A distribution is a mathematical description of probabilities or frequencies.
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Trouble in understanding probability density functions and zero-mean noise in the CUSUM (cumulated sum) test / Page-Hinkley test
I was going through this paper An algorithm for QRS onset and offset detection in single lead electrocardiogram records by Al Manriquez and Qinghua Zhang.
I've ...
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0answers
16 views
Statistical test for comparing two frequency distributions expressed as arrays (buckets) of values
I am looking for an appropriate statistical test that will compare two frequency distributions, where the data is in the form of two arrays (or buckets) of values.
For example, suppose I have two ...
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21 views
Filling missing values with distribution [migrated]
So i have 2 dataset.
On the first one i have values for each hour of a day. Example:
...
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1answer
18 views
Which distribution in this case?
Let's say I am taking a sample size of n=1000 of a country population, and every one of them decides with '1' (for a specifc political party) or with '2' (for another political party). Which ...
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1answer
17 views
Distribution of successes of poisson process followed by a binomial distribution
I have been stuck with a problem for a couple of days regarding the distribution of outcomes from a two-stage process. Specifically, what is the distribution of the number of successes in a poisson ...
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1answer
17 views
Are the marginals of the multivariate t distribution univariate Student t distributions?
Are the marginals of the Multivariate t distribution with $\nu$ degrees of freedom univariate Student t distributions with $\nu$ degrees of freedom?
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1answer
21 views
Is this poission Distribution problem?
In a retirement village the average length of stay is 15.6 years. what is the probability that someone lived 8.8 years will vacate soon?
thanks
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20 views
50th percentile from z-score is not exactly 0 [on hold]
I try to find the percentile of z-score and then the result show that the percentile 50th is not exactly 0 but 0,065. how to solve this problem?
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5 views
how can we write the posterior distribution of Bayesian multilevel logistic regression?
i try to write the posterior distribution of Bayesian multilevel logistic regression with normal prior distribution. but it is difficult to me. so would you help me please?
I TRY to write the model ...
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29 views
AR-GARCH - Extreme Value Theory
I am looking at Extreme value Theory (EVT) in an AR GARCH context.
I follow the following procedure to estimate :
Fit an AR-GARCH to data log-returns.
Standardize the residuals of the above fit (...
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1answer
29 views
Random Variables independently distributed
Q) Find an example of two discrete random variables $X$ and $Y$ such that $X$ and $Y$ have the same distribution, but the event $X = Y$ never occurs.
Now I thought of these as distributions that are ...
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22 views
How can the Tukey-Lambda Distribution Be Parameterized with a Location and Scale?
I recently ran into a snag while trying to code the cumulative distribution function (CDF) of the Tukey-Lambda distribution: several sections of the Wikipedia article appear to be lifted almost word-...
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3answers
214 views
Unsolvable Integral?
Is the following integral solvable?
$$P(X) = \int^{\infty}_{-\infty} \int^{\infty}_{-\infty} P(X|\mu,K)P(\mu|K)P(K) d\mu dK$$
with
$$P(K) = \frac{|K| ^{(v-d-1)/2}}{2^{vd/2}|V|^{v/2}\Gamma_d|\frac{...
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Separability measure of two time-series distributions
I would like to assess separability of two time series distributions. As an example, I have two groups of sine-waves shifted in amplitude and in phase with Gaussian noise added:
So far I've been ...
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1answer
41 views
Is this sensible: $P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$
I want to write:
$$P(y_{1}<Y\le y_{2}\mid Y\sim\mathcal{D}(\mu))$$
to say:
The probability of $Y$ being between $y_1$ and $y_2$
given that $Y$ is a random variable distributed according to ...
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1answer
25 views
Can we show this sum of Gamma CDF converges, and if so can we derive its limit?
This is a bit of a strange question, but suppose I have some random variables.
$$Y_i \sim Gamma(i,\lambda)$$
Where this comes from the fact that each $Y_i$ is defined as the sum of $i$ independent ...
