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

• jimbof85
In summary, the conversation is about finding a mathematical expression to convey the statement "f(x) > y 95% of the time" in reference to an experiment with multiple variations and the use of a chi-squared test to determine success. The concept of confidence intervals and the notation of a caret or "hat" symbol to denote estimation are suggested. However, it is noted that some explanation in plain English may still be necessary.
jimbof85
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) $\stackrel{95\%}{>}$10)1000

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

Thanks

James

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

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!

jimbof85 said:
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.

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

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' : $x\in C$

'natural log tends to infinity as x tends to infinity' : $\lim\limits_{x\to+\infty}$$\ln(x)\to+\infty$

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

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:$$p(f(x) > 10) = 0.95$$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:$$\hat p_{1000}(f(x) > 10) = 0.95$$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.

## 1. What is a "maths statement for point when condition is met some fraction of the time"?

A "maths statement for point when condition is met some fraction of the time" refers to a mathematical statement or equation that is only true for a certain portion of the time. This means that the statement is not always true, but it is true for a specific fraction or percentage of the time.

## 2. How is this different from a regular mathematical statement?

This type of statement differs from a regular mathematical statement because it is only applicable for a certain fraction of the time, whereas a regular mathematical statement is true for all values and conditions.

## 3. Can you provide an example of a "maths statement for point when condition is met some fraction of the time"?

An example of this type of statement would be "When rolling a six-sided die, the probability of rolling a 5 is 1/6". This statement is only true for 1 out of 6 possible outcomes or 1/6 of the time.

## 4. Why is it important to consider this type of statement in mathematics?

Understanding and using "maths statement for point when condition is met some fraction of the time" is important in many areas of mathematics, such as probability and statistics. It allows for a more accurate representation of real-world situations where outcomes may not always be certain.

## 5. How can one determine the fraction of time when the condition is met for a specific statement?

The fraction of time when the condition is met can be determined using various mathematical methods, such as calculating probabilities or conducting experiments and collecting data. It is important to note that this fraction may vary depending on the specific scenario and conditions.

Replies
5
Views
904
Replies
8
Views
2K
Replies
3
Views
833
Replies
1
Views
2K
Replies
61
Views
8K
Replies
114
Views
7K
Replies
1
Views
734
Replies
46
Views
5K
Replies
5
Views
1K
Replies
107
Views
16K