# Confidence that data belongs to distribution

• coolnessitself
In summary, the conversation discusses finding a numeric value for the probability that a set of non-uniformly spaced data points comes from a given piecewise pdf. The question also asks about a methodology for finding the best fit for the data by shifting the data points. The mentioned pdf is provided for reference. The suggested method for this task is maximum likelihood estimation, with the parameter to be estimated being xshift.
coolnessitself
Hi all,
This seems like a simple question, but I'm just not too knowledgeable about statistical methods.

I have a piecewise pdf $$f(x;\gamma)$$ (not any regular distribution) where $$\gamma$$ is known, and a set of non-uniformly spaced data points I obtained that somewhat resemble $$f(x;\gamma)$$. How do I go about finding some numeric value that shows the probability that my data comes from this distribution?
Also, once I'm able to do this, is there a methodology that allows me to find the best way the data fits, i.e. find $$x_\mathrm{shift}$$ such that if all data points are shifted right by $$x\rightarrow x+x_\mathrm{shift}$$, the data has the highest probability of coming from $$f(x;\gamma)$$?

(If it makes a difference, the pdf is http://nvl.nist.gov/pub/nistpubs/jres/106/2/j62mil.pdf" )

Last edited by a moderator:
Would that be "maximum likelihood estimation", where the parameter to be estimated is xshift?

## 1. What is "confidence that data belongs to distribution"?

"Confidence that data belongs to distribution" refers to the statistical measure of the likelihood that a given dataset follows a specific probability distribution. It is used to determine how well a particular model or hypothesis fits the observed data.

## 2. How is confidence that data belongs to distribution calculated?

The calculation of confidence that data belongs to distribution involves comparing the observed data to the theoretical distribution using statistical tests such as the chi-square test or the Kolmogorov-Smirnov test. The resulting p-value indicates the level of confidence in the fit of the data to the distribution.

## 3. Why is it important to determine the confidence that data belongs to distribution?

Determining the confidence that data belongs to distribution is important because it allows us to assess the validity and reliability of our statistical models and hypotheses. It also helps us to make informed decisions and draw accurate conclusions based on the data.

## 4. What factors can affect the confidence that data belongs to distribution?

The confidence that data belongs to distribution can be affected by various factors, such as sample size, data quality, and the appropriateness of the chosen probability distribution. Additionally, the assumptions made in the statistical tests used to calculate confidence can also impact the results.

## 5. How can one improve the confidence that data belongs to distribution?

To improve the confidence that data belongs to distribution, one can increase the sample size, ensure the data is of high quality, and choose a probability distribution that best fits the data. It is also important to carefully consider the assumptions made in the statistical tests and use appropriate methods to address any violations of these assumptions.

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