Questions tagged [distributions]
A distribution is a mathematical description of probabilities or frequencies.
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Which distribution is it?
I recently came across the following distribution
$$
\Pr(X\le x)=e^{\tfrac{1}{a}-\tfrac{1}{x}}\left(\dfrac{a}{x}\right)^{\tfrac{1}{a}},\; 0\le x< a,
$$
and the cdf is 0 for all $x\lt 0$ and 1 for ...
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Is there a distribution for use with generalized linear models that captures both heavy tails and "pointyness" near the mean?
If I fit a regular linear mixed model to my data with lmer, I get a pattern of residuals that, at a glance, looks to me to deviate from Gaussian in two ways. The ...
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How to interpret below, which formular is meant to be used [closed]
A study shows that 70% of consumers believe cheaper supermarket brands are just as good as national name brands. In response to these findings, the manufacturer of a national brand asked a sample of ...
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Calibrating the probabilities of Ridge Classifier on imbalanced dataset
I have a classification project on an imbalanced dataset (HomeCredit Kaggle dataset) and I have chosen Ridge Classifier (sklearn's implementation) as the most efficient both in terms of time and in ...
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Does a misspecified model always have lower likelihood value than the correct model?
Suppose the true dgp is
$$
x_i \sim d_1(\theta_1), \quad i=1,\ldots,N
$$
where $d_1$ is some probability distribution with parameter(s) $\theta_1$,
but I wrongly assume
$$
x_i \sim d_2(\theta_2).
$$
...
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How do I multiply two discrete distributions together?
As part of my PhD research, I am simulating a system that comprises multiple sensors, and I want to perform sensor fusion. My sensors give me sets of measurements (values between 0 and 1 mm) that I ...
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How do I perform maximum likelihood estimation for one variable?
This is a simpleton's question, I appreciate. But I'm having a little confusion with discussion of dependent/independent variables, and many more things I thought I'd imagine.
I have a N samples of a ...
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How are probability density functions, that are computed from real-world datasets, stored and represented by computational software?
In probability and statistics, density estimation is the construction of an estimate, based on observed data, of an unobservable underlying probability density function. The unobservable density ...
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Analyzing distribution of vector samples
I have a neural network that can be well trained with CNN features from AlexNet (a neural network that is pretrained for image recognition).
I have obtained these CNN features from previous studies ...
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Computing the inverse Beta cdf in R [closed]
In MATLAB, the function betainv(P, A, B) computes the beta CDF inverse with parameters A and B specified for the corresponding probabilities in P. Is there a similar function in R that can do the same?...
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What is a perfect distribution to consider for the step increase/ decrease for the reversible jump MCMC
I am trying to understand the hyper parameters in the paper [1] for the model order selection with reversible jump MCMC (RJ-MCMC). There is a hyper parameter $\Lambda$ (The parameter of the Poisson ...
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Largest possible area of a scaled normal distribution dominated by N(0,1)
I'm trying to understand and replicate a method for understanding stem distributions from 1955. However, replication in R indicates my understanding is wrong.
This original work is available online (p....
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Probability of completing a task on time given a start delay
I am trying to model the probability of completing a task in time given the scheduled time and a starting delay.
In the plot below, the x-axis (deviation from schedule) is the ...
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Are there better measures of entropy
Related question here
I am trying to measure the uniformity of multimodal distributions and am looking into using entropy.
I would like a measure of entropy that is higher for the first distribution ...
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How to estimate the parameters of a Burr XII distribution using MLE
I have a dataset and I am wondering if would be a reasonable fit for a number of distribution types.
I was looking to fit the Burr XII distribution in Python initially (using scipy library) and then ...
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Compare distributions after transforming from continuous to discrete [closed]
I have two variables: X and Y.
X variable (varies between 0 and 300) is continuous and Y with same range of variation but is discrete and have 3 classes (0-100, 100-200 and 200-300), which is pretty ...
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What is the distribution of bit counts of a binomial random variable?
Suppose I have a binomial random variable $X \sim B(n,p)$ and I apply the following bit counting operation $$Y = \operatorname{bit\_count}(X)$$
where $\operatorname{bit\_count}$ is defined in the ...
