All Questions
Tagged with nonparametric distributions
107
questions
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11
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How to compare peak location and tail length of two different distributions?
I have the distributions of the fraction of people in each income bracket in a town in 1990 and 2020. The total sample size is the same in both, and assume that the incomes have been adjusted to ...
0
votes
0
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40
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Estimate the likelihood of two continuous samples of unknown distribution
Consider two continuous and unknown distributions
$$X : {x_1, x_2, ..., x_n}$$
and
$$Y : {y_1, y_2, ..., y_n}$$
both can be tagged as time series with $n > 8000$.
I need to estimate the likelihood ...
1
vote
1
answer
72
views
Does taking the ratio of Empirical Distributions (histogram bins) show their differences?
Background
I have two Empirical distributions, both derived from social media data.
The first represents a broad sample of ~4.8 million posts and the number of followers each post author has. The ...
- 655
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0
answers
150
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Comparing the output distribution of two ML models
Consider a regression task (e.g. predicting house prices) with a given train and test sets.
We start with constructing a linear regression model, in which we assume $y_i=X^T\beta+\epsilon$ with $E[\...
- 4,012
1
vote
0
answers
50
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The hunt for a 'nice' flexible distribution [duplicate]
Background
Suppose I have data $\mathcal{D}_1, \cdots, \mathcal{D}_n$ with each $\mathcal{D}_i$ containing $m$ observations $X_{i1}, \cdots, X_{im}$; these observations are of unknown distribution, ...
- 621
5
votes
2
answers
226
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Calculation of a nonparametric equal-tailed (central) tolerance interval for an unknown continuous distribution
Assume we have a sample of size $n$ from an unspecified continuous distribution $F(\cdot)$. We wish to construct a tolerance interval to contain $(100\,\beta)\%$ of the population with a pre-specified ...
- 30.9k
2
votes
2
answers
115
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Distribution and variable analysis
I am doing a statistical test (program used is SPSS). On the basis of distribution and sample size, I have to chose the correct variable analysis. I also have to justify every decision. I have two ...
- 21
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65
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Comparing averages of non normal distributions
I want to compare the daily average revenue of a promotion period (7 days) of a business with the daily average of the rest of the year.
So, sample 1 has 7 data points, whereas sample 2 has 300 data ...
- 1
2
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0
answers
69
views
When is the central limit theorem not applied?
I am trying to compare two matched samples. In total I have a sample of 34 people. Each patient receives two treatments, a C1 treatment and a C2 treatment. So each patient will be compared to himself ...
- 909
3
votes
3
answers
149
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Problem with a single outlier, non-normal data, and unequal sample distributions
I am wanting to compare two independent groups on a likert-like item. To explain, the dependent variable is structured so that a 1 = <1 units, 2 = 1-<2, 3 = 2-<3, all the way up to option 7 = ...
- 31
1
vote
1
answer
43
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Which pair of two distributions are more similar?
Suppose I have two pairs of distributions: distributions A and B in Pair 1, distribution C and D in Pair 2. There are non-parametric tests to determine if there is evidence to say that the ...
- 125
4
votes
3
answers
547
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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, ...
-1
votes
1
answer
184
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Independent Sample T-test or Mann-Whitney U test?
I am a very young stats learner, and I need help understanding the justification of a test choice. I have a sample of 39 participants (20 females and 19 males) been measured on task performance, and I ...
- 1
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1
answer
132
views
Compare nonparametric distributions
I generated distributions of travel times of commuters using transportation simulation tools (for different scenarios). The distributions are attached below. I wish to statistically compare each pair ...
- 141
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0
answers
37
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Show that an event is improbable for exponential families iff it's improbable for all absolutely continuous distributions
Since all the exponential families are absolutely continuous, if part is trivial. However, I could not prove the only if part. My idea is to prove by contradiction, i.e. given an event $A$ such that $...
- 545
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1
answer
131
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How to find the type of my distribution?
I checked the normality of my data on SPSS and one of the variables is not normally distributed. I have the mean, standard deviation, skewness, kurtosis , min and max values of my distribution. But I ...
user310572
6
votes
2
answers
1k
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What is a medcouple?
What is a medcouple? I understand that it is the median of a couple of data points but it is not clear to me what these pairs of data actually are. E.g. https://wis.kuleuven.be/stat/robust/papers/2008/...
- 579
2
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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
4
votes
1
answer
106
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Nonparemetric tests: how to support the null hypothesis you claim to be testing
Let us assume that we have taken an unbalanced number of independent random samples from 5 different populations, which will be analogous to 5 different locations in this example. Each observation ...
- 351
2
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0
answers
104
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Fitting a range of distribution and test for goodness of fit - choose based on p-value or chi-squared values?
I have data for which I want to study the best distribution that fits this data. I am following this blog post to do my experiments. Basically the following things are happening:
fit a number of ...
- 521
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0
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30
views
Sampling distribution from a parametric curve?
I'm not sure if this question is well-founded, given that it seems to be mixing random and deterministic processes, but I'm wondering if there's a meaningful answer. Suppose we have a parametric curve ...
- 255
2
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2
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135
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How to prove a multivariate r.v. does not follow the nonparanormal distribution?
Background
You may find the definition of the non-paranormal distribution at the 2nd paragraph in p.2296 of this paper.
In short, $(X_1, \ldots, X_p)$ is non-paranormal if there exists a set of ...
