All Questions
16
questions
4
votes
3
answers
547
views
Nonparametric Order Statistics - Does this Exist?
I was reading about order statistics on Wikipedia [retrieved 29 June 2022]:
Apparently, if we have a sample with $k$ elements (e.g., $x_1, x_2, ..., x_k$) and assume a probability distribution for ...
1
vote
1
answer
136
views
Deciding the Number of Clusters : Standard Methods vs. Non-Parametric Methods
I was watching this video over here (https://www.youtube.com/watch?v=UBiaLq5V7mE) that discussed a Non-Parametric based Bayesian approach for deciding the number of clusters in a dataset.
Essentially, ...
2
votes
1
answer
170
views
How to estimate the probability that a single value follows the same distribution as a a set of values
This question is a possible duplicate of this one but I would like to go a bit further.
I have a set of values $X=x_1, x_2, \cdots, x_n$ that are iid estimates of a reference value $y$ given by a ...
- 121
3
votes
1
answer
2k
views
Test to show one distribution is bigger than another
Here is a MWE of my problem:
I measure the size, $S$, of 10 red apples and 32 green apples.
$\bar S_\mathrm{red} = 8 \pm 1\,\mathrm{cm}$ and $\bar S_\mathrm{green} = 4 \pm 2\,\mathrm{cm}$.
I want ...
- 55
2
votes
1
answer
144
views
When a function of two random variables is Gumbel?
Consider two random variables $X,Y$.
Is there any example in which $X$ and $Y$ have a known parametric distribution such that $f(X,Y)$ is Gumbel with scale $\sigma$ and location $\beta$, for some ...
- 891
1
vote
0
answers
41
views
Prove the relation between two distribution functions
I have been given a homework in a subject called "Non-Parametric Statistics" and I'm a bit stuck with it. I would be very thankful if you could give me any advice or help, which would lead to a ...
- 49
2
votes
0
answers
150
views
Derive probability distributions from i.i.d. Gumbel
I have a question on how to derive (if possible) the following probability distributions.
Consider 3 random variables $(X,Y,Z)$ mutually independent and identically distributed. Specifically, $X$ is ...
- 891
1
vote
0
answers
692
views
Type of parameter of the chi-squared distribution
Chi-squared distribution $\chi^2(k)$ has parameter $k$.
On the one hand, $k$ should be the shape parameter because chi-squared distribution is a special case of Gamma distribution: $\chi^2(k) \equiv ...
- 1,008
1
vote
0
answers
31
views
Estimating Gamma PDF parameters from data with negative increments
Say we have collected data, and from a physical perspective we know that the collected data should increase positively with time. However the data looks more like this:
This data shown in the figure ...
- 565
2
votes
1
answer
89
views
Distributions of parameters
What are the traditional distributions for assigning probabilities to model parameters?
For instance, assume that we have a binomial distribution:
$$y \sim Bin(n,\theta)$$
Then we can distribute $\...
- 338
3
votes
1
answer
4k
views
Empirical probability and Dirac distribution
According to Deep Learning p.65(Ian Goodfellow and Yoshua Bengio and Aaron Courville, available online):
(...) This can be accomplished by defining PDF using the Dirac delta
function $\delta(x)$: ...
- 273
1
vote
0
answers
60
views
Probability that a random variable is k-th when ordered - simplification needed.
My first post... I'm trying to simplify the following problem:
Let $F_e(x)$ be a continuous cdf of some distribution parametrised by $e$. Let us assume that:
(a) The mean of this distribution ...
- 11
2
votes
1
answer
3k
views
Probability of an unknown distribution
I have the sample of a variable $X$ whose distribution is unknown and I would like to know how to estimate the probability of $X$ taking some values. How can I do that? I assume that there's a non ...
- 157
7
votes
2
answers
2k
views
Probability that randomly chosen value from one distribution is greater than randomly chosen value from another distribution
Say I have $n$ values sampled from two distributions, $A$ and $B$ . That is, I have a sample $A_1, A_2, \dots, A_n$ and a sample $B_1, B_2, \dots, B_n$. How would I go about finding $P\left(A_i>...
- 425
0
votes
0
answers
2k
views
Example of parametric and non-parametric method
I have not understood this example from wikipedia.
Suppose we have a sample of 99 test scores with a mean of 100 and a standard deviation of 1. If we assume all 99 test scores are random samples ...
- 1,607