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Maths statement for point when condition is met some fraction of the time 
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#1
Jan2913, 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 


#2
Jan2913, 08:44 AM

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PF Gold
P: 39,524

Sounds to me like you are talking about a "95% confidence level".



#3
Jan2913, 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! 


#4
Jan2913, 09:41 AM

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P: 21,280

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



#5
Jan2913, 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 


#6
Jan2913, 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 


#7
Jan2913, 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 phat means in your context. My 2 cents.



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