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0answers
9 views
Intensity deconvolution
We have a set of intensities (measured)
$I_{j} = \cos(\theta_{j}) + N_j$
where $\theta_{j}$ is distributed according to some distribution between 0 and 180 degrees (well, in reality between 0 and ...
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2answers
38 views
Interperating Wilcoxon Signed-Rank Test's p-value
I am trying one-sample wilcoxon signed rank test on my data. Data contains 100 values, summary of my data is:
...
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0answers
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Probability of false negative in uniform distribution test
Let's say I have a set of $n$ objects, and I select an object from the set with uniform probability. I do this many times, and record how many times I select each object. These counts will tend toward ...
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14 views
How do I assign a probability distribution to all combinations (4500+) of a single variable?
I'm trying to simulate the delivery times for a fast food restaurant (i.e. the time it takes the delivery guy to reach the client from the restaurant).
The locations of all clients are put in ...
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1answer
19 views
What's the distribution of fixed effects?
A general nonlinear mixed effect model for the $j$th observation on the $i$th individual is
$y_{ij} = f(\phi_i, x_{ij}) + e_{ij}$
$\phi_i = A_i\beta + B_ib_i$, where $b_i \sim N(0, \sigma^2D) $
I ...
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1answer
35 views
Likelihood ratio test for non-Gaussian distributions
I am learning about the likelihood ratio test. Is the LRT applicable for non-Gaussian distributions too? Up to now I have only been able to find examples of the LRT for Gaussian and Gaussian mixture ...
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1answer
32 views
How likely is it, that a value belongs to a given non-uniform distribution? [closed]
My question is very much relevant to this question. But as it was closed and not properly answered, I am asking here again.
I have created 100 random values and their distribution is not normal. I ...
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0answers
37 views
Distribution of the initializing set at K-means++
There is a well-known modification of the initializing step of K-means, named K-means++. It chooses cluster centers with probability proportional to its squared distance from the point's closest ...
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1answer
22 views
What is the support of a mixture model?
The pymc3 documentation says that the support of the mixture model $f(x|w, \theta) = \Sigma_{i=1}^{n}w_if_i(x|\theta_i)$ is $\cap_{i=1}support(f_i)$.
I was thinking that it should be the union of ...
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17 views
Why are IID normal random variables spherically simmetrical?
Given a finite sequence of $s+1$ IID normal random variables $X_1, \ldots, X_{s+1}$ They are spherically symmetrical.
This means that the radial projection of the point $(X_1, \ldots, X_{s+1}) $ onto ...
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19 views
Distribution of a non-central(?) generalized gamma random variable
I Know that if X follows a gamma distribution with shape parameter k and scale parameter theta, then X^2 follows a generalized gamma distribution with parameters p=1/2, d=k/2 and a=theta^2. Given this,...
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13 views
christoffersen statistic simulation
I'd like to analyze the convergence of the distribution of the christoffersen statistic defined as
$\Lambda = -2\log\frac{(1-q^*)^{a_{01}+a_{11}} (q^*)^{a_{00}+a_{10}}}{(1-q_0)^{a_{01}} q_0^{a_{00}} (...
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2answers
94 views
How to identify the subset of a large dataset that has a similar distribution with the another dataset
I am trying to implement transfer learning to make predictions on test set using a model trained on another dataset collected from a different sample.
For this, I need to identify the subset of ...
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0answers
21 views
Test for equality of distributions in non-independent samples
I am investigating the differences between six crime rates for 288 different locations, with each rate calculated using different denominators. My data are of the format:
Location Rate 1 Rate 2 ...
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14 views
Using $\chi^2$ result to find asymptotic distribution of $S^2$ when $X_i$ normally distributed
At the end of this answer it is mentioned that
Note: the above result of course holds also for normally distributed samples -but in this last case we have also available a finite-sample chi-square ...
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1answer
29 views
Method of Moments for $\nu$ of standard t-distribution: what if true $\nu=2$?
Note I am considering the standard $t$ distribution $(\mu=0,\sigma=1)$
The method of moments for $\nu>2$ is derived in this question
My question is, if the true (population) value of $\nu$ is $2$,...
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19 views
Besides skewness and kurtosis, how else can I investigate changes on a distribution?
