New answers tagged distributions
7
votes
Accepted
Why can a model's SHAP values change on a new dataset?
Why can a model's SHAP values change on a new dataset?
WHY SHOULDN'T THEY?
When you calculate a mean on a new data set, you expect to get a slightly (or radically) different value.
When you calculate ...
- 58.1k
13
votes
Accepted
What is the specific name of this distribution?
This is the PDF of a logistic distribution with its location parameter set to zero and scale parameter set to one.
In general, a logistic distribution has a PDF as follows, where $\mu$ is the mean and ...
- 58.1k
3
votes
Joint distribution of a random variable and the sample maximum
A fundamental result in order statistics is Theorem 2.4.2 of Balakrishnan & Cohen:
Let $X_1, X_2, \ldots, X_n$ be i.i.id. random variables from a population with cdf $F$ and pdf $f,$ and let $X_{...
- 316k
5
votes
Accepted
Can i have a distribution that is not a marginal of another distribution?
The answer is NO.
To reformulate the question: Given any two univariate distributions $F, G$ (represented with their cumulative distribution functions) is there always a bivariate distribution with $...
- 74.6k
1
vote
Conjugate prior for the gaussian distribution
It is better to look at this in a more general way. So you have a Bayesian model with a likelihood function $L_x(\theta)$ and a prior $\pi(\theta)$, say.
Then the posterior is proportional to $L_x(\...
- 74.6k
4
votes
Accepted
Does this type of distribution have a name?
The distribution is a beta binomial distribution with parameters n=300 and $\alpha=\beta=0.5$.
For an approach to derive this, you can consider the distribution of the counting variable $x$ after $n$ ...
- 71.6k
3
votes
Does this type of distribution have a name?
Natural Distributions
In terms of the typical visual form of this distribution, it looks to be closest to the uniquely named U-shape distribution, which are distributions that have two extremes in ...
- 8,385
7
votes
Accepted
expectation value, distribution function and the central limit theorem
You don't use CLT to get this result. What is needed is a direct evaluation of the term $E[S_n^3]$.
To begin with, note that for $n \geq 3$:
\begin{align*}
S_n^3 = (X_1 + X_2 + \cdots + X_n)^3 = \...
- 16.5k
0
votes
Joint distribution of $Y$ and $S^2-Y^2$
we know, $$\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$$
$$Y = \sum_{i=1}^{n} b_iX_i$$
notice, this is a linear combination of normal random variables so, this should follow normal distribution with
$$...
- 1
1
vote
How to simulate n Uniform[0,1] variables with a specified correlation?
Inspired by @whuber 's approach, I created my own approximation that I hope might be useful to future readers. The essential insight is that the function $f^{-1}(\rho)$ (which allows one to determine ...
- 63
1
vote
Accepted
What is the resultant distribution of this two-step sampling process?
The distribution of a point given all the first stage samples is
$$
g(X = x_i \mid x_1, \ldots, x_n) = \frac{f(x_i)}{\sum_{j=1}^n f(x_j)}.
$$
So the marginal distribution for finite $n$ is
$$
\int \...
- 20.2k
0
votes
What is the resultant distribution of this two-step sampling process?
It's not quite that, because your actual weight distribution (as written) has only the observed values in the denominator, not all values.
To take the extreme case, suppose $n=1$. You sample one value,...
- 34.5k
1
vote
What's the best clustering algorithm for Fraud Data?
I woud propose to start simple. For now, you are just "exploring" your data and it is okay to cut corners.
To make your life easier, convert your categorical variables to numerical. For ...
- 63
2
votes
Approximating the distribution of the product of iid beta variates
This is just an extended comment. One can obtain the exact distribution (and mean and variance) of $\phi_{i>0}$ although for the values of $\alpha$ and $\beta$ you mention, the result differs ...
- 3,414
1
vote
Approximating the distribution of the product of iid beta variates
Here is a "visual" approach (using Mathematica) to check on the gamma approximation for the distribution of $\theta_0$.
...
- 3,414
5
votes
Accepted
Calculating the cumulative distribution function and the probability density function of an interval with ratio of a shorter and longer segment
$L_1$ follows a Uniform $(0,1)$ and $L_2 = 2-L_1$.
So
$$X = \frac{L_1}{L_2} = \frac{L_1}{2-L_1}.$$
Use this, together with the definition of the cumulative distribution function $F_X(x)$, that for ...
- 57.4k
0
votes
Understanding "variance" intuitively
Preliminary Discussion
I felt I would add another visual example, but first I use a very simple piece of data to illustrate a basic and known point for people who already know a fair amount about ...
- 8,385
1
vote
Understanding "variance" intuitively
The most intuitive explanation I know for SD is the average magnitude of error. However, this explanation applies for MAD as well, and this is perfectly fine. But why?
The bounty definition states
...
- 3,400
1
vote
Accepted
In a 2-arm clinical trial where ten centers recruited patients, how does one test that two distributions are statistically similar?
Assuming you have numeric data in the variable site, the first thing I would do is to inspect the histograms for this variable in each arm and do a simple "...
- 56.6k
0
votes
Understanding "variance" intuitively
In my opinion, a rough explanation (that will get them to more than 60% understanding) is to tell them is simply a measure of how much something varies.
If you ate the same amount of food every day ...
- 93
1
vote
Methods for fitting a distribution to regression data
I don't see a reason why the standard survival analysis methods wouldn't work here, you can choose to go non-parametric (e.g. Kaplan-Meier), semi-parametric (Cox proportional hazards) or fully ...
- 1,901
0
votes
How to approach problem
If I have understood correctly, this scenario involves creating a distribution for a function of several independent discrete random variables. Here is one approach to achieve this:
Know Each ...
- 56.6k
1
vote
Accepted
How to approximate non-central chisquare distribution to Poisson weighted sum of central chi-square distribution in case of non-unit variances?
If I understand your question correctly, you are interested in the distribution of $S_X = \sum_i^n X_i^2$ where $X \sim \mathcal{N}(\mu, \sigma^2 I_n)$. Because the texts that you reference give you a ...
- 1,077
2
votes
Accepted
Pinsker-type inequality for moments?
Consider a Pareto distribution with lower bound $x_m = 1$: $p(x;\alpha) = \alpha / x^{1 + \alpha}$, with mean $\alpha / (\alpha - 1)$. The K-L divergence of this distribution from a Pareto ...
- 37.6k
2
votes
Understanding "variance" intuitively
An important property of the variance is that it is a natural way to describe the spread of a distribution. It is the second moment of a distribution and its definition has a direct connection to the ...
- 191
7
votes
Goodness-of-fit test for very skewed data
Your post reminds me of the guy who wouldn't accept "yes" for an answer.
G tests are quite similar to chi-square, but have some better properties. In your case, both give overwhelming ...
- 109k
7
votes
Goodness-of-fit test for very skewed data
I wouldn't call these distributions "very skewed" on two grounds. The idea of skewness does not easily apply to categorical variables. Even if there is some kind of natural or conventional ...
- 54k
Top 50 recent answers are included