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Question about how to think of the binomial distribution with a combination vs a permutation
I know there are many questions on why use a combination formula over a permutation formula for the binomial distribution ( for example here), but looking through multiple of these, I still don't ...
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Alternative formula for the Bernoulli pmf?
If I understand correctly, a Bernoulli pmf just needs to assign a probability $p$ if there is a success $(x=1)$, and $1-p$ otherwise $(x = 0)$. Rather than the usual formula, can't the following ...
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To check if the churn probability score from old and new model is similar
I have calculated the churn probability score for every customer id using glm model. So, I have a data frame with every customer id and its churn probability score. Ex cust_id 1 has a score of 0.11 ...
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How to draw recurrent weights uniformly frandomly from same range as Mexican hat weight profile
I am trying to understand this paper. In the methods section, they say that they want to draw weights (N x N) by "drawing lower-triangular recurrent weights uniformly randomly from the same range ...
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Binomial to Poisson Approximation
So, a little context. The image you see is from the GCE A-LEVEL syllabus where they have defined the conditions for approximating binomial to poisson.
But why did they have mention that the ...
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Calculate the variance of a distribution analytically
I want to calculate the variance of a certain distribution.
I have a rectangle that is getting shifted to the right (i.e. shear transformation). To obtain the distribution I am computing the value of ...
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Deriving distribution under change of variables between spaces of unequal dimension
For a function of random variables $T:\mathbb{R}^n \mapsto \mathbb{R}^m$ Wikipedia outlines how to handle three cases:
$m = n = 1$
$m=n > 1$
$n>1 \land m=1$
There seems to be two missing cases:...
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Statistical Test of the significance of difference between 2 ordered columns
I'm trying to come up with an appropriate statistical test for the significance of the difference between 2 ordered columns A = [a0, a1, ..., aN] and B = [b0, b1, ..., bN]. Each of the columns is of ...
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Quantile Prediction of Cartesian Sum
I want to predict (or find exactly if it is possible) the quantiles of all pairs sum of two arrays. More clearly,
Say I have two sets: {2,5,7,11,23,56} and {10,15,25,50,100,123,180}
All pairs (...
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Constructing vine copulas from separately estimated bivariate copulas?
I recently came across copulas. I then wondered if you could construct complex multivariate copulas from simpler bivariate copulas... and I discovered vine copulas. One thing that is not clear to me ...
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Finding difference in models across data-sets [closed]
Suppose I have two datasets $X_0, X_1$ both sampled from the same multivariate distribution, and a binary response variable $Y_0, Y_1$.
I want to test in which features (and if) the two conditional ...
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How to get $f(x)$ for this continuous random variables? [duplicate]
A probability density function for a continuous random variables, $X$, is shown below:
What will be the equation of $f(x)$ in this case?
and how $f(x)$ will change if I vary $v_{x}$, for example ...
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Is there a test that can tell me, even for low counts, the probability that the obtained distribution of values eg from a die is truly random?
The background is that I have data and a number of independent variables. For each variable I want to ascertain the probability that the distribution of that variable's values is random for that data.
...
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How much error will there be if one models the multivariate hypergeometric distribution using a multinomial distribution?
See the title. I stumbled upon this answer which explains the approximation in more detail. One can approximate the multivariate hypergeometric distribution by using the multinomial distribution.
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Complicated Transform of a Beta Random Variable
Consider a Beta distributed random variable, $X \sim Beta(a,b)$ Then consider the transform $$Y = \sqrt{K\frac{X}{1-X}}$$ where $K > 0$ is a constant.
How could you go about finding the PDF of $Y$?...
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PDF of $Z=X^2 + Y^2$ where $X,Y\sim N(0,\sigma)$
Using normal distribution probablilty density function(pdf),
\begin{align}
f_Y(x) = f_X(X) &= \frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{x^2}{2\sigma^2}} \\
\end{align}
Taking $Z' = X^2 = Y^2$, the ...