I want to look for changes on the distribution of the laying date of a bird (i.e. if the phenology or nesting synchrony has changed). Are the coefficient of variation, skewness, kurtosis the only way ...
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1answer
22 views
Test set distribution different than train set distribution
I am doing regression to predict a target. My model is giving low mse on the training data but very high mse on the testing data( even worse than baseline predict all as mean model). I thought this ...
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50 views
How to fit a truncated distribution to binned data?
I have the age at deaths data in the form of intervals ie 0-4, 5-9, 10-14, ... 80 & above years.I have converted inclusive class intervals to exclusive class intervals ie
age: 0-4.5, 4.5-9.5, 9.5-...
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Probability of Given Event and Cumulative Distribution Function
For the given Random Variable X, Cumulative Distributive Function is defined as below:
$$F(x) =
\begin{cases} 0, & \text{$x \le 0$} \\
x^2/8, &\text{$0\le x \lt 2$}\\
1,& \text{$x \ge 2$}...
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1answer
51 views
If X and Y both have the same pdf, they are identically distributed, but can I say that they are independent? [duplicate]
More specific: I have two variables, X and Y, they are exponentially distributed with parameter a. I know that the distribution of X + Y follows a Gamma(2,a) distribution IF they are independent (I ...
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28 views
What does it mean for a probability distribution to not have a density function?
I understand the distinction between probability mass and density functions. But I don't understand what it means for a continuous random variable to have a probability distribution but not a density. ...
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1answer
65 views
Expected value of logarithm of distribution
I'm studying variational inference and I'm checking an example from Bishop, Pattern recognition and machine learning (2006).
In the page 470 (10.1.3) there is an example with the univariate Gaussian.
...
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1answer
43 views
Obtaining a Bayes Factor for the difference between two proportions (R code provided)
Below (in R code), I'm showing the Bayesian estimation of the Difference between two proportions resulted from two binomially distributed groups (groups) of scores (...
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0answers
13 views
Sufficiently small/large number in your distribution
This might be a very simple question but I am wondering if we have any statistical method to detect a sufficiently small/large number in your distribution. I am sure some would suggest using the 3 ...
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0answers
33 views
mathematical difference between two functions used in scaling data and viewing distribution
I am trying to understand the difference between f(x) and g(x) below. I am not a mathematician or statistician, so please bear ...
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1answer
32 views
Which sampling distributions of the normal correspond to which sample statistics? [closed]
Question: Which sampling distributions of a normally distributed, i.e. $\mathcal{N}(\mu, \sigma^2)$, population correspond to which sample statistics?
In particular, which sample statistics (if any), ...
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20 views
How can I find the probability distribution function from the observed data to use in a Monte Carlo Simulation?
In exploring a data set, I think I've found an interesting instance where using a Monte Carlo method to plot a simulated group of points could yield somewhat accurate results.
The plotted data looks ...
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0answers
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For univariate outlier analysis should I use z score if my data is skewed? [duplicate]
If my data is skewed, does it mean that my data does not follow a normal distribution? How do we define various distributions?
What type of outlier analysis do I perform for the different type of ...
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2answers
54 views
How can i sample from posterior distribution which contains integration using MCMC?
I want to find sample from posterior distribution but it is complex, so i want to sample the posterior using MCMC. The posterior distribution contains integration (because the reliability function is ...
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38 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 ...
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1answer
21 views
Distribution matching by subsampling
I have two groups, Group 1 and Group 2, where the distribution of var is quite different. However, Group 1 has much more people than Group 2, and the support of ...
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0answers
21 views
Central and Non-Central Chi-Squared bivariate distribution
I have an urgent question for you, if you could please help me out:
Let X and Y be central chi-squared RV with Ux degrees of freedom and non-central chi-squared RV with Uy degrees of freedom and ...
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1answer
143 views
What to do when count data does not fit a Poisson distribution
I'm a PhD stats student. I'm working with a data set of count data. It's counts of users who are involved in an n-way real time chat conversation. The # of users range from 1 to 6 and there are approx ...
