#11
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Re: MLB Betting
[ 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. |
#12
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Re: MLB Betting
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. |
#13
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Re: MLB Betting
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. |
#14
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Re: MLB Betting
[ 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. |
#15
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Re: MLB Betting
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. |
#16
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Re: MLB Betting
[ 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. |
#17
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Re: MLB Betting
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. |
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