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Distribution of the Square Root of a Beta Prime Random Variable
Given a Beta Prime distributed random variable $X \sim BP(a,b) $ with probability density $$\rho_X(x) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\frac{x^{\alpha - 1}}{(1+x)^{a+b}}, x > 0$$ Consider ...
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Finding Cities with Similar Population Distributions [duplicate]
Using census data, what is the best statistical test/method to find cities that the most similar and dissimilar population distribution for both age and sex?
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Log input data multi target regression [duplicate]
I'm building a multi target regression model with random forest regressor, in python. My database has 20 variables, from which 13 are x values and 7 are y values (targets).
I've treated 3 of these 13 ...
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Is there a general method to estimate the parameter of a Poisson distribution numerically using MLE in R? [duplicate]
I am trying to solve this problem:
Assuming for the phishing values to come from a Poisson distribution of
unknown lambda parameter, use the sample values to numerically estimate the parameter with
...
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Score of LGBM Classifier ranging only between a short interval
I am working on a fraud problem and I am trying to predict either some market/stores has done fraudulent transactions or not.
I've trained a boosting model (lgbm algorithm) on a unbalanced dataset. I'...
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Why does central limit theorem give such big x in $\phi(x)$
I am solving a problem : The number of new customers in the mall each day follows Poisson distirbution with $\lambda = 50$. Find approximately the probability that after one year (200 working days) ...
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Independence/ Asymptotic independence of asymptotic normal random variables
Let $\{X_{n}\}_{n\in I}$ be a sequence of random variables, where $X_{n}$ takes value $\{-c_n,c_n\}$, each with probability $1/2$, $|c_{n}|\leq \alpha \in \mathbb{R}$ and $I$ denotes the index set ...
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How to estimate the parameters of Beta distribution from an empirical graph?
Suppose I have some empirical data which I plot and I believe it be a Beta distribution, how can I make sure that I have a Beta distribution, and how can I estimate the alpha and beta parameters of ...
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How to formulate the distribution and conduct a hypothesis test on the following situation?
The situation is that we toss a coin N times. We note the outcome of each flip and we find the distribution of how many times the coin flipped the 'same way' n times in a row, for n = 1,2,3 etc (for N ...
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Estimating the average building size
Suppose you want to estimate the average building size (defined as the number of people living in the building) in a small city. You randomly sample N people from this city, and each person tells you ...
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Using KDE to approximate a Price vs Quantity curve
I am trying to approximate Price-vs-Quantity (P-Q) curve of a dynamic product (think Hotels, Airlines etc). As you can imagine, if you take a hotel property, the price of rooms (assuming the same room ...
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Sampling time series that are X distance away from a given time series
Given a time series $T_1$, I want to sample time series that are a $\epsilon$-distance away from $T_1$. Let's assume the distance metric is Dynamic Time Warping.
The specific problem is, I have a ...
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Time distribution: is it possible to determine whether calls are human-made or machine-made by patterns of the distribution
I'm relatively new to statistics, so the question is primarily about your advice on where I should start with this problem and read related material.
So, suppose I've got a temporal distribution of ...
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What information can I extract from an overlap of two personal probability distributions?
Inspiration: https://www.snopes.com/fact-check/trees-stars-milky-way/
Let's say I take a Bayesian approach and use probability distributions to represent my beliefs about the number of stars in the ...
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Erroneous Argument for uncorrelated implies Independence
I've been working on the problem where for a bivariate normal random variable (X,Y), uncorrelated implies Independence. However, I realized that I didn't use the bivariate normal assumption, so there ...
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Maximum likelihood of Normal density under selection
Consider the density function given by
$$
\left[\dfrac{\gamma_{\leq0} \mathbb{1}(t \leq 0) + \gamma_{>0} \mathbb{1}(t > 0)}{\gamma_{\leq0}\Phi\left(- \mu / \sigma\right) + \gamma_{>0}\Phi\...
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Comparison between multiple curves/probability distributions
I have several sets of numerical data, and we'll call those sets $i=1...n$. Each set describes a normalized probability mass distributions $y_{i,j}$ such that
$$\sum_j y_{i,j} = 1$$
These $y_{i,j}$ ...
