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Maths statement for point when condition is met some fraction of the time

by jimbof85
Tags: condition, fraction, maths, point, statement, time
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jimbof85
#1
Jan29-13, 05:42 AM
P: 4
Hello all,

I would like to express the following as an equation, but don't know the nomenclature.

'The point at which a condition is true 95% of the time'

ie. I have a function, f(x) which returns some value in the presence of random and uncharicterizable noise. I run this 1000 times. I find the condition f(x)>10 is true 50% of the time. I adjust f(x), and rerun 1000 times and find f(x)>10 is true 80%. I keep rejecting f(x) until I reach the point where f(x)>10 for 95% of samples.

Basically I want something like (f(x) [itex]\stackrel{95\%}{>}[/itex]10)1000

but there is bound to be a correct way to do this

Thanks

James
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HallsofIvy
#2
Jan29-13, 08:44 AM
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P: 39,569
Sounds to me like you are talking about a "95% confidence level".
jimbof85
#3
Jan29-13, 08:54 AM
P: 4
Hi HallsofIvy,

Thanks for the reply. It is not (I believe) fair to talk about confidence levels in the way I think you suggest - this is not a normally distributed random variable, it is not a two tailed distribution. I am in fact fitting a model to my data to get a chi sqrd, comparing this chi sqrd to a threshold, and if it is below this claim a success. I simply extract the point where some percentage of these results are successes - I chose 95%. The distribution of the number of successes in each of the many variations of the experiment is not normally distributed. I simply want an mathematical expression that says the equivalent of 'x > y 95% of the time' rather than 'x>y'

Sorry i can't put it clearer than that!

Mark44
#4
Jan29-13, 09:41 AM
Mentor
P: 21,321
Maths statement for point when condition is met some fraction of the time

Quote Quote by jimbof85 View Post
Hi HallsofIvy,

Thanks for the reply. It is not (I believe) fair to talk about confidence levels in the way I think you suggest - this is not a normally distributed random variable, it is not a two tailed distribution. I am in fact fitting a model to my data to get a chi sqrd, comparing this chi sqrd to a threshold, and if it is below this claim a success. I simply extract the point where some percentage of these results are successes - I chose 95%. The distribution of the number of successes in each of the many variations of the experiment is not normally distributed. I simply want an mathematical expression that says the equivalent of 'x > y 95% of the time' rather than 'x>y'

Sorry i can't put it clearer than that!
Confidence intervals are not limited just to normal distributions. This concept can be applied to ##\chi^2## distributions for inferences about ##\sigma^2 ##. The hypothesis tests can be one-tailed or two-tailed.
jimbof85
#5
Jan29-13, 04:50 PM
P: 4
Hi Mark44,

Thanks for the reply. Ok, I understand your point, but i am not asking for a confidence interval. My question is on nomenclature. I simply need a mathematical way of conveying the following statement 'f(x) > y 95% of the time'. I do not need the distribution behind it, or the mathematics that control it - I am just after the correct symbols to properly convey that I have chosen a set of values for f(x) such that it meets some criterion for some fraction of realisations of the experiment.

Thanks
jimbof85
#6
Jan29-13, 05:06 PM
P: 4
Just to further clarify, I simply want to do as follows, take an expression in words and write it using mathematical notation. i.e.

'x is a complex number' : [itex]x\in C[/itex]

'natural log tends to infinity as x tends to infinity' : [itex]\lim\limits_{x\to+\infty}[/itex][itex]\ln(x)\to+\infty[/itex]

'f(x) > y 95% of the time' : ???

Thanks for your help
dodo
#7
Jan29-13, 07:11 PM
P: 688
It seems to me that, if P(E) denotes the probability of an event E, you are referring to an estimation of the following statement:[tex]p(f(x) > 10) = 0.95[/tex]This statement, however, speaks of a theoretical (and unknown) probability, which your experiment is trying to estimate. An often used notation is to write a caret or "hat" symbol over the letter, to denote it is an estimation:[tex]\hat p_{1000}(f(x) > 10) = 0.95[/tex]But I think it is unavoidable to accompany these lines with a few words in plain English (as I did) that define what p-hat means in your context. My 2 cents.


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