# Tag Info

• 6,190

• 1,254

### Turning sleep schedule data into a statistical distribution

Initial thought: Asleep versus Awake at time $t$ is a binary outcome. Let $x_{it} \mid \pi_t \sim \text{Bernoulli}(x_{it}\mid\pi_t)$, then have $\pi_t$ be a probit transformation of a Gaussian ...
• 173
1 vote

### Turning sleep schedule data into a statistical distribution

Strictly speaking (in my humble opinion), you cannot build up an empirical distribution from the data to then detect outliers in the data (sort of a chicken and the egg problem). You can evaluate the ...
• 51

### Normal Distribution or Not

It seems to be normal, but the transformation you've chosen breaks that assumption. There are way too fat tails in your distribution (left and right), because of the 0% and 12% data transformation. I ...
1 vote
Accepted

### Questions the calculation of Z score and confidence intervals in biology

My question/concern is, shouldn’t we adjust for the actual distribution of the data? Yes. For example, this helpful Technical Perspective on Empowering statistical methods for cellular and molecular ...
• 62.4k

### Questions the calculation of Z score and confidence intervals in biology

Mean and sd have an interpretation that isn't exclusive to the normal distribution, so I don't think such a Z score should be seen as requiring normality (normality may be required for certain ...
• 11.5k

### Shapiro Wilk test of normality

One very basic but useful rule* to interpret this kind of test (normality, heteroskedasticity, autocorrelation) is to remember that when the p-value is less than 0.05, it means that something is "...

• 94.6k
1 vote
Accepted

### Infinitesimal Robustness, influence function of $T$ at $F$

You are working in a function space, specifically, the space of probability distributions equipped with some useful topology. In this case, we can choose two probability distributions in that space - ...
• 32.7k
1 vote

### Get probability distribution function from density function and calculate the cumulative value

Firstly, your density function does not presently integrate to one --- to get the correct density you need to add an additional multiplicative term $2^{-n/2}$. I will make this adjustment in my ...
• 94.6k

• 9,120
Accepted

### n-th quantile for bivariate variable

The documentation says ...
• 23.9k
1 vote
Accepted

### Describing / fitting a highly skewed distribution

You should consider comparing distributions. One handy Python library to compare distributions to describing empirical data is the powerlaw library. It has a paper that explains how to use it: ...
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### transformation of a kernel density estimate to uniform distribution

Background As stated in this as well in his prior question the OP wants to perform Bayes quadrature of an expensive function against a density, which is a Gaussian mixture as the result of applying a ...
• 1,663

### Log-normal mean and standard deviation change after sampling

I did this in R and got very similar results to you, even when I tried sampling from the corresponding normal then exponentiating. The issue here is the scale of the values you're trying to sample. ...
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### t- test for non normally distributed sample

For testing a difference between the means of both groups, a t-test (aka "Welch test" to make clear that no assumption of equal variances is made) can even be used when the data of both ...
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### transformation of a kernel density estimate to uniform distribution

The multivariate $d$ dimensional extension of the inverse cdf generation is incorrect, both because $F^{−1}(\cdot)$ does not exist and because $F(X)$ is not Uniform (0,1). (For instance, in the ...
• 91.8k
I think I've found the error in my original method. I'd appreciate feedback on my solution! We will solve this in generality; that is, we will show, as @JimB asserted, that $P(X<kY) = 1/2$ for any ...