- 528
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votes
0
answers
53
views
Finding the right hypothesis test
I have two distributions (Generic and Generic Masked) that I want to compare. I want to show that one is distributed closer to 1 than the other, but don't know which hypothesis to test for this. I ...
- 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
1
vote
0
answers
131
views
What is the resulting distribution of a data set that was originally normally distributed but has been quantized and had all negative values removed?
I am trying to benchmark a seasonal forecasting model and calculate not just the point forecasts but the forecast densities from the model.
To do this, I generated a simulated data set in the ...
- 1,381
1
vote
0
answers
23
views
Ways to make parametric statistics work with real time (often non-normal) data
BACKGROUND:
I have been tasked with teaching basic data analysis methods with R to a group of people in a business setting.
While my stance is that I am most difinitely not at the level where I ...
- 13
2
votes
1
answer
182
views
Binomial distribution for two groups if success rate is not given
Two groups of twelve statisticians are taught two different methods of Statistics. (Assume that a statistician in group one is matched in terms of their Statistics ability with a statistician in group ...
user125163
2
votes
0
answers
83
views
Estimating conditional probability distribution from samples
I have three continuous variables, $X$, $Y_1$ and $Y_2$. All three are correlated. For a given value of $X$, the conditional probability distributions of $Y_1$ and $Y_2$ are typically bimodal. I'm ...
- 131
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
2
votes
1
answer
58
views
Non norma distribution
I have a non-normal distribution (Kilograms ~ Years), so I can't use ANOVA test to reject the null hypothesis (that the tree means are equal).
There is a tendency of weight to be 100kg.
Is there a way ...
- 141
0
votes
1
answer
99
views
Parametric or non parametric test
I want to compare trends of R&D expenditures before and after a crisis. I was planning to use a paired T-test or a non-parametric alternative. But, before of that, I tested the data for normality. ...
user248229
0
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0
answers
22
views
Confused about the statistical tests to choose or any transformation to apply
I am new to the stackexchange, so please forgive me for my editing ignorance. I am confused and stuck about how to proceed further with my data. I have the following data
...
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0
answers
149
views
Determining differences between curves with the K-S test
I'm running an experiment where my treatments have a significant and highly sensitive effect of the distribution of a result.
For example, if i alter a certain nutrient in a vegetable, the ...
32
votes
3
answers
5k
views
Why does the Kolmogorov-Smirnov test work?
In reading about the 2-sample KS test, I understand exactly what it is doing but I don't understand why it works.
In other words, I can follow all the steps to compute the empirical distribution ...
- 915
1
vote
3
answers
197
views
Confused on normality assumption
I know that the sampling distribution of the mean can be assumed to be normal if N>30, but does this have an implication on the "30" itself (the sample data)?
I have three different time series with ...
- 11
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
95
views
What among location, scale and shape is Kolmogorov–Smirnov test statistic sensitive to and why? [closed]
I understand that the Kolmogorov–Smirnov test statistic for a given cumulative distribution function $F(x)$ is $D_n = \sup_x |F_n(x) - F(x)|$. However, if I have to rank its sensitivity to location, ...
- 5,643
5
votes
4
answers
2k
views
Why use parametric test at all if non parametric tests are 'less strict'
I have read from several sources, even in my undergrad courses, that parametric tests require the data to have a certain distribution, for instance normal, whilst non-parametric don't.
I have ...
- 211
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
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votes
1
answer
2k
views
Nonparametric test suggestion for distribution comparison
I am not sure if this is appropriate place to ask, but I appreciate any help on this issue. I want to compare the distributions of the results of the two experiments played by the same group of people....
- 119
1
vote
1
answer
1k
views
What if half of your data is not normally distributed? [closed]
My experiment is to test the different diets (Pk, Hg, BYD & Control) in order to check the development of insect, what are the most preferred diets by insect. For this purpose, I used 3 parameters;...
- 11
2
votes
1
answer
738
views
Possible explanations for Imputation before train-test split?
I'm working on a real world data set containing missing information. I understand imputing missing values before data partitioning can lead to leakage of information. I'm using this R package MissMech ...
- 33
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
1
vote
2
answers
173
views
Closeness of 2-parametric discrete distributions when first 2 moments are matching
Let $\mathcal{D}$ be a particular 2-parameter uni-variate discrete distribution family, and let $D(\theta_1, \theta_2) \in \mathcal{D}$ be one particular distribution from this family, where $\theta_i ...
6
votes
1
answer
2k
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Plotting non-parametric (E)CDF confidence envelopes for comparison
I have previously asked about a way to test whether two samples are drawn from the same distribution (Non-parametric test if two samples are drawn from the same distribution). I was very glad to learn ...
- 467
1
vote
0
answers
366
views
Distribution (group) comparison based on PCA
I am looking for a way to compare the first the k principal components belonging to two separate groups of two-dimensional data, in order to see how similar the two groups are. I do not know which ...
- 11
5
votes
1
answer
680
views
Non parametric estimation/regression for conditional distribution
Context : one continuous variable $Y$ dependent on $X$ ($X$ can be anything)
Linear regression, generalized linear model... focus on estimating the conditional expectation $E(Y\mid X)$. I want to ...
- 8,707
0
votes
1
answer
102
views
Which stats should I use when samples are uneven and data are not normally distributed?
My data have four groups: "A" normal group (AN), "B" normal group (BN), "A" group with a clinical diagnosis (AC) and "B" group with a clinical diagnosis (BC). They were tested on a task that included ...
- 21