covering distribution functions.

[rjp]

jelly, is this cleared up by the post I made after the one you quoted? I understand that for this situation we're not dealing with an entire distribution but a single number, which I tried to clarify in that post.

I guess I shouldn't have bothered with quoting the book as it directly speaks to an entire distribution function and not a single number.

[jelly]

[ QUOTE ]
jelly, is this cleared up by the post I made after the one you quoted? I understand that for this situation we're not dealing with an entire distribution but a single number, which I tried to clarify in that post.


[/ QUOTE ]

I think so. Crockpot's FYP was initiated by different meanings of "interval" in the two situations.

[rjp]

OK, I just want to make sure we're talking about the same thing [img]/images/graemlins/smile.gif[/img]

This paper seems to clear it up (assuming it's correct, of course):

"Therefore, in this framework of repeated sampling under the same conditions, a probability statement can be made, saying that the probability that the stochastic interval will cover the unknown fixed population value equals 1 - alpha."

I take this to again mean that there is a alpha% chance that the calculated interval does not contain the true value.

If I have interpreted this wrong please